Daily Papers

Long-horizon planning is widely recognized as a core capability of autonomous LLM-based agents; however, current evaluation frameworks suffer from being largely episodic, domain-specific, or insufficiently grounded in persistent economic dynamics. We introduce EcoGym, a generalizable benchmark for continuous plan-and-execute decision making in interactive economies. EcoGym comprises three diverse environments: Vending, Freelance, and Operation, implemented in a unified decision-making process with standardized interfaces, and budgeted actions over an effectively unbounded horizon (1000+ steps if 365 day-loops for evaluation). The evaluation of EcoGym is based on business-relevant outcomes (e.g., net worth, income, and DAU), targeting long-term strategic coherence and robustness under partial observability and stochasticity. Experiments across eleven leading LLMs expose a systematic tension: no single model dominates across all three scenarios. Critically, we find that models exhibit significant suboptimality in either high-level strategies or efficient actions executions. EcoGym is released as an open, extensible testbed for transparent long-horizon agent evaluation and for studying controllability-utility trade-offs in realistic economic settings.

As AI systems increasingly assume roles where trust and alignment with human values are essential, understanding when and why they engage in deception has become a critical research priority. We introduce The Traitors, a multi-agent simulation framework inspired by social deduction games, designed to probe deception, trust formation, and strategic communication among large language model (LLM) agents under asymmetric information. A minority of agents the traitors seek to mislead the majority, while the faithful must infer hidden identities through dialogue and reasoning. Our contributions are: (1) we ground the environment in formal frameworks from game theory, behavioral economics, and social cognition; (2) we develop a suite of evaluation metrics capturing deception success, trust dynamics, and collective inference quality; (3) we implement a fully autonomous simulation platform where LLMs reason over persistent memory and evolving social dynamics, with support for heterogeneous agent populations, specialized traits, and adaptive behaviors. Our initial experiments across DeepSeek-V3, GPT-4o-mini, and GPT-4o (10 runs per model) reveal a notable asymmetry: advanced models like GPT-4o demonstrate superior deceptive capabilities yet exhibit disproportionate vulnerability to others' falsehoods. This suggests deception skills may scale faster than detection abilities. Overall, The Traitors provides a focused, configurable testbed for investigating LLM behavior in socially nuanced interactions. We position this work as a contribution toward more rigorous research on deception mechanisms, alignment challenges, and the broader social reliability of AI systems.

How can a population of agents self-orchestrate and self-adapt into stronger collective intelligence without centralized control? Inspired by Friedrich Hayek's economic theory of decentralized coordination in markets, we study this question through an agent economy in which agents compete via auctions for the right to act, exchange payments, and accumulate wealth from environmental rewards. These simple economic signals induce decentralized credit assignment, driving planning without global orchestration or explicit communication protocols. The population evolves through economic selection: effective agents accumulate wealth and are mutated via exploitation, while ineffective ones go bankrupt and are replaced via exploration. We show that, initialized with weak agents, the economy produces emergent multi-step reasoning strategies and outperforms stronger monolithic baselines across five agentic tasks, including mathematical reasoning, financial research, scientific research, accelerator design, and distributed-system optimization. We further provide theoretical insights into how economic dynamics shape agent behaviors, linking local incentives to long-term global performance. Our results suggest a new path to multi-agent intelligence: rather than engineering coordination, we can design decentralized incentive structures under which it automatically emerges.

Computing stable partitions in hedonic games is a challenging task because there exist games in which stable outcomes do not exist. Even more, these No-instances can often be leveraged to prove computational hardness results. We make this impression rigorous in a dynamic model of cardinal hedonic games by providing meta theorems. These imply hardness of deciding about the possible or necessary convergence of deviation dynamics based on the mere existence of No-instances. Our results hold for additively separable, fractional, and modified fractional hedonic games (ASHGs, FHGs, and MFHGs). Moreover, they encompass essentially all reasonable stability notions based on single-agent deviations. In addition, we propose dynamics as a method to find individually rational and contractually individual stable (CIS) partitions in ASHGs. In particular, we find that CIS dynamics from the singleton partition possibly converge after a linear number of deviations but may require an exponential number of deviations in the worst case.

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.

We study how a central bank should dynamically set short-term nominal interest rates to stabilize inflation and unemployment when macroeconomic relationships are uncertain and time-varying. We model monetary policy as a sequential decision-making problem where the central bank observes macroeconomic conditions quarterly and chooses interest rate adjustments. Using publically accessible historical Federal Reserve Economic Data (FRED), we construct a linear-Gaussian transition model and implement a discrete-action Markov Decision Process with a quadratic loss reward function. We chose to compare nine different reinforcement learning style approaches against Taylor Rule and naive baselines, including tabular Q-learning variants, SARSA, Actor-Critic, Deep Q-Networks, Bayesian Q-learning with uncertainty quantification, and POMDP formulations with partial observability. Surprisingly, standard tabular Q-learning achieved the best performance (-615.13 +- 309.58 mean return), outperforming both enhanced RL methods and traditional policy rules. Our results suggest that while sophisticated RL techniques show promise for monetary policy applications, simpler approaches may be more robust in this domain, highlighting important challenges in applying modern RL to macroeconomic policy.

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.

Large language model agents are increasingly evaluated as autonomous tool users, yet most benchmarks focus on bounded tasks with immediate success criteria. Real-world deployments often require Long-Term Coherence, the capacity to preserve purposeful behavior across extended horizons while adapting decisions to accumulated evidence. Evaluating this capacity requires a persistent environment in which actions constrain future choices, feedback arrives at heterogeneous delays, and incoherent behavior produces measurable cumulative effects. Seller-side e-commerce provides a suitable setting for this evaluation through recurrent and interdependent decisions over Product Sourcing, Listing and Pricing Control, Cash-Flow Management, and Mixed-Latency Feedback Adaptation. We introduce MerchantBench, a 365-day order-level simulation grounded in 98,843 real e-commerce product records and equipped with 26 tools for agent interaction. MerchantBench couples promptly observable Upstream Supplier Events with delayed Downstream Order Outcomes, requiring agents to follow individual order lifecycles and revisit earlier decisions. We evaluate eight LLMs under two agent frameworks in 48 runs, each spanning 365 simulated days. Our results reveal a substantial gap between even the latest LLMs and human participants, with the best LLM configuration attaining only 27.3\% of the mean final net assets achieved by human participants.

Economic World Models (EWMs) are generative economic models that simulate how economies evolve from within by modeling heterogeneous agents, their beliefs and actions, and the market and institutional mechanisms through which their interactions produce aggregate outcomes. This paper develops an implementation roadmap for building economic world models as generative engines in which heterogeneous agents act, interact, adapt, and co-evolve with markets and institutions, thereby producing economic dynamics from the inside. We organize EWM systems into a six-level capability ladder, from fixed rule-based agent worlds to adaptive and LLM-based agent worlds, self-evolving agents, evolving institutional worlds, and sim-to-real economic twins aligned with real observations. A systematic literature survey across these levels reveals that existing work remains concentrated in lower-level agent and simulation environments, while systems with self-evolving agents, endogenous institutions, persistent empirical alignment, and validated economic mechanisms remain rare. By translating the EWM agenda into an implementation blueprint, this paper aims to accelerate the development of the next generation of economic simulation environments that can serve as high-fidelity sandboxes for human decision-makers and as training, planning, evaluation, and safety substrates for AI agents. We release a curated paper list and related resources to support future research.

Climate-economic modeling under uncertainty presents significant computational challenges that may limit policymakers' ability to address climate change effectively. This paper explores neural network-based approaches for solving high-dimensional optimal control problems arising from models that incorporate ambiguity aversion in climate mitigation decisions. We develop a continuous-time endogenous-growth economic model that accounts for multiple mitigation pathways, including emission-free capital and carbon intensity reductions. Given the inherent complexity and high dimensionality of these models, traditional numerical methods become computationally intractable. We benchmark several neural network architectures against finite-difference generated solutions, evaluating their ability to capture the dynamic interactions between uncertainty, technology transitions, and optimal climate policy. Our findings demonstrate that appropriate neural architecture selection significantly impacts both solution accuracy and computational efficiency when modeling climate-economic systems under uncertainty. These methodological advances enable more sophisticated modeling of climate policy decisions, allowing for better representation of technology transitions and uncertainty-critical elements for developing effective mitigation strategies in the face of climate change.

As LLM agents become capable of increasingly long-horizon tasks, evaluating their performance in economic systems is becoming increasingly important. Unlike existing benchmarks that primarily evaluate a single agent interacting with a passive environment, economic systems are inherently multi-agent, requiring autonomous agents to communicate, negotiate, and transact while pursuing their own objectives over extended periods. We introduce CoffeeBench, a benchmark for evaluating LLM agents in a long-horizon multi-agent economy composed of heterogeneous firms. In CoffeeBench, two farmers, two roasters, and two retailers autonomously operate their businesses over a 90-day simulation, each seeking to maximize cumulative net income through communication and transactions while managing cash, inventory, and pricing. The evaluated model controls one coffee roaster, while the remaining firms are controlled by fixed reference agents. Across several recent open-weight and proprietary LLMs, all models outperform a passive baseline that takes no actions, with most achieving positive net income. Analysis of agent behavior reveals substantial differences in long-horizon economic interaction: higher-performing models communicate more actively with other firms, whereas Claude~Haiku~4.5 exhibits an idle-drift failure mode, repeatedly choosing inaction despite producing coherent assessments and plans. We release our code and agent trajectories to support future research.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent temporal correlation of the EUC behaviors, and may result in large errors when predicting the actual responses of EUCs in real-time pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to capture the temporal behavior of the EUCs. The states in the proposed dynamical DR model can be explicitly chosen, in which case the model can be represented by a linear function or a multi-layer feedforward neural network, or implicitly chosen, in which case the model can be represented by a recurrent neural network or a long short-term memory unit network. In both cases, the dynamical DR model can be learned from historical price and energy consumption data. Numerical simulation illustrated how the states are chosen and also showed the proposed dynamical DR model significantly outperforms the static ones.

The study of social emergence has long been a central focus in social science. Traditional modeling approaches, such as rule-based Agent-Based Models (ABMs), struggle to capture the diversity and complexity of human behavior, particularly the irrational factors emphasized in behavioral economics. Recently, large language model (LLM) agents have gained traction as simulation tools for modeling human behavior in social science and role-playing applications. Studies suggest that LLMs can account for cognitive biases, emotional fluctuations, and other non-rational influences, enabling more realistic simulations of socio-economic dynamics. In this work, we introduce TwinMarket, a novel multi-agent framework that leverages LLMs to simulate socio-economic systems. Specifically, we examine how individual behaviors, through interactions and feedback mechanisms, give rise to collective dynamics and emergent phenomena. Through experiments in a simulated stock market environment, we demonstrate how individual actions can trigger group behaviors, leading to emergent outcomes such as financial bubbles and recessions. Our approach provides valuable insights into the complex interplay between individual decision-making and collective socio-economic patterns.

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Optimal execution is an important problem faced by any trader. Most solutions are based on the assumption of constant market impact, while liquidity is known to be dynamic. Moreover, models with time-varying liquidity typically assume that it is observable, despite the fact that, in reality, it is latent and hard to measure in real time. In this paper we show that the use of Double Deep Q-learning, a form of Reinforcement Learning based on neural networks, is able to learn optimal trading policies when liquidity is time-varying. Specifically, we consider an Almgren-Chriss framework with temporary and permanent impact parameters following several deterministic and stochastic dynamics. Using extensive numerical experiments, we show that the trained algorithm learns the optimal policy when the analytical solution is available, and overcomes benchmarks and approximated solutions when the solution is not available.

The rapid development of large language models (LLMs) has renewed interest in agent-based modeling (ABM). However, current LLM-based ABM research faces several key challenges: modeling evolving agent-environment interactions, enabling flexible counterfactual reasoning, and automating simulation workflows for scientific research. In this paper, we propose Eco3S, a socio-economic system simulation framework for economic research and policy analysis that addresses these challenges through three key mechanisms: (1) Co-evolving Environment Design, a bidirectional feedback loop where agents and the environment co-evolve, producing realistic emergent behaviors; (2) Structural Causal Simulation, a structural causal model (SCM)-inspired counterfactual mechanism that allows flexible interventions for diverse causal inference tasks; (3) Simulation-Analysis-Refinement Paradigm, a self-corrective mechanism that iteratively refines experimental designs based on prior simulation results. Experiments on diverse economic scenarios confirm Eco3S's effectiveness in replicating multiple established economic studies (canal decay, origins of governance, and information propagation) and phenomena across domains. Additional results further demonstrate its scalability and generalizability, highlighting the framework's potential for rigorous economic research and policy-making.

We revisit Tirole's classic paper "Asset Bubbles and Overlapping Generations" (1985, Econometrica) in the case of a dividend-paying asset. Recently, Pham and Toda (2026) constructed a counterexample to Proposition 1(c), showing that Tirole's equilibrium classification is incorrect as stated and that long-run outcomes can depend on initial capital. This paper characterizes the entire set of equilibrium initial asset prices under capital over-accumulation. Exactly one of three regimes occurs: (i) a unique bubbleless equilibrium with capital converging to zero (capital collapse), (ii) a unique asymptotically bubbly equilibrium converging to a positive steady state (bubble necessity), or (iii) a continuum of equilibria with different long-run bubble behavior (indeterminacy). We further derive a threshold for initial capital under the bubble necessity condition, establish preference-free sufficient conditions for capital collapse, and show that the continuum in the pure bubble model survives sufficiently small dividend perturbations. Closed-form examples illustrate the possible long-run outcomes.

Large Language Models (LLMs) show significant potential in economic and strategic interactions, where communication via natural language is often prevalent. This raises key questions: Do LLMs behave rationally? Can they mimic human behavior? Do they tend to reach an efficient and fair outcome? What is the role of natural language in the strategic interaction? How do characteristics of the economic environment influence these dynamics? These questions become crucial concerning the economic and societal implications of integrating LLM-based agents into real-world data-driven systems, such as online retail platforms and recommender systems. While the ML community has been exploring the potential of LLMs in such multi-agent setups, varying assumptions, design choices and evaluation criteria across studies make it difficult to draw robust and meaningful conclusions. To address this, we introduce a benchmark for standardizing research on two-player, sequential, language-based games. Inspired by the economic literature, we define three base families of games with consistent parameterization, degrees of freedom and economic measures to evaluate agents' performance (self-gain), as well as the game outcome (efficiency and fairness). We develop an open-source framework for interaction simulation and analysis, and utilize it to collect a dataset of LLM vs. LLM interactions across numerous game configurations and an additional dataset of human vs. LLM interactions. Through extensive experimentation, we demonstrate how our framework and dataset can be used to: (i) compare the behavior of LLM-based agents to human players in various economic contexts; (ii) evaluate agents in both individual and collective performance measures; and (iii) quantify the effect of the economic characteristics of the environments on the behavior of agents.

We placed 100 memory-equipped large language model (LLM) agents in charge of a closed, money-conserving spatial economy on real Pokhara Lakeside geography (earning wages, running businesses, setting prices) and ran this multi-agent simulation for up to 26 simulated weeks, well past the 1-2 weeks typical of agent-society studies. Across 91 validated runs (2.44M agent decisions, 21.5B tokens), the money stops moving, in a specific and measurable way. A 12x tourist demand shock raises business revenue 4.62x (p<0.001), which we decompose exactly into a 1.50x extensive margin (more businesses trading) and a 3.07x intensive margin (more revenue each). Monetary transmission stops there. Wages move 1.03x (p=0.42); 0.3% of 3,981 menu items are ever repriced (p=0.47). A randomized cash transfer (NPR 5,000 to 20 of 100 agents) shows the same pattern from the opposite direction: 96.7% is still held 311 pulses later, marginal propensity to consume 3-4% by two independent measures, indistinguishable from zero. The wealth distribution is consequently near-frozen at the horizon this literature uses (ρ=0.964 over 2 simulated weeks), but not frozen. ρ falls to 0.832 at 12 weeks and 0.752 at 26, a horizon-dependence no short study can see. Matched ablations show which knob actually matters. Swapping the backing LLM moves every outcome we measure (p=0.0039); deleting agents' memory moves none of them detectably. A purely social tool fails 94-97% of the time across two model families, compared with ~96% success on economic tools, with no measurable shift away from it. Every headline number is verified twice, by a live validator and by an offline recomputation that reconciles each agent's wealth against its own signed transaction history, and we release the full run corpus for reanalysis.

The emergence and impact of tipping points have garnered significant interest in both the social and natural sciences. Despite widespread recognition of the importance of feedbacks between human and natural systems, it is often assumed that the observed nonlinear dynamics in these coupled systems rests within either underlying human or natural processes, rather than the rates at which they interact. Using adoption of agricultural diversification practices as a case study, we show how two stable management paradigms (one dominated by conventional, homogeneous practices, the other by diversified practices) can emerge purely from temporal feedbacks between human decisions and ecological responses. We explore how this temporal mechanism of tipping points provides insight into designing more effective interventions that promote farmers transitions towards sustainable agriculture. Moreover, our flexible modeling framework could be applied to other cases to provide insight into numerous questions in social-ecological systems research and environmental policy.

This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by mahi2025ska. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems.

Tackling real-world socio-economic challenges requires designing and testing economic policies. However, this is hard in practice, due to a lack of appropriate (micro-level) economic data and limited opportunity to experiment. In this work, we train social planners that discover tax policies in dynamic economies that can effectively trade-off economic equality and productivity. We propose a two-level deep reinforcement learning approach to learn dynamic tax policies, based on economic simulations in which both agents and a government learn and adapt. Our data-driven approach does not make use of economic modeling assumptions, and learns from observational data alone. We make four main contributions. First, we present an economic simulation environment that features competitive pressures and market dynamics. We validate the simulation by showing that baseline tax systems perform in a way that is consistent with economic theory, including in regard to learned agent behaviors and specializations. Second, we show that AI-driven tax policies improve the trade-off between equality and productivity by 16% over baseline policies, including the prominent Saez tax framework. Third, we showcase several emergent features: AI-driven tax policies are qualitatively different from baselines, setting a higher top tax rate and higher net subsidies for low incomes. Moreover, AI-driven tax policies perform strongly in the face of emergent tax-gaming strategies learned by AI agents. Lastly, AI-driven tax policies are also effective when used in experiments with human participants. In experiments conducted on MTurk, an AI tax policy provides an equality-productivity trade-off that is similar to that provided by the Saez framework along with higher inverse-income weighted social welfare.

Economic activities favor mutual geographical proximity and concentrate spatially to form cities. In a world of diminishing transport costs, however, the advantage of physical proximity is fading, and the role of cities in the economy may be declining. To provide insights into the long-run evolution of cities, we analyzed Japan's census data over the 1970--2015 period. We found that fewer and larger cities thrived at the national scale, suggesting an eventual mono-centric economy with a single megacity; simultaneously, each larger city flattened out at the local scale, suggesting an eventual extinction of cities. We interpret this multi-scale phenomenon as an instance of pattern formation by self-organization, which is widely studied in mathematics and biology. However, cities' dynamics are distinct from mathematical or biological mechanisms because they are governed by economic interactions mediated by transport costs between locations. Our results call for the synthesis of knowledge in mathematics, biology, and economics to open the door for a general pattern formation theory that is applicable to socioeconomic phenomena.

Signal decay and regime shifts pose recurring challenges for data-driven investment strategies in non-stationary markets. Conventional time-series and machine learning approaches, which rely primarily on historical correlations, often struggle to generalize when the economic environment changes. While large language models (LLMs) offer strong capabilities for processing unstructured information, their potential to support quantitative factor screening through explicit economic reasoning remains underexplored. Existing factor-based methods typically reduce alphas to numerical time series, overlooking the semantic rationale that determines when a factor is economically relevant. We propose Alpha-R1, an 8B-parameter reasoning model trained via reinforcement learning for context-aware alpha screening. Alpha-R1 reasons over factor logic and real-time news to evaluate alpha relevance under changing market conditions, selectively activating or deactivating factors based on contextual consistency. Empirical results across multiple asset pools show that Alpha-R1 consistently outperforms benchmark strategies and exhibits improved robustness to alpha decay. The full implementation and resources are available at https://github.com/FinStep-AI/Alpha-R1.

We present a new approach to formulating and solving heterogeneous agent models with aggregate risk. We replace the cross-sectional distribution with low-dimensional prices as state variables and let agents learn equilibrium price dynamics directly from simulated paths. To do so, we introduce a structural reinforcement learning (SRL) method which treats prices via simulation while exploiting agents' structural knowledge of their own individual dynamics. Our SRL method yields a general and highly efficient global solution method for heterogeneous agent models that sidesteps the Master equation and handles problems traditional methods struggle with, in particular nontrivial market-clearing conditions. We illustrate the approach in the Krusell-Smith model, the Huggett model with aggregate shocks, and a HANK model with a forward-looking Phillips curve, all of which we solve globally within minutes.

We present a concise dynamical picture of infant-driven household chaos. The framework has three postulations: recurrent daily chaos, overall entropy growth in household organization, and transient local ordering episodes with switching rules (a volatile Maxwell-demon effect). We illustrate entropy growth with a two-region toy model (organizer vs. play area), where entropy production is nonnegative and long-time behavior is typically play-area dominated. We also model toy diffusion and curiosity-driven behavior, where novelty matters more than punishment in the short term, while gradual learning still occurs.

Learning a precise dynamics model can be crucial for offline reinforcement learning, which, unfortunately, has been found to be quite challenging. Dynamics models that are learned by fitting historical transitions often struggle to generalize to unseen transitions. In this study, we identify a hidden but pivotal factor termed dynamics reward that remains consistent across transitions, offering a pathway to better generalization. Therefore, we propose the idea of reward-consistent dynamics models: any trajectory generated by the dynamics model should maximize the dynamics reward derived from the data. We implement this idea as the MOREC (Model-based Offline reinforcement learning with Reward Consistency) method, which can be seamlessly integrated into previous offline model-based reinforcement learning (MBRL) methods. MOREC learns a generalizable dynamics reward function from offline data, which is subsequently employed as a transition filter in any offline MBRL method: when generating transitions, the dynamics model generates a batch of transitions and selects the one with the highest dynamics reward value. On a synthetic task, we visualize that MOREC has a strong generalization ability and can surprisingly recover some distant unseen transitions. On 21 offline tasks in D4RL and NeoRL benchmarks, MOREC improves the previous state-of-the-art performance by a significant margin, i.e., 4.6% on D4RL tasks and 25.9% on NeoRL tasks. Notably, MOREC is the first method that can achieve above 95% online RL performance in 6 out of 12 D4RL tasks and 3 out of 9 NeoRL tasks.

Algorithmic trading relies on machine learning models to make trading decisions. Despite strong in-sample performance, these models often degrade when confronted with evolving real-world market regimes, which can shift dramatically due to macroeconomic changes-e.g., monetary policy updates or unanticipated fluctuations in participant behavior. We identify two challenges that perpetuate this mismatch: (1) insufficient robustness in existing policy against uncertainties in high-level market fluctuations, and (2) the absence of a realistic and diverse simulation environment for training, leading to policy overfitting. To address these issues, we propose a Bayesian Robust Framework that systematically integrates a macro-conditioned generative model with robust policy learning. On the data side, to generate realistic and diverse data, we propose a macro-conditioned GAN-based generator that leverages macroeconomic indicators as primary control variables, synthesizing data with faithful temporal, cross-instrument, and macro correlations. On the policy side, to learn robust policy against market fluctuations, we cast the trading process as a two-player zero-sum Bayesian Markov game, wherein an adversarial agent simulates shifting regimes by perturbing macroeconomic indicators in the macro-conditioned generator, while the trading agent-guided by a quantile belief network-maintains and updates its belief over hidden market states. The trading agent seeks a Robust Perfect Bayesian Equilibrium via Bayesian neural fictitious self-play, stabilizing learning under adversarial market perturbations. Extensive experiments on 9 financial instruments demonstrate that our framework outperforms 9 state-of-the-art baselines. In extreme events like the COVID, our method shows improved profitability and risk management, offering a reliable solution for trading under uncertain and shifting market dynamics.

Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a latent preference state matrix, where the spread between an agent's internal ask price (the unconditional maximum) and the market's best bid (the reachable maximum) creates a structural liquidity constraint. We establish a Threshold Impossibility Theorem showing that linear compensation cannot close these spreads unless it induces a categorical identity shift. A dynamic discrete choice execution model further demonstrates that matches occur only when the market to book ratio crosses a time decaying liquidity threshold, analogous to order execution under inventory pressure. Numerical experiments validate persistent slippage, regional invariance of preference orderings, and high tier zero spread executions. The model provides a unified microstructure explanation for matching failures, compensation inefficiency, and post match regret in illiquid order driven environments.

As LLM agents advance, they are increasingly mediating economic decisions, ranging from product discovery to transactions, on behalf of users. Such applications promise benefits but also raise many questions about agent accountability and value for users. Addressing these questions requires understanding how agents behave in realistic market conditions. However, previous research has largely evaluated agents in constrained settings, such as single-task marketplaces (e.g., negotiation) or structured two-agent interactions. Real-world markets are fundamentally different: they require agents to handle diverse economic activities and coordinate within large, dynamic ecosystems where multiple agents with opaque behaviors may engage in open-ended dialogues. To bridge this gap, we investigate two-sided agentic marketplaces where Assistant agents represent consumers and Service agents represent competing businesses. To study these interactions safely, we develop Magentic-Marketplace-- a simulated environment where Assistants and Services can operate. This environment enables us to study key market dynamics: the utility agents achieve, behavioral biases, vulnerability to manipulation, and how search mechanisms shape market outcomes. Our experiments show that frontier models can approach optimal welfare-- but only under ideal search conditions. Performance degrades sharply with scale, and all models exhibit severe first-proposal bias, creating 10-30x advantages for response speed over quality. These findings reveal how behaviors emerge across market conditions, informing the design of fair and efficient agentic marketplaces.

Achieving robust coordination and cooperation is a central challenge in multi-agent reinforcement learning (MARL). Uncovering the mechanisms underlying such emergent behaviors calls for a dynamical understanding of learn processes. In this work, we investigate the dynamics of actor-critic agents in stochastic games, focusing on the impact of entropy regularization. By leveraging time-scale separation, we derive the system's evolution equations, which are then formally analyzed using dynamical systems theory. We find that in the constant-sum game of Matching Pennies, the system exhibits chaotic behavior. Entropy regularization mitigates this chaos and drives the dynamics toward convergence to fair cooperation. In contrast, in the general-sum game of the Prisoner's Dilemma, the system displays multistability. Interestingly, the three stable equilibria of the system correspond to the well-known ALLC (Always Cooperate), ALLD (Always Defect), and GRIM (Grim Trigger) strategies from evolutionary game theory (EGT). Entropy regularization strengthens system resilience by enlarging the basin of attraction of the cooperative equilibrium. Our findings reveal a close link between the mechanism of direct reciprocity in EGT and how cooperation emerges in MARL, offering insights for designing more robust and collaborative multi-agent systems.

The rapid adoption of autonomous AI agents is giving rise to a new economic layer where agents transact and coordinate at scales and speeds beyond direct human oversight. We propose the "sandbox economy" as a framework for analyzing this emergent system, characterizing it along two key dimensions: its origins (emergent vs. intentional) and its degree of separateness from the established human economy (permeable vs. impermeable). Our current trajectory points toward a spontaneous emergence of a vast and highly permeable AI agent economy, presenting us with opportunities for an unprecedented degree of coordination as well as significant challenges, including systemic economic risk and exacerbated inequality. Here we discuss a number of possible design choices that may lead to safely steerable AI agent markets. In particular, we consider auction mechanisms for fair resource allocation and preference resolution, the design of AI "mission economies" to coordinate around achieving collective goals, and socio-technical infrastructure needed to ensure trust, safety, and accountability. By doing this, we argue for the proactive design of steerable agent markets to ensure the coming technological shift aligns with humanity's long-term collective flourishing.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.

Effective macroeconomic policies play a crucial role in promoting economic growth and social stability. This paper models the optimal macroeconomic policy problem based on the Stackelberg Mean Field Game (SMFG), where the government acts as the leader in policy-making, and large-scale households dynamically respond as followers. This modeling method captures the asymmetric dynamic game between the government and large-scale households, and interpretably evaluates the effects of macroeconomic policies based on microfoundations, which is difficult for existing methods to achieve. We also propose a solution for SMFGs, incorporating pre-training on real data and a model-free Stackelberg mean-field reinforcement learning (SMFRL) algorithm, which operates independently of prior environmental knowledge and transitions. Our experimental results showcase the superiority of the SMFG method over other economic policies in terms of performance, efficiency-equity tradeoff, and SMFG assumption analysis. This paper significantly contributes to the domain of AI for economics by providing a powerful tool for modeling and solving optimal macroeconomic policies.

The deployment of Large Language Models (LLMs) as autonomous economic agents introduces systemic risks that extend beyond individual capability failures. As agents transition to directly interacting with marketplaces, their collective behavior can amplify volatility and mask deception at scale. We introduce the Agent Bazaar, a multi-agent simulation framework for evaluating Economic Alignment, the capacity of agentic systems to preserve market stability and integrity. We identify two failure modes: (1) Algorithmic Instability in a B2C market ("The Crash"), where firms amplify price volatility until the market collapses, and (2) Sybil Deception in a C2C market ("The Lemon Market"), where a single deceptive agent controlling multiple coordinated seller identities floods the market with fraudulent listings, eroding trust and consumer welfare. We evaluate frontier and open-weight models across both scenarios and find that models largely fail to self-regulate, with failure severity varying by model rather than by size. We propose economically aligned harnesses, Stabilizing Firms and Skeptical Guardians, that improve outcomes but remain fragile under harder market conditions. To close this gap, we train agents with REINFORCE++ using an adaptive curriculum, producing a 9B model that outperforms all evaluated frontier and open-weight models. We propose the Economic Alignment Score (EAS), a 4-component scalar metric aggregating stability, integrity, welfare, and profitability, enabling direct cross-model comparison. Our results show that economic alignment is orthogonal to general capability and can be directly trained with targeted RL.

Large-language models (LLMs) are rapidly becoming part of human culture, reshaping how information is produced, transmitted, and used. Here we propose that their diffusion can be understood through a viral analogy, with LLM use spreading through populations, becoming embedded in cognitive and cultural practices. We model transitions among uncoupled, coupled, and persistently dependent users, and show that the interplay between social transmission, recovery, and collective reinforcement can generate tipping points and technological lock-in. A central consequence is the possibility of runaway dynamics: once a critical threshold is crossed, small increases in adoption can trigger rapid population-level shifts toward persistent dependence, with abrupt losses in cognitive competence. The same framework, however, identifies conditions for cognitive immunization, based on reducing transmission and facilitating reversibility. Our results highlight how LLM adoption may involve nonlinear collective transitions with important consequences for cognitive autonomy.

The strategic choice of model "openness" has become a defining issue for the foundation model (FM) ecosystem. While this choice is intensely debated, its underlying economic drivers remain underexplored. We construct a two-period game-theoretic model to analyze how openness shapes competition in an AI value chain, featuring an incumbent developer, a downstream deployer, and an entrant developer. Openness exerts a dual effect: it amplifies knowledge spillovers to the entrant, but it also enhances the incumbent's advantage through a "data flywheel effect," whereby greater user engagement today further lowers the deployer's future fine-tuning cost. Our analysis reveals that the incumbent's optimal first-period openness is surprisingly non-monotonic in the strength of the data flywheel effect. When the data flywheel effect is either weak or very strong, the incumbent prefers a higher level of openness; however, for an intermediate range, it strategically restricts openness to impair the entrant's learning. This dynamic gives rise to an "openness trap," a critical policy paradox where transparency mandates can backfire by removing firms' strategic flexibility, reducing investment, and lowering welfare. We extend the model to show that other common interventions can be similarly ineffective. Vertical integration, for instance, only benefits the ecosystem when the data flywheel effect is strong enough to overcome the loss of a potentially more efficient competitor. Likewise, government subsidies intended to spur adoption can be captured entirely by the incumbent through strategic price and openness adjustments, leaving the rest of the value chain worse off. By modeling the developer's strategic response to competitive and regulatory pressures, we provide a robust framework for analyzing competition and designing effective policy in the complex and rapidly evolving FM ecosystem.

We present the LLM Economist, a novel framework that uses agent-based modeling to design and assess economic policies in strategic environments with hierarchical decision-making. At the lower level, bounded rational worker agents -- instantiated as persona-conditioned prompts sampled from U.S. Census-calibrated income and demographic statistics -- choose labor supply to maximize text-based utility functions learned in-context. At the upper level, a planner agent employs in-context reinforcement learning to propose piecewise-linear marginal tax schedules anchored to the current U.S. federal brackets. This construction endows economic simulacra with three capabilities requisite for credible fiscal experimentation: (i) optimization of heterogeneous utilities, (ii) principled generation of large, demographically realistic agent populations, and (iii) mechanism design -- the ultimate nudging problem -- expressed entirely in natural language. Experiments with populations of up to one hundred interacting agents show that the planner converges near Stackelberg equilibria that improve aggregate social welfare relative to Saez solutions, while a periodic, persona-level voting procedure furthers these gains under decentralized governance. These results demonstrate that large language model-based agents can jointly model, simulate, and govern complex economic systems, providing a tractable test bed for policy evaluation at the societal scale to help build better civilizations.

A 20-year analysis of CrossRef metadata demonstrates that global scholarly output -- encompassing publications, retractions, and preprints -- exhibits strikingly inertial growth, well-described by exponential, quadratic, and logistic models with nearly indistinguishable goodness-of-fit. Retraction dynamics, in particular, remain stable and minimally affected by the COVID-19 shock, which contributed less than 1% to total notices. Since 2004, publications doubled every 9.8 years, retractions every 11.4 years, and preprints at the fastest rate, every 5.6 years. The findings underscore a system primed for ongoing stress at unchanged structural bottlenecks. Although model forecasts diverge beyond 2024, the evidence suggests that the future trajectory of scholarly communication will be determined by persistent systemic inertia rather than episodic disruptions -- unless intentionally redirected by policy or AI-driven reform.

AI and reinforcement learning (RL) have improved many areas, but are not yet widely adopted in economic policy design, mechanism design, or economics at large. At the same time, current economic methodology is limited by a lack of counterfactual data, simplistic behavioral models, and limited opportunities to experiment with policies and evaluate behavioral responses. Here we show that machine-learning-based economic simulation is a powerful policy and mechanism design framework to overcome these limitations. The AI Economist is a two-level, deep RL framework that trains both agents and a social planner who co-adapt, providing a tractable solution to the highly unstable and novel two-level RL challenge. From a simple specification of an economy, we learn rational agent behaviors that adapt to learned planner policies and vice versa. We demonstrate the efficacy of the AI Economist on the problem of optimal taxation. In simple one-step economies, the AI Economist recovers the optimal tax policy of economic theory. In complex, dynamic economies, the AI Economist substantially improves both utilitarian social welfare and the trade-off between equality and productivity over baselines. It does so despite emergent tax-gaming strategies, while accounting for agent interactions and behavioral change more accurately than economic theory. These results demonstrate for the first time that two-level, deep RL can be used for understanding and as a complement to theory for economic design, unlocking a new computational learning-based approach to understanding economic policy.

Large Language Models demonstrate remarkable proficiency in static reasoning, yet training them as autonomous agents through Reinforcement Learning (RL) for long-horizon tasks is often hindered by severe reward sparsity. While conventional agent-side warming up via supervised fine-tuning (SFT) can alleviate this, it is frequently limited by data scarcity and constrained exploration. To address this, we propose a paradigm shift to environment-side adaptation by constructing Feedback-Enriched Environments (FEEs). Through a pilot study, we establish a feedback design strategy that reformulates environments by transitioning from action guidance to observation enrichment during the later stages of both intra-episode exploration and inter-episode evolution. Large-scale experiments on SciWorld and BFCL benchmarks using various Qwen3 model scales and RL algorithms such as GRPO, GSPO, and DAPO demonstrate that FEEs consistently yield performance improvements over standard settings. Furthermore, our analysis reveals that training with FEEs (1) stabilizes training dynamics by reducing entropy volatility, (2) facilitates proactive state-space exploration in difficult tasks, (3) ensures the internalization of environmental guidance into policy weights rather than acting as a mere inference-time prior, and (4) identifies intra-group feedback consistency as a critical boundary for stable optimization.

We study the discrete Bertrand pricing game with a non-increasing demand function. The game has n ge 2 players who simultaneously choose prices from the set {1/k, 2/k, ldots, 1}, where kinN. The player who sets the lowest price captures the entire demand; if multiple players tie for the lowest price, they split the demand equally. We study the Bertrand paradox, where classical theory predicts low prices, yet real markets often sustain high prices. To understand this gap, we analyze a repeated-game model in which firms set prices using no-regret learners. Our goal is to characterize the equilibrium outcomes that can arise under different no-regret learning guarantees. We are particularly interested in questions such as whether no-external-regret learners can converge to undesirable high-price outcomes, and how stronger guarantees such as no-swap regret shape the emergence of competitive low-price behavior. We address these and related questions through a theoretical analysis, complemented by experiments that support the theory and reveal surprising phenomena for no-swap regret learners.

Electricity systems are key to transforming today's society into a carbon-free economy. Long-term electricity market mechanisms, including auctions, support schemes, and other policy instruments, are critical in shaping the electricity generation mix. In light of the need for more advanced tools to support policymakers and other stakeholders in designing, testing, and evaluating long-term markets, this work presents a multi-agent reinforcement learning model capable of capturing the key features of decarbonizing energy systems. Profit-maximizing generation companies make investment decisions in the wholesale electricity market, responding to system needs, competitive dynamics, and policy signals. The model employs independent proximal policy optimization, which was selected for suitability to the decentralized and competitive environment. Nevertheless, given the inherent challenges of independent learning in multi-agent settings, an extensive hyperparameter search ensures that decentralized training yields market outcomes consistent with competitive behavior. The model is applied to a stylized version of the Italian electricity system and tested under varying levels of competition, market designs, and policy scenarios. Results highlight the critical role of market design for decarbonizing the electricity sector and avoiding price volatility. The proposed framework allows assessing long-term electricity markets in which multiple policy and market mechanisms interact simultaneously, with market participants responding and adapting to decarbonization pathways.

Common-pool resource governance requires users to cooperate and avoid overexploitation, but defection and free-riding often undermine cooperation. We model a human-environmental system that integrates dynamics of resource and users' strategies. The resource follows a logistic function that depends on natural growth rate, carrying capacity, and extraction rates of cooperators and defectors. The users' strategies evolve according to different processes that capture effects of payoff, resource, and noise. We analyze the feedback between resource availability and strategic adaptation, and explores the conditions for the emergence and maintenance of cooperation. We find different processes lead to different regimes of equilibrium solutions and resource levels depending on the parameter configuration and initial conditions. We also show that some processes can enhance the sustainability of the resource by making the users more responsive to the resource scarcity. The paper advances the understanding of human-environmental system and offers insights for resource governance policies and interventions.

Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we study a minimal continual learning agent designed to isolate representational dynamics from architectural complexity and optimization objectives. The agent maintains a persistent state vector across executions and incrementally updates it as new textual data is introduced. We quantify representational change using cosine similarity between successive normalized state vectors and define a stability metric over time intervals. Longitudinal experiments across eight executions reveal a transition from an initial plastic regime to a stable representational regime under consistent input. A deliberately introduced semantic perturbation produces a bounded decrease in similarity, followed by recovery and restabilization under subsequent coherent input. These results demonstrate that meaningful stability plasticity tradeoffs can emerge in a minimal, stateful learning system without explicit regularization, replay, or architectural complexity. The work establishes a transparent empirical baseline for studying representational accumulation and adaptation in continual learning systems.

Regulatory institutions (from content moderation platforms to financial supervisors) observe, deliberate, and intervene only after a characteristic delay. We ask whether this processing lag alone can destabilize a multi-agent system that would otherwise remain stable, without exogenous shocks, coordination among agents, or malicious actors. We study this question in two stages. First, we analyze a delayed replicator equation in which autonomous agents receive a benefit from radical behavior but face punishment based on a lagged institutional alarm signal. We derive a closed-form critical delay threshold beyond which the unique interior equilibrium loses stability through a Hopf bifurcation, and prove via center manifold reduction that the bifurcation is supercritical (producing bounded oscillations, not explosive growth) for the entire sigmoid response-function family. Second, we embed N=240 agents on a network and equip them with reinforcement learning (tabular Q-learning), comparing three decision architectures in a factorial design: non-reactive agents (fixed policy), reactive agents (threshold heuristic without memory), and Q-learning agents (adaptive with cumulative value estimates). The results reveal a hierarchy opposite to the naive expectation that learning amplifies instability: non-reactive agents are immune to delay (0% runaway across all tested values), reactive agents collapse catastrophically (96% runaway by delay geq 8 steps), and Q-learning agents achieve partial resilience (66% runaway at delay = 20). The destabilizing ingredient is reactivity to delayed signals: agents that immediately exploit low-alarm windows trigger oscillatory feedback loops. Learning buffers this through implicit punishment memory encoded in Q-values

We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.

Optimizing user engagement is a key goal for modern recommendation systems, but blindly pushing users towards increased consumption risks burn-out, churn, or even addictive habits. To promote digital well-being, most platforms now offer a service that periodically prompts users to take breaks. These, however, must be set up manually, and so may be suboptimal for both users and the system. In this paper, we study the role of breaks in recommendation, and propose a framework for learning optimal breaking policies that promote and sustain long-term engagement. Based on the notion that recommendation dynamics are susceptible to both positive and negative feedback, we cast recommendation as a Lotka-Volterra dynamical system, where breaking reduces to a problem of optimal control. We then give an efficient learning algorithm, provide theoretical guarantees, and empirically demonstrate the utility of our approach on semi-synthetic data.

AI agents are increasingly transacting on behalf of users -- delegating tasks, spending budgets, and negotiating with unfamiliar counterparties. Unlike human marketplaces, which operate under institutional designs refined over centuries, the rules governing emerging agent marketplaces are being built ad-hoc, and early choices tend to lock in. Understanding what dynamics these rules produce is urgent. We present diagon, a programmable market system serving as a rule-agnostic experimental testbed for institutional design in emerging agent cognitive-labour markets. diagon makes institutional choices experimentally manipulable: heterogeneous tool-using agents post jobs, bid, negotiate, execute, pay, and accumulate reputation, with every mechanism end-to-end observable. We instantiate one market form to demonstrate diagon. We find that market exchange generates more productivity gains over self-sufficient agents, but these gains depend strongly on institutional structure; for example, interventions such as identity transparency and stronger competitive selection can degrade market performance rather than improve it. These findings highlight concrete design requirements for the economic infrastructure of the agent era. Code and data are available at https://github.com/assassin808/diagon.

Classical continual learning (CL) has primarily focused on enabling models to update and retain knowledge through parameter-centric mechanisms, e.g., training strategies, architectural designs, and weight adaptation. However, emerging paradigms are reshaping the scope of CL beyond this traditional model adaptation view. For instance, on-policy learning broadens the space of update mechanisms; test-time training extends CL from the training phase to inference; and external harness components such as memory, skill libraries, and interaction protocols extend the evolutionary boundaries of model capabilities far beyond the static parameter space. Collectively, these developments indicate a transition from parameter-centric learning toward system-level adaptation. To characterize this transition, we examine the evolution of continual learning through three dimensions: When, How, and Where learning occurs. The How dimension encompasses off-policy, on-policy, and beyond-gradient optimization mechanics. The When dimension captures evolution across pre-training, post-training, and inference-time stages. The Where dimension delineates updates occurring within internal parameters versus external structural constraints. Anchored by this tri-axial framework, we systematically survey representative methods, trace the ongoing transition of continual learning, and discuss the key challenges, broader implications, and future directions arising from this paradigm shift.

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated as a non-equilibrium thermodynamic process, where price impact represents dissipative work and market noise plays the role of thermal fluctuations. The paper proves a Financial Second Law: under general convex impact functionals, any round-trip trading strategy yields non-positive expected profit. This structural constraint is complemented by a fluctuation theorem that bounds the probability of profitable cycles in terms of dissipated work and market volatility. The framework introduces a statistical ensemble of trading strategies governed by a Gibbs measure, leading to a free energy decomposition that connects expected cost, strategy entropy, and a market temperature parameter. The framework provides rigorous, testable inequalities linking microstructural impact to macroscopic no-arbitrage conditions, offering a novel physics-inspired perspective on market efficiency. The paper derives explicit analytical results for prototypical trading strategies and discusses empirical validation protocols.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Interactive world models continually generate video by responding to a user's actions, enabling open-ended generation capabilities. However, existing models typically lack a 3D representation of the environment, meaning 3D consistency must be implicitly learned from data, and spatial memory is restricted to limited temporal context windows. This results in an unrealistic user experience and presents significant obstacles to down-stream tasks such as training agents. To address this, we present PERSIST, a new paradigm of world model which simulates the evolution of a latent 3D scene: environment, camera, and renderer. This allows us to synthesize new frames with persistent spatial memory and consistent geometry. Both quantitative metrics and a qualitative user study show substantial improvements in spatial memory, 3D consistency, and long-horizon stability over existing methods, enabling coherent, evolving 3D worlds. We further demonstrate novel capabilities, including synthesising diverse 3D environments from a single image, as well as enabling fine-grained, geometry-aware control over generated experiences by supporting environment editing and specification directly in 3D space. Project page: https://francelico.github.io/persist.github.io

This paper reformulates the Greenwood and Guner (2009) marriage and divorce model in continuous time using the HACT methods of Achdou et al. (2022). Replacing the AR(1) match quality process with an Ornstein-Uhlenbeck process yields a tridiagonal generator, reducing the computational complexity of both the value function and stationary distribution calculations from quadratic to linear in the number of grid points. The continuous-time model closely replicates the discrete-time equilibrium across all key outcomes, including the share of married households, the marriage rate, and the divorce rate, while achieving substantial gains in computation time and memory usage.

In lifelong learning, an agent learns throughout its entire life without resets, in a constantly changing environment, as we humans do. Consequently, lifelong learning comes with a plethora of research problems such as continual domain shifts, which result in non-stationary rewards and environment dynamics. These non-stationarities are difficult to detect and cope with due to their continuous nature. Therefore, exploration strategies and learning methods are required that are capable of tracking the steady domain shifts, and adapting to them. We propose Reactive Exploration to track and react to continual domain shifts in lifelong reinforcement learning, and to update the policy correspondingly. To this end, we conduct experiments in order to investigate different exploration strategies. We empirically show that representatives of the policy-gradient family are better suited for lifelong learning, as they adapt more quickly to distribution shifts than Q-learning. Thereby, policy-gradient methods profit the most from Reactive Exploration and show good results in lifelong learning with continual domain shifts. Our code is available at: https://github.com/ml-jku/reactive-exploration.

In many real-world sequential decision-making problems, an action does not immediately reflect on the feedback and spreads its effects over a long time frame. For instance, in online advertising, investing in a platform produces an instantaneous increase of awareness, but the actual reward, i.e., a conversion, might occur far in the future. Furthermore, whether a conversion takes place depends on: how fast the awareness grows, its vanishing effects, and the synergy or interference with other advertising platforms. Previous work has investigated the Multi-Armed Bandit framework with the possibility of delayed and aggregated feedback, without a particular structure on how an action propagates in the future, disregarding possible dynamical effects. In this paper, we introduce a novel setting, the Dynamical Linear Bandits (DLB), an extension of the linear bandits characterized by a hidden state. When an action is performed, the learner observes a noisy reward whose mean is a linear function of the hidden state and of the action. Then, the hidden state evolves according to linear dynamics, affected by the performed action too. We start by introducing the setting, discussing the notion of optimal policy, and deriving an expected regret lower bound. Then, we provide an optimistic regret minimization algorithm, Dynamical Linear Upper Confidence Bound (DynLin-UCB), that suffers an expected regret of order mathcal{O} Big( d sqrt{T}{(1-rho)^{3/2}} Big), where rho is a measure of the stability of the system, and d is the dimension of the action vector. Finally, we conduct a numerical validation on a synthetic environment and on real-world data to show the effectiveness of DynLin-UCB in comparison with several baselines.

Trader-facing dynamic fees are increasingly proposed for automated market makers (AMMs), but historical data do not identify how order flow would respond: trader-facing fees do not vary, trader types are latent, and a replayed tape is not a sequential decision environment. We therefore construct a minimal closed-loop simulator in which the missing signal exists by construction: two constant-product pools repriced by an equilibrium-inspired dynamic-fee rule, fee-sensitive noise flow, and closed-form CEX--AMM arbitrage. Equilibrium is used as a closure principle, not as an object the trader learns. Against a tuned benchmark ladder of schedule, planning, lookahead, and tabular policies, a small DQN is the only evaluated valid policy whose paired improvement over tuned one-step routing excludes zero. On a reserved final block of 1{,}000 seeds with completion forced to 1.0 for every policy, it reduces implementation shortfall under every tested intra-step ordering, by 13.3bps of order notional under the pre-specified agent-last ordering, and the edge is concentrated in, and learned from, dynamic-fee environments: under constant fees the paired difference is indistinguishable from zero. The result is model-conditioned counterfactual evidence about execution control in AMMs, not evidence about historical traders, equilibrium play, or deployable profit.

This study analyzes Sri Lankan migration and remittances over 32 years (1994-2025). Using a 384-month harmonized dataset, we apply exploratory data analysis, stationarity corrected time-series modeling (ADF, Johansen, VAR/VECM), and supervised learning. Results reveal remittance inflows are primarily driven by external macroeconomic variables, specifically exchange rate dynamics and global oil prices, rather than domestic indicators. Impulse response analysis confirms the asymmetric impact of currency depreciation and oil price shocks. Predictively, multivariate machine learning models outperform traditional univariate approaches; Ridge Regression achieves a 73.8% accuracy improvement over SARIMA (Annualized RMSE: USD 494.8 Mn). The optimized framework projects 2026 remittances at USD 9,001 million under stable conditions. These findings highlight the structural dependence of remittances on global economies, emphasizing the need for robust exchange rate policies, skilled migration, and formal financial channels to enhance long-term economic resilience.

Understanding how market participants react to shocks like scheduled macroeconomic news is crucial for both traders and policymakers. We develop a calibrated data generation process DGP that embeds four stylized trader archetypes retail, pension, institutional, and hedge funds into an extended CAPM augmented by CPI surprises. Each agents order size choice is driven by a softmax discrete choice rule over small, medium, and large trades, where utility depends on risk aversion, surprise magnitude, and liquidity. We aim to analyze each agent's reaction to shocks and Monte Carlo experiments show that higher information, lower aversion agents take systematically larger positions and achieve higher average wealth. Retail investors under react on average, exhibiting smaller allocations and more dispersed outcomes. And ambient liquidity amplifies the sensitivity of order flow to surprise shocks. Our framework offers a transparent benchmark for analyzing order flow dynamics around macro releases and suggests how real time flow data could inform news impact inference.

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: trust region continual learning that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly re-converges to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.

Understanding how households consume electricity in response to socioeconomic and climatic drivers is important for decision-makers designing energy policies in a changing climate and under geopolitical tensions. Consumers respond differently to thermal stress depending on income, consumption habits and the surrounding built environment, a nonlinear behaviour that most approaches oversimplify. In this study, households are treated as agents interacting with complex environments, and Inverse Reinforcement Learning is used to represent their consumption behaviour as model implied reward functions. Specifically, we observe how these reward functions change when households undergo socioeconomic and climatic shocks. The framework is tested on different clusters of electricity consumption profiles in Italy. Clusters' reward functions are retrieved and used to understand how cooling behaviour changes from summer 2021 to summer 2022 and 2023, before, during and after the energy crisis and a heatwave. We find that these shocks reshaped cooling behaviour heterogeneously across consumer groups, in directions conditioned by their prior habits and built environment. Across the 2021 to 2023 summers, we identify a spectrum of responses: transient adjustments that receded as the shocks eased, durable shifts persisting into 2023, and consumers exhibiting negligible change. At the intradaily scale, groups comparable in socioeconomic and environmental context but differing in their daily timing of consumption responded distinctly, identifying time of use as a separate dimension of behavioural heterogeneity. Energy policies and demand-response schemes should therefore account not only for who consumers are and where they live, but for when they consume and whether their response to a shock persists.

Digital services face a fundamental trade-off in content selection: they must balance the immediate revenue gained from high-reward content against the long-term benefits of maintaining user engagement. Traditional multi-armed bandit models assume that users remain perpetually engaged, failing to capture the possibility that users may disengage when dissatisfied, thereby reducing future revenue potential. In this work, we introduce a model for the content selection problem that explicitly accounts for variable user engagement and disengagement. In our framework, content that maximizes immediate reward is not necessarily optimal in terms of fostering sustained user engagement. Our contributions are twofold. First, we develop computational and statistical methods for offline optimization and online learning of content selection policies. For users whose engagement patterns are defined by k distinct levels, we design a dynamic programming algorithm that computes the exact optimal policy in O(k^2) time. Moreover, we derive no-regret learning guarantees for an online learning setting in which the platform serves a series of users with unknown and potentially adversarial engagement patterns. Second, we introduce the concept of modified demand elasticity which captures how small changes in a user's overall satisfaction affect the platform's ability to secure long-term revenue. This notion generalizes classical demand elasticity by incorporating the dynamics of user re-engagement, thereby revealing key insights into the interplay between engagement and revenue. Notably, our analysis uncovers a counterintuitive phenomenon: although higher friction (i.e., a reduced likelihood of re-engagement) typically lowers overall revenue, it can simultaneously lead to higher user engagement under optimal content selection policies.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

Robots capable of learning from demonstration (LfD) must exhibit stability while executing learned motion skills. To be effective in the real world, they should also remember multiple skills over time -- a capability lacking in current stable-LfD methods. We propose an approach to stable, continual LfD, and highlight the role of stability in improving continual learning. Our proposed hypernetwork generates the parameters of two neural networks: a trajectory learning dynamics model, and a trajectory-stabilizing Lyapunov function. These generated networks form a clock-augmented stable neural ODE solver (sNODE), a stable dynamics model that offers a superior stability-accuracy trade-off compared to the state-of-the-art. We further propose stochastic hypernetwork regularization with a single, uniformly-sampled task embedding, reducing the cumulative training time for N tasks from O(N^2) to O(N) without degrading performance on real-world tasks. We introduce high-dimensional variants of the popular LASA dataset to assess scalability and extend a dataset of robotic LfD tasks to assess real-world performance. We empirically evaluate our approach on multiple LfD datasets of varying complexity, including sequences of 7--26 tasks, trajectories of 2--32 dimensions, and real-world tasks involving position and orientation. Our thorough evaluation on multiple LfD datasets demonstrates that our approach sequentially learns and retains multiple motion skills without retraining on past demonstrations, and outperforms other relevant baselines in terms of trajectory errors, continual learning scores, and stability metrics. Notably, we show that stability greatly enhances continual learning performance, particularly in size-efficient chunked hypernetworks. Our code is available at https://github.com/sayantanauddy/clfd-snode.

Most economic theories typically assume that financial market participants are fully rational individuals and use mathematical models to simulate human behavior in financial markets. However, human behavior is often not entirely rational and is challenging to predict accurately with mathematical models. In this paper, we propose Agent-based Simulated Financial Market (ASFM), which first constructs a simulated stock market with a real order matching system. Then, we propose a large language model based agent as the stock trader, which contains the profile, observation, and tool-learning based action module. The trading agent can comprehensively understand current market dynamics and financial policy information, and make decisions that align with their trading strategy. In the experiments, we first verify that the reactions of our ASFM are consistent with the real stock market in two controllable scenarios. In addition, we also conduct experiments in two popular economics research directions, and we find that conclusions drawn in our \model align with the preliminary findings in economics research. Based on these observations, we believe our proposed ASFM provides a new paradigm for economic research.

Training-free verbal reinforcement learning enables LLM agents to learn from world feedback -- objective signals such as dynamic task outcomes, market returns, or demand forecasts -- by extracting verbal rules from experience and injecting them as context, updating the agent's behavior without parameter changes. However, in non-stationary environments these agents face a retention-forgetting dilemma: retaining stale insights causes negative transfer, while discarding them causes catastrophic forgetting when conditions recur. We identify four requirements for navigating this dilemma -- outcome-driven evaluation, persistent structured evidence, non-monotonic knowledge lifecycle, and compositional governance -- and show that existing methods invest heavily in experience extraction while underinvesting in insight governance. We propose a three-layer architecture -- rules, evidence, and skills -- connected by a feedback-driven curation loop that closes the governance gap. Rules capture distilled experience from world outcomes; evidence logs track each rule's reliability across episodes; skills govern which rules to apply, how to resolve conflicts, and when to abstain. On financial forecasting as a case study, where world feedback is naturally abundant, noisy, and non-stationary, we show that the same accumulated experience either degrades performance below the zero-shot baseline or dramatically improves accuracy and risk-adjusted returns, depending on whether the curation loop is present.

Accurately forecasting the impact of macroeconomic events is critical for investors and policymakers. Salient events like monetary policy decisions and employment reports often trigger market movements by shaping expectations of economic growth and risk, thereby establishing causal relationships between events and market behavior. Existing forecasting methods typically focus either on textual analysis or time-series modeling, but fail to capture the multi-modal nature of financial markets and the causal relationship between events and price movements. To address these gaps, we propose CAMEF (Causal-Augmented Multi-Modality Event-Driven Financial Forecasting), a multi-modality framework that effectively integrates textual and time-series data with a causal learning mechanism and an LLM-based counterfactual event augmentation technique for causal-enhanced financial forecasting. Our contributions include: (1) a multi-modal framework that captures causal relationships between policy texts and historical price data; (2) a new financial dataset with six types of macroeconomic releases from 2008 to April 2024, and high-frequency real trading data for five key U.S. financial assets; and (3) an LLM-based counterfactual event augmentation strategy. We compare CAMEF to state-of-the-art transformer-based time-series and multi-modal baselines, and perform ablation studies to validate the effectiveness of the causal learning mechanism and event types.

Vegetable prices in Sri Lanka are highly volatile because the market is largely import-isolated, so supply disruptions quickly drive prices up. This study develops a machine learning framework to forecast such volatility by incorporating supply-chain-aware features and explicitly modelling the country's two cultivation seasons, Maha (October-April) and Yala (May-September). An integrated dataset was constructed by combining retail and farmer-gate prices with origin-aligned weather variables, diesel costs, and exchange rates across 12 vegetable varieties and 14 market centres from 2013 to 2019. A gradient-boosted ensemble model (XGBoost and LightGBM) was trained and optimised using Optuna, and unified and season-specific configurations were compared. Results show that season-specific models improve within-season fit, with the Yala-specific model achieving the highest R2 of 0.9420 (95% CI [0.690, 1.000]), while the unified model delivers the best overall predictive accuracy of 90.84% (95% CI [88.34%, 91.52%]) and an R2 of 0.9281 (95% CI [0.760, 1.000]). Notably, the unified model maintains 85.96% accuracy on a completely unseen 2024 hyperinflationary period without retraining, successfully tracking major price surges. These findings suggest that agricultural price movements in import-constrained markets are meaningfully predictable when models capture supply-chain dynamics, offering practical value for early warning and decision making by farmers, traders, and policymakers. Existing studies on Sri Lankan vegetable prices are confined to Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) applied to single markets, with no supply-chain features, seasonal segmentation, or cross-regime validation.

This research employs quantitative techniques interpreted through relevant economic theories to analyze a proposed U.S. "Discounted Reciprocal Tariff" structure. Statistical modeling (linear regression) quantifies the policy's consistent 'discounted reciprocity' pattern, which is interpreted using a Game Theory perspective on strategic interaction. Machine learning (K-Means clustering) identifies distinct country typologies based on tariff exposure and Economic Complexity Index (ECI), linking the policy to Economic Complexity theory. The study's primary application focuses on the major coffee exporting sector, utilizing simulation modeling grounded in principles of demand elasticity and substitution to project potential trade flow impacts. Specifically, for coffee, this simulation demonstrates how the proposed tariff differentials can induce significant substitution effects, projecting a potential shift in U.S. import demand away from high-tariff origins toward lower-tariff competitors. This disruption, stemming from the tariffs impacting exporting countries, is projected to ultimately increase coffee prices for consumers in the United States. Findings throughout are contextualized within Political Economy considerations. Overall, the study demonstrates how integrating regression, clustering, and simulation with economic theory exemplified through the coffee sector analysis provides a robust framework for assessing the potential systemic impacts, including consumer price effects, of strategic trade policies.

Long-term forecasting of chaotic systems from short-term observations remains a fundamental and underexplored challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Existing approaches often rely on long-term training data or focus on short-term sequence correlations, struggling to maintain predictive stability and dynamical coherence over extended horizons. We propose PhyxMamba, a novel framework that integrates a Mamba-based state-space model with physics-informed principles to capture the underlying dynamics of chaotic systems. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate forecasting. Our generative training scheme enables Mamba to replicate the physical process, augmented by multi-token prediction and attractor geometry regularization for physical constraints, enhancing prediction accuracy and preserving key statistical invariants. Extensive evaluations on diverse simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior long-term forecasting and faithfully captures essential dynamical invariants from short-term data. This framework opens new avenues for reliably predicting chaotic systems under observation-scarce conditions, with broad implications across climate science, neuroscience, epidemiology, and beyond. Our code is open-source at https://github.com/tsinghua-fib-lab/PhyxMamba.

Autoregressive models are trained to predict a system's behavior one step at a time, and recursive generation allows the learned dynamics to unfold over long horizons. To what extent can such dynamics learned from local observations recover broader organization of an underlying system that was only partially observed during training? Here we study small autoregressive transformers trained from scratch on trajectories sampled from restricted parameter regimes of several non-linear dynamical systems, including logistic and sine maps, the Lorenz system, and the generalized Hopf system, with control parameters and state trajectories represented as sequences of continuous tokens. Under closed-loop evaluation at parameters far outside the training distribution, the models can recover self-similar period-doubling cascades, chaotic dynamics, and attractor structures with remarkable visual and numerical fidelity. For the logistic map, a transformer reproduces successive period doublings up to period 128, yielding a finite-order scaling ratio of 4.6687, matching the Feigenbaum constant to within 5times10^{-4}. We further investigate how these structures emerge over the course of training, and reveal with causal interventions how control-parameter information is processed through attention into state prediction and shapes the resulting closed-loop dynamics. These results suggest that a surprisingly narrow window into a system's local behavior may suffice for autoregressive transformers to generalize to its unseen global dynamical organization.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

To cope with real-world dynamics, an intelligent system needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative methods address continual learning, and how they are adapted to particular challenges in realistic applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

We present a new type of game, the Liquidity Game. We draw inspiration from the UK government bond market and apply game theoretic approaches to its analysis. In Liquidity Games, market participants (agents) use non-cooperative games where the players' utility is directly defined by the liquidity of the game itself, offering a paradigm shift in our understanding of market dynamics. Each player's utility is intricately linked to the liquidity generated within the game, making the utility endogenous and dynamic. Players are not just passive recipients of utility based on external factors but active participants whose strategies and actions collectively shape and are shaped by the liquidity of the market. This reflexivity introduces a level of complexity and realism previously unattainable in conventional models. We apply Liquidity Game theoretic approaches to a simple UK bond market interaction and present results for market design and strategic behavior of participants. We tackle one of the largest issues within this mechanism, namely what strategy should market makers utilize when uncertain about the type of market maker they are interacting with, and what structure might regulators wish to see.

The endeavor of stock trend forecasting is principally focused on predicting the future trajectory of the stock market, utilizing either manual or technical methodologies to optimize profitability. Recent advancements in machine learning technologies have showcased their efficacy in discerning authentic profit signals within the realm of stock trend forecasting, predominantly employing temporal data derived from historical stock price patterns. Nevertheless, the inherently volatile and dynamic characteristics of the stock market render the learning and capture of multi-scale temporal dependencies and stable trading opportunities a formidable challenge. This predicament is primarily attributed to the difficulty in distinguishing real profit signal patterns amidst a plethora of mixed, noisy data. In response to these complexities, we propose a Multi-Scale Temporal Memory Learning and Efficient Debiasing (MTMD) model. This innovative approach encompasses the creation of a learnable embedding coupled with external attention, serving as a memory module through self-similarity. It aims to mitigate noise interference and bolster temporal consistency within the model. The MTMD model adeptly amalgamates comprehensive local data at each timestamp while concurrently focusing on salient historical patterns on a global scale. Furthermore, the incorporation of a graph network, tailored to assimilate global and local information, facilitates the adaptive fusion of heterogeneous multi-scale data. Rigorous ablation studies and experimental evaluations affirm that the MTMD model surpasses contemporary state-of-the-art methodologies by a substantial margin in benchmark datasets. The source code can be found at https://github.com/MingjieWang0606/MDMT-Public.

Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that demonstrate how autoassociative neural network models can elucidate the computational mechanisms underlying attractor-based information processing in biological neural systems performing cognitive functions. Drawing on empirical evidence, we explore hippocampal spatial representations, visual classification in the inferotemporal cortex, perceptual adaptation and priming, and working-memory biases shaped by sensory history. Across these domains, attractor network models reveal common computational principles and provide analytical insights into how experience shapes neural activity and behavior. Our synthesis underscores the value of attractor models as powerful tools for probing the neural basis of cognition and behavior.

Automated agent design improves agent harnesses through iterative revision, evaluation, and feedback summarization. Existing methods are largely candidate-centric: cross-round experience is organized around candidate agents, which leaves the repair progress implicit. This causes inefficient repair targeting, slow consolidation of partial progress, and propagation of ineffective interventions across rounds. Therefore, we formulate issue-centric agent optimization, in which repair progress is carried forward as an explicit persistent issue state to guide optimization, rather than re-derived from candidate history in each round. We instantiate the formulation in ADIAS, a framework for automated full-code agent design with two mechanisms. A persistent issue state maintains stable issue identities, lifecycle status, supporting evidence, and intervention-outcome histories. Issue-guided optimization uses this state to jointly propose repair targets and revision directions for subsequent focused full-code modification. Across five interactive benchmarks, ADIAS outperforms the strongest baseline by 25.2% on average and achieves consistent gains across four backbone models. Controlled ablations further show that removing persistent issue state or replacing issue-centric revision with candidate-centric policies leads to performance drops of up to 40.7%.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous "square-root law" of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the linear impact of order imbalances? Can one entirely explain the volatility of prices as resulting from the flow of uninformed metaorders that mechanically impact them? We introduce a new theoretical framework to describe metaorders with different signs, sizes and durations, which all impact prices as a square-root of volume but with a subsequent time decay. We show that, as in the original propagator model, price diffusion is ensured by the long memory of cross-correlations between metaorders. In order to account for the effect of strongly fluctuating volumes q of individual trades, we further introduce two q-dependent exponents, which allow us to describe how the moments of generalized volume imbalance and the correlation between price changes and generalized order flow imbalance scale with T. We predict in particular that the corresponding power-laws depend in a non-monotonic fashion on a parameter a, which allows one to put the same weight on all child orders or to overweight large ones, a behaviour that is clearly borne out by empirical data. We also predict that the correlation between price changes and volume imbalances should display a maximum as a function of a, which again matches observations. Such noteworthy agreement between theory and data suggests that our framework correctly captures the basic mechanism at the heart of price formation, namely the average impact of metaorders. We argue that our results support the "Order-Driven" theory of excess volatility, and are at odds with the idea that a "Fundamental" component accounts for a large share of the volatility of financial markets.

Offline reinforcement learning (RL) can fail spectacularly when bootstrapped temporal-difference (TD) updates amplify their own errors, driving the critic toward extreme and unusable Q-values. A key counterintuitive insight of this work is that collapse is not only a property of the backup rule or network architecture: optimizer dynamics themselves can directly trigger or suppress instability. From a control-theoretic viewpoint, we model offline TD learning as a feedback system and analyze Adam-based critic updates. This yields a necessary and sufficient condition for stability of the induced local update dynamics: within the regime we analyze, these dynamics are stable if and only if the spectral radius of the corresponding update operator is strictly below one. Further analysis suggests that standard Adam updates can inadvertently distort the parameter geometry, motivating explicit orthogonality constraints to prevent TD error amplification. To this end, we propose AdamO, an Adam-based optimizer with a decoupled orthogonality correction regulated by a strict task-alignment budget. We prove that this design theoretically guarantees worst-case task safety and preserves Adam's continuous-time dissipative dynamics. Empirically, AdamO is broadly compatible with diverse offline RL baselines, improving stability and returns across a broad suite of benchmarks.

Traditional frameworks of political communication operate under linear, event-driven assumptions that treat voter persuasion as a static, transactional function. This paper introduces Dynamic Consent Engineering (DCE), a novel interdisciplinary paradigm that synthesizes Edward Bernays' foundational principles of public relations with the S-E-E-D (Snowball, Equilibrium, Elasticity, Dominance) framework of system dynamics. By expanding Bernaysian operational constraints into a four-dimensional resource matrix (incorporating algorithmic media infrastructure alongside manpower, mindpower, and capital), we mathematically formalize how democratic institutions construct, optimize, and sustain political dominance. We map Bernays' classic eight-step engineering workflow directly onto non-linear feedback loops, information time lags, and demographic carrying capacities. Through rigorous modeling of systemic feedback structures, we isolate the dynamic root causes of political elasticity, policy resistance plateaus, and threshold-triggered trust collapses. Finally, we establish a four-step diagnostic pipeline and validate the framework via historical reference mode verification, demonstrating that long-term political stability depends not on ephemeral rhetoric, but on the structural synchronization of policy execution and dynamic feedback calibration.

Congestion is a common failure mode of markets, where consumers compete inefficiently on the same subset of goods (e.g., chasing the same small set of properties on a vacation rental platform). The typical economic story is that prices decongest by balancing supply and demand. But in modern online marketplaces, prices are typically set in a decentralized way by sellers, and the information about items is inevitably partial. The power of a platform is limited to controlling representations -- the subset of information about items presented by default to users. This motivates the present study of decongestion by representation, where a platform seeks to learn representations that reduce congestion and thus improve social welfare. The technical challenge is twofold: relying only on revealed preferences from the choices of consumers, rather than true preferences; and the combinatorial problem associated with representations that determine the features to reveal in the default view. We tackle both challenges by proposing a differentiable proxy of welfare that can be trained end-to-end on consumer choice data. We develop sufficient conditions for when decongestion promotes welfare, and present the results of extensive experiments on both synthetic and real data that demonstrate the utility of our approach.

Effective planning in model-based reinforcement learning (MBRL) and model-predictive control (MPC) relies on the accuracy of the learned dynamics model. In many instances of MBRL and MPC, this model is assumed to be stationary and is periodically re-trained from scratch on state transition experience collected from the beginning of environment interactions. This implies that the time required to train the dynamics model - and the pause required between plan executions - grows linearly with the size of the collected experience. We argue that this is too slow for lifelong robot learning and propose HyperCRL, a method that continually learns the encountered dynamics in a sequence of tasks using task-conditional hypernetworks. Our method has three main attributes: first, it includes dynamics learning sessions that do not revisit training data from previous tasks, so it only needs to store the most recent fixed-size portion of the state transition experience; second, it uses fixed-capacity hypernetworks to represent non-stationary and task-aware dynamics; third, it outperforms existing continual learning alternatives that rely on fixed-capacity networks, and does competitively with baselines that remember an ever increasing coreset of past experience. We show that HyperCRL is effective in continual model-based reinforcement learning in robot locomotion and manipulation scenarios, such as tasks involving pushing and door opening. Our project website with videos is at this link https://rvl.cs.toronto.edu/blog/2020/hypercrl

We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists ubiquitously in social media, finance and health informatics but is rarely investigated by the conventional research in reinforcement learning. To this end, we present a novel framework of the model-based reinforcement learning where the agent's actions and observations are asynchronous stochastic discrete events occurring in continuous-time. We model the dynamics of the environment by Hawkes process with external intervention control term and develop an algorithm to embed such process in the Bellman equation which guides the direction of the value gradient. We demonstrate the superiority of our method in both synthetic simulator and real-world problem.

Advances in generative models have improved video fidelity, enabling long-horizon generation, interactive world modeling, and evolving visual environments. Autoregressive (AR) video generation extends visual sequences through causal rollouts. However, a fundamental bottleneck emerges: as the generated sequence expands, practical models must operate under strictly bounded context windows, storage, and computational limits. Consequently, critical historical information, e.g., entity identities, dynamic states, and intervention-induced causal changes, often leaves the active context long before its relevance diminishes. Overcoming this limitation and maintaining temporal persistence constitutes a fundamental memory problem. We present a systematic and comprehensive review of memory mechanisms in AR video generation. We formulate memory operationally as persistent historical information maintained across outer AR steps, capable of influencing future generation even after the originating evidence is no longer locally accessible. Building upon this unified framework, we organize the literature through five complementary perspectives: (I) Forms, the representational carriers of history; (II) Functions, the specific semantic and physical information requiring preservation; (III) Operations, the lifecycle of writing, reading, updating, managing, and integrating memory; (IV) Learning, the optimization of memory behaviors under closed-loop rollouts; and (V) Evaluation, the paradigms for diagnosing genuine memory capabilities. We conclude by synthesizing open challenges, including composable and resource-aware memory architectures, trustworthy state updating, self-rollout learning, and standardized evaluation. By bridging representations, mechanisms, and learning paradigms, this paper establishes a structured foundation for developing reliable, memory-conditioned video generation systems.

Cognitive dynamics are pivotal to advance human understanding of the world. Recent advancements in large language models (LLMs) reveal their potential for cognitive simulation. However, these LLM-based cognitive studies primarily focus on static modeling, overlooking the dynamic nature of cognition. To bridge this gap, we propose the concept of the cognitive dynamics of LLMs and present a corresponding task with the inspiration of longitudinal studies. Towards the task, we develop CogBench, a novel benchmark to assess the cognitive dynamics of LLMs and validate it through participant surveys. We also design two evaluation metrics for CogBench, including Authenticity and Rationality. Recognizing the inherent static nature of LLMs, we introduce CogGPT for the task, which features an innovative iterative cognitive mechanism aimed at enhancing lifelong cognitive dynamics. Empirical results demonstrate the superiority of CogGPT over existing methods, particularly in its ability to facilitate role-specific cognitive dynamics under continuous information flows.

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solutions to a class of BSDEs. A key ingredient in our approach is a necessary stochastic maximum principle tailored to Epstein-Zin utility and a nonlinear transformation. In the deterministic setting, we further derive an explicit closed-form solution for the equilibrium investment and consumption policies.

Machine Learning models in finance are highly susceptible to model drift, where predictive performance declines as data distributions shift. This issue is especially acute in developing economies such as those in Central Asia and the Caucasus - including Tajikistan, Uzbekistan, Kazakhstan, and Azerbaijan - where frequent and unpredictable macroeconomics shocks destabilize financial data. To the best of our knowledge, this is among the first studies to examine drift mitigation methods on financial datasets from these regions. We investigate the use of synthetic outliers, a largely unexplored approach, to improve model stability against unforeseen shocks. To evaluate effectiveness, we introduce a two-level framework that measures both the extent of performance degradation and the severity of shocks. Our experiments on macroeconomic tabular datasets show that adding a small proportion of synthetic outliers generally improves stability compared to baseline models, though the optimal amount varies by dataset and model

The labor market is a complex ecosystem comprising diverse, interconnected entities, such as industries, occupations, skills, and firms. Due to the lack of a systematic method to map these heterogeneous entities together, each entity has been analyzed in isolation or only through pairwise relationships, inhibiting comprehensive understanding of the whole ecosystem. Here, we introduce Labor Space, a vector-space embedding of heterogeneous labor market entities, derived through applying a large language model with fine-tuning. Labor Space exposes the complex relational fabric of various labor market constituents, facilitating coherent integrative analysis of industries, occupations, skills, and firms, while retaining type-specific clustering. We demonstrate its unprecedented analytical capacities, including positioning heterogeneous entities on an economic axes, such as `Manufacturing--Healthcare'. Furthermore, by allowing vector arithmetic of these entities, Labor Space enables the exploration of complex inter-unit relations, and subsequently the estimation of the ramifications of economic shocks on individual units and their ripple effect across the labor market. We posit that Labor Space provides policymakers and business leaders with a comprehensive unifying framework for labor market analysis and simulation, fostering more nuanced and effective strategic decision-making.

Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both practical and theoretical insights on the empirical success of the probabilistic dynamics model ensemble through the lens of Lipschitz continuity. We find that, for a value function, the stronger the Lipschitz condition is, the smaller the gap between the true dynamics- and learned dynamics-induced Bellman operators is, thus enabling the converged value function to be closer to the optimal value function. Hence, we hypothesize that the key functionality of the probabilistic dynamics model ensemble is to regularize the Lipschitz condition of the value function using generated samples. To test this hypothesis, we devise two practical robust training mechanisms through computing the adversarial noise and regularizing the value network's spectral norm to directly regularize the Lipschitz condition of the value functions. Empirical results show that combined with our mechanisms, model-based RL algorithms with a single dynamics model outperform those with an ensemble of probabilistic dynamics models. These findings not only support the theoretical insight, but also provide a practical solution for developing computationally efficient model-based RL algorithms.

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a game adequately capture the limit behavior of natural game dynamics. These two results have created a need and opportunity to articulate a principled computational theory of the meaning of the game that is based on game dynamics. Given any game in normal form, and any prior distribution of play, we study the problem of computing the asymptotic behavior of a class of natural dynamics called the noisy replicator dynamics as a limit distribution over the sink equilibria of the game. When the prior distribution has pure strategy support, we prove this distribution can be computed efficiently, in near-linear time to the size of the best-response graph. When the distribution can be sampled -- for example, if it is the uniform distribution over all mixed strategy profiles -- we show through experiments that the limit distribution of reasonably large games can be estimated quite accurately through sampling and simulation.

This study examines the relationship between trade openness, logistics performance, and economic growth within G20 economies. Using a Bootstrap Autoregressive Distributed Lag (ARDL) model augmented by a dynamic error correction mechanism (ECM), the analysis quantifies both short run and long run effects of trade facilitation and logistics infrastructure, measured via the World Bank's Logistics Performance Index (LPI) from 2007 to 2023, on economic growth. The G20, as a consortium of the world's leading economies, exhibits significant variation in logistics efficiency and degrees of trade openness, providing a robust context for comparative analysis. The ARDL-ECM approach, reinforced by bootstrap resampling, delivers reliable estimates even in the presence of small samples and complex variable linkages. Findings are intended to inform policymakers seeking to enhance trade competitiveness and economic development through targeted investment in infrastructure and regulatory reforms supporting trade facilitation. The results underscore the critical role of efficient logistics specifically customs administration, physical infrastructure, and shipment reliability in driving international trade and fostering sustained economic growth. Improvements in these areas can substantially increase a country's trade capacity and overall economic performance.

Understanding labor market dynamics is essential for policymakers, employers, and job seekers. However, comprehensive datasets that capture real-world career trajectories are scarce. In this paper, we introduce JobHop, a large-scale public dataset derived from anonymized resumes provided by VDAB, the public employment service in Flanders, Belgium. Utilizing Large Language Models (LLMs), we process unstructured resume data to extract structured career information, which is then mapped to standardized ESCO occupation codes using a multi-label classification model. This results in a rich dataset of over 2.3 million work experiences, extracted from and grouped into more than 391,000 user resumes and mapped to standardized ESCO occupation codes, offering valuable insights into real-world occupational transitions. This dataset enables diverse applications, such as analyzing labor market mobility, job stability, and the effects of career breaks on occupational transitions. It also supports career path prediction and other data-driven decision-making processes. To illustrate its potential, we explore key dataset characteristics, including job distributions, career breaks, and job transitions, demonstrating its value for advancing labor market research.

Transaction data from digital payment systems can be used to study economic processes at such a detail that was not possible previously. Here, we analyse the data from Sarafu token network, a community inclusion currency in Kenya. During the COVID-19 emergency, the Sarafu was disbursed as part of a humanitarian aid project. In this work, the transactions are analysed using network science. A topological categorisation is defined to identify cyclic and acyclic components. Furthermore, temporal aspects of circulation taking place within these components are considered. The significant presence of different types of strongly connected components as compared to randomized null models shows the importance of cycles in this economic network. Especially, indicating their key role in currency recirculation. In some acyclic components, the most significant triad suggests the presence of a group of users collecting currency from accounts active only once, hinting at a misuse of the system. In some other acyclic components, small isolated groups of users were active only once, suggesting the presence of users only interested in trying out the system. The methods used in this paper can answer specific questions related to user activities, currency design, and assessment of monetary interventions. Our methodology provides a general quantitative tool for analysing the behaviour of users in a currency network.

The inherent volatility and dynamic fluctuations within the financial stock market underscore the necessity for investors to employ a comprehensive and reliable approach that integrates risk management strategies, market trends, and the movement trends of individual securities. By evaluating specific data, investors can make more informed decisions. However, the current body of literature lacks substantial evidence supporting the practical efficacy of reinforcement learning (RL) agents, as many models have only demonstrated success in back testing using historical data. This highlights the urgent need for a more advanced methodology capable of addressing these challenges. There is a significant disconnect in the effective utilization of financial indicators to better understand the potential market trends of individual securities. The disclosure of successful trading strategies is often restricted within financial markets, resulting in a scarcity of widely documented and published strategies leveraging RL. Furthermore, current research frequently overlooks the identification of financial indicators correlated with various market trends and their potential advantages. This research endeavors to address these complexities by enhancing the ability of RL agents to effectively differentiate between positive and negative buy/sell actions using financial indicators. While we do not address all concerns, this paper provides deeper insights and commentary on the utilization of technical indicators and their benefits within reinforcement learning. This work establishes a foundational framework for further exploration and investigation of more complex scenarios.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

We study a model of innovation with a large number of firms that create new technologies by combining several discrete ideas. These ideas are created via private investment and spread between firms. Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates learning from others. Their decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a learning network. Higher interaction rates impose both positive and negative externalities, as there is more learning but also more competition. We show that the equilibrium learning network is at a critical threshold between sparse and dense networks. At equilibrium, the positive externality from interaction dominates: the innovation rate and welfare would be dramatically higher if the network were denser. So there are large returns to increasing interaction rates above the critical threshold. Nevertheless, several natural types of interventions fail to move the equilibrium away from criticality. One effective policy solution is to introduce informational intermediaries, such as public innovators who do not have incentives to be secretive. These intermediaries can facilitate a high-innovation equilibrium by transmitting ideas from one private firm to another.

With the great success of diffusion models (DMs) in generating realistic synthetic vision data, many researchers have investigated their potential in decision-making and control. Most of these works utilized DMs to sample directly from the trajectory space, where DMs can be viewed as a combination of dynamics models and policies. In this work, we explore how to decouple DMs' ability as dynamics models in fully offline settings, allowing the learning policy to roll out trajectories. As DMs learn the data distribution from the dataset, their intrinsic policy is actually the behavior policy induced from the dataset, which results in a mismatch between the behavior policy and the learning policy. We propose Dynamics Diffusion, short as DyDiff, which can inject information from the learning policy to DMs iteratively. DyDiff ensures long-horizon rollout accuracy while maintaining policy consistency and can be easily deployed on model-free algorithms. We provide theoretical analysis to show the advantage of DMs on long-horizon rollout over models and demonstrate the effectiveness of DyDiff in the context of offline reinforcement learning, where the rollout dataset is provided but no online environment for interaction.

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

Auto-bidding systems aim to maximize advertiser value over long horizons under budget constraints and ratio targets such as cost-per-acquisition, yet future traffic and auction dynamics are non-stationary and uncertain. Existing approaches face distinct limitations: control-based pacing reacts to deviations but cannot anticipate future conditions, while RL and generative methods fold constraints into reward signals, obscuring violations and degrading under distribution shift. We shift the learning target from actions to responses with the Generative Response Model (GRM), a history-conditioned sequence model that jointly predicts future traffic volume and horizon-aggregate cost/value curves as functions of a single bid multiplier. We show that under mild monotonicity conditions, the optimality gap relative to full per-tick control is bounded by the dispersion of per-tick marginal value-per-cost. Given predicted responses, a lightweight analytic controller enforces each active constraint via a 1D root-finding step. We prove this controller is exact for the single-multiplier problem and bound constraint violations under receding-horizon replanning in terms of prediction error. Experiments on AuctionNet show that GRM improves constraint stability and overall score compared to existing baselines.

The European Union Emissions Trading System (EU ETS) is a key policy tool for reducing greenhouse gas emissions and advancing toward a net-zero economy. Under this scheme, tradeable carbon credits, European Union Allowances (EUAs), are issued to large emitters, who can buy and sell them on regulated markets. We investigate the influence of financial, economic, and energy-related factors on EUA futures prices using discrete and dynamic Bayesian networks to model both contemporaneous and time-lagged dependencies. The analysis is based on daily data spanning the third and fourth ETS trading phases (2013-2025), incorporating a wide range of indicators including energy commodities, equity indices, exchange rates, and bond markets. Results reveal that EUA pricing is most influenced by energy commodities, especially coal and oil futures, and by the performance of the European energy sector. Broader market sentiment, captured through stock indices and volatility measures, affects EUA prices indirectly via changes in energy demand. The dynamic model confirms a modest next-day predictive influence from oil markets, while most other effects remain contemporaneous. These insights offer regulators, institutional investors, and firms subject to ETS compliance a clearer understanding of the interconnected forces shaping the carbon market, supporting more effective hedging, investment strategies, and policy design.

Transformer architectures have dramatically advanced representation learning and inference in deep models through self-attention mechanisms. In parallel,associative memory (AM) frameworks map representations onto energy landscapes, offering interpretable retrieval mechanisms. However, their continuous-time inference dynamics lack the biological plausibility of classical Continuous Attractor Neural Networks (CANNs). To bridge this gap, we propose Controlled Dynamics Attractor Transformer (CDAT), which couples a mixture von Mises-Fisher (Mo-vMF) attention energy with a Hopfield refinement energy, while augmenting energy descent with a CANN-inspired excitation-inhibition modulation. CDAT instantiates a topology-constrained dynamical system whose couplings encode relational structure among tokens, thereby linking attractor-style dynamics to modern energy-based attention. We further provide a constructive dissipation analysis to formally establish their controlled inference dynamics. Benefiting from these robust and structured dynamics, CDAT achieves state-of-the-art performance across multiple benchmarks in graph anomaly detection and graph classification.

Persistent memory is a central capability for AI agents, yet the mathematical foundations of memory retrieval, lifecycle management, and consistency remain unexplored. Current systems employ cosine similarity for retrieval, heuristic decay for salience, and provide no formal contradiction detection. We establish information-geometric foundations through three contributions. First, a retrieval metric derived from the Fisher information structure of diagonal Gaussian families, satisfying Riemannian metric axioms, invariant under sufficient statistics, and computable in O(d) time. Second, memory lifecycle formulated as Riemannian Langevin dynamics with proven existence and uniqueness of the stationary distribution via the Fokker-Planck equation, replacing hand-tuned decay with principled convergence guarantees. Third, a cellular sheaf model where non-trivial first cohomology classes correspond precisely to irreconcilable contradictions across memory contexts. On the LoCoMo benchmark, the mathematical layers yield +12.7 percentage points over engineering baselines across six conversations, reaching +19.9 pp on the most challenging dialogues. A four-channel retrieval architecture achieves 75% accuracy without cloud dependency. Cloud-augmented results reach 87.7%. A zero-LLM configuration satisfies EU AI Act data sovereignty requirements by architectural design. To our knowledge, this is the first work establishing information-geometric, sheaf-theoretic, and stochastic-dynamical foundations for AI agent memory systems.

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Chaos and unpredictability are traditionally synonymous, yet large-scale machine learning methods recently have demonstrated a surprising ability to forecast chaotic systems well beyond typical predictability horizons. However, recent works disagree on whether specialized methods grounded in dynamical systems theory, such as reservoir computers or neural ordinary differential equations, outperform general-purpose large-scale learning methods such as transformers or recurrent neural networks. These prior studies perform comparisons on few individually-chosen chaotic systems, thereby precluding robust quantification of how statistical modeling choices and dynamical invariants of different chaotic systems jointly determine empirical predictability. Here, we perform the largest to-date comparative study of forecasting methods on the classical problem of forecasting chaos: we benchmark 24 state-of-the-art forecasting methods on a crowdsourced database of 135 low-dimensional systems with 17 forecast metrics. We find that large-scale, domain-agnostic forecasting methods consistently produce predictions that remain accurate up to two dozen Lyapunov times, thereby accessing a new long-horizon forecasting regime well beyond classical methods. We find that, in this regime, accuracy decorrelates with classical invariant measures of predictability like the Lyapunov exponent. However, in data-limited settings outside the long-horizon regime, we find that physics-based hybrid methods retain a comparative advantage due to their strong inductive biases.

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a stock, as revealed through the order book, to subsequent variations in its market price. We assess the model by testing its out-of-sample predictions for the direction of price moves given the history of price and order flow, across a wide range of stocks and time periods. The universal price formation model is shown to exhibit a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific. The universal model --- trained on data from all stocks --- outperforms, in terms of out-of-sample prediction accuracy, asset-specific linear and nonlinear models trained on time series of any given stock, showing that the universal nature of price formation weighs in favour of pooling together financial data from various stocks, rather than designing asset- or sector-specific models as commonly done. Standard data normalizations based on volatility, price level or average spread, or partitioning the training data into sectors or categories such as large/small tick stocks, do not improve training results. On the other hand, inclusion of price and order flow history over many past observations is shown to improve forecasting performance, showing evidence of path-dependence in price dynamics.

Reinforcement Learning (RL) is an important machine learning paradigm for solving sequential decision-making problems. Recent years have witnessed remarkable progress in this field due to the rapid development of deep neural networks. However, the success of RL currently relies on extensive training data and computational resources. In addition, RL's limited ability to generalize across tasks restricts its applicability in dynamic and real-world environments. With the arisen of Continual Learning (CL), Continual Reinforcement Learning (CRL) has emerged as a promising research direction to address these limitations by enabling agents to learn continuously, adapt to new tasks, and retain previously acquired knowledge. In this survey, we provide a comprehensive examination of CRL, focusing on its core concepts, challenges, and methodologies. Firstly, we conduct a detailed review of existing works, organizing and analyzing their metrics, tasks, benchmarks, and scenario settings. Secondly, we propose a new taxonomy of CRL methods, categorizing them into four types from the perspective of knowledge storage and/or transfer. Finally, our analysis highlights the unique challenges of CRL and provides practical insights into future directions.

We introduce Option Kernel Bellman Equations (OKBEs) for a new reward-free Markov Decision Process. Rather than a value function, OKBEs directly construct and optimize a predictive map called a state-time option kernel (STOK) to maximize the probability of completing a goal while avoiding constraint violations. STOKs are compositional, modular, and interpretable initiation-to-termination transition kernels for policies in the Options Framework of Reinforcement Learning. This means: 1) STOKs can be composed using Chapman-Kolmogorov equations to make spatiotemporal predictions for multiple policies over long horizons, 2) high-dimensional STOKs can be represented and computed efficiently in a factorized and reconfigurable form, and 3) STOKs record the probabilities of semantically interpretable goal-success and constraint-violation events, needed for formal verification. Given a high-dimensional state-transition model for an intractable planning problem, we can decompose it with local STOKs and goal-conditioned policies that are aggregated into a factorized goal kernel, making it possible to forward-plan at the level of goals in high-dimensions to solve the problem. These properties lead to highly flexible agents that can rapidly synthesize meta-policies, reuse planning representations across many tasks, and justify goals using empowerment, an intrinsic motivation function. We argue that reward-maximization is in conflict with the properties of compositionality, modularity, and interpretability. Alternatively, OKBEs facilitate these properties to support verifiable long-horizon planning and intrinsic motivation that scales to dynamic high-dimensional world-models.

Continual learning refers to a dynamical framework in which a model receives a stream of non-stationary data over time and must adapt to new data while preserving previously acquired knowledge. Unluckily, neural networks fail to meet these two desiderata, incurring the so-called catastrophic forgetting phenomenon. Whereas a vast array of strategies have been proposed to attenuate forgetting in the computer vision domain, for speech-related tasks, on the other hand, there is a dearth of works. In this paper, we consider the joint use of rehearsal and knowledge distillation (KD) approaches for spoken language understanding under a class-incremental learning scenario. We report on multiple KD combinations at different levels in the network, showing that combining feature-level and predictions-level KDs leads to the best results. Finally, we provide an ablation study on the effect of the size of the rehearsal memory that corroborates the efficacy of our approach for low-resource devices.

Online inclusive financial services encounter significant financial risks due to their expansive user base and low default costs. By real-world practice, we reveal that utilizing longer-term user payment behaviors can enhance models' ability to forecast financial risks. However, learning long behavior sequences is non-trivial for deep sequential models. Additionally, the diverse fields of payment behaviors carry rich information, requiring thorough exploitation. These factors collectively complicate the task of long-term user behavior modeling. To tackle these challenges, we propose a Long-term Payment Behavior Sequence Folding method, referred to as LBSF. In LBSF, payment behavior sequences are folded based on merchants, using the merchant field as an intrinsic grouping criterion, which enables informative parallelism without reliance on external knowledge. Meanwhile, we maximize the utility of payment details through a multi-field behavior encoding mechanism. Subsequently, behavior aggregation at the merchant level followed by relational learning across merchants facilitates comprehensive user financial representation. We evaluate LBSF on the financial risk assessment task using a large-scale real-world dataset. The results demonstrate that folding long behavior sequences based on internal behavioral cues effectively models long-term patterns and changes, thereby generating more accurate user financial profiles for practical applications.

This paper examines the fiscal and macroeconomic strategies essential for transition of India to a high income economy by 2047, aligning with the vision of Viksit Bharat. A sustainable annual GDP growth rate of 7 to 8 percent is projected as necessary to achieve this milestone while maintaining fiscal prudence through a targeted deficit threshold below 3.5 percent of GDP. The study underscores the role of disciplined fiscal management in financing critical public investments in infrastructure, human capital development and technological innovation. Given constraints on domestic resource mobilization, the paper highlights the importance of multilateral financial institutions, including the World Bank, IMF and ADB, in expanding fiscal space in India through concessional financing, technical cooperation, and risk sharing mechanisms. Using econometric modeling and scenario analysis, the research identifies key policy interventions in infrastructure, healthcare, education and sustainable energy that can maximize growth while ensuring fiscal sustainability. Policy recommendations include enhancing tax buoyancy, rationalizing expenditure, optimizing public private partnerships and strengthening fiscal responsibility frameworks. The findings suggest that a calibrated approach to growth, prudent fiscal management and strategic international collaborations are critical to achieving long term economic aspirations of India.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Continual learning aims to enable neural networks to acquire new knowledge without forgetting previously learned information. While recent prompt-based methods perform strongly in class-incremental settings, they remain vulnerable under domain shifts, where the input distribution changes but the label space remains fixed. This exposes a persistent problem known as representation drift. Shared representations evolve in ways that overwrite previously useful features and cause forgetting even when prompts isolate task-specific parameters. To address this issue, we introduce InTAct, a method that preserves functional behavior in shared layers without freezing parameters or storing past data. InTAct captures the characteristic activation ranges associated with previously learned tasks and constrains updates to ensure the network remains consistent within these regions, while still allowing for flexible adaptation elsewhere. In doing so, InTAct stabilizes the functional role of important neurons rather than directly restricting parameter values. The approach is architecture-agnostic and integrates seamlessly into existing prompt-based continual learning frameworks. By regulating representation changes where past knowledge is encoded, InTAct achieves a principled balance between stability and plasticity. Across diverse domain-incremental benchmarks, including DomainNet and ImageNet-R, InTAct consistently reduces representation drift and improves performance, increasing Average Accuracy by up to 8 percentage points over state-of-the-art baselines.

Learning-based memory systems for self-evolving LLM agents face two tightly coupled challenges. First, trajectory-indexed utilities grow with the interaction history, thereby dispersing limited feedback over an ever-expanding state space. Second, because trajectory-level rewards are jointly assigned to co-retrieved memories, irrelevant experiences may receive misleading utility updates and consequently enter the memory-reward trap. To address these challenges, we introduce Reduced-Order Memory Reinforcement Learning (RoMeRL), which represents the growing trajectory-indexed utility space using a fixed-dimensional per-task memory state factorized by outcome polarity and memory dynamics. RoMeRL incorporates new experiences through a fixed set of semantic coordinates whose contents are updated or replaced over time, thereby concentrating feedback over a bounded utility support. Theoretically, we show that this reduced-order parameterization increases the average feedback received by each utility coordinate and characterize the steady-state occupancy of erroneous coordinates under a generic coordinate-transition model. Empirically, across ALFWorld and LifelongAgentBench, RoMeRL improves task performance, reduces the Cold-Q ratio by 80.0%, increases feedback density by approximately 6.0 times, reduces the maintained memory size by 84.4%, and cuts LLM calls by 21.1%. These results show that reduced-order utility states support efficient self-evolving agent memory while limiting persistent reward contamination. Code is available at: https://github.com/YOUNG-fnxm/RoMeRL

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance but lacks support for off-policy learning. Recent research suggests that regression oracles can bridge this gap by combining non-uniform exploration with supervised learning. In this paper, we analyze these approaches within a real-world industrial context at Adyen, a large global payments processor characterized by batch logged delayed feedback, short-term memory, and dynamic action spaces under the Empirical Risk Minimization (ERM) framework. Our analysis reveals that while regression oracles significantly improve performance, they introduce challenges due to rigid algorithmic assumptions. Specifically, we observe that as a policy improves, subsequent generations may perform worse due to shifts in the reward distribution and increased class imbalance in the training data. This degradation occurs de spite improvements in other aspects of the training data, leading to decreased performance in successive policy iterations. We further explore the long-term impact of regression oracles, identifying a potential "oscillation effect." This effect arises when regression oracles influence probability estimates and the realizability of subsequent policy models, leading to fluctuations in performance across iterations. Our findings highlight the need for more adaptable algorithms that can leverage the benefits of regression oracles without introducing instability in policy performance over time.