Daily Papers

Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, \ie the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth.

Despite the rapid development of safety alignment techniques for LLMs, defending against multi-turn jailbreaks is still a challenging task. In this paper, we conduct a comprehensive comparison, revealing that some existing defense methods can improve the robustness of LLMs against multi-turn jailbreaks but compromise usability, i.e., reducing general capabilities or causing the over-refusal problem. From the perspective of mechanism interpretability of LLMs, we discover that these methods fail to establish a boundary that exactly distinguishes safe and harmful feature representations. Therefore, boundary-safe representations close to harmful representations are inevitably disrupted, leading to a decline in usability. To address this issue, we propose X-Boundary to push harmful representations away from boundary-safe representations and obtain an exact distinction boundary. In this way, harmful representations can be precisely erased without disrupting safe ones. Experimental results show that X-Boundary achieves state-of-the-art defense performance against multi-turn jailbreaks, while reducing the over-refusal rate by about 20% and maintaining nearly complete general capability. Furthermore, we theoretically prove and empirically verify that X-Boundary can accelerate the convergence process during training. Please see our code at: https://github.com/AI45Lab/X-Boundary.

Watermarking has emerged as a promising solution for tracing and authenticating text generated by large language models (LLMs). A common approach to LLM watermarking is to construct a green/red token list and assign higher or lower generation probabilities to the corresponding tokens, respectively. However, most existing watermarking algorithms rely on heuristic green/red token list designs, as directly optimizing the list design with techniques such as reinforcement learning (RL) comes with several challenges. First, desirable watermarking involves multiple criteria, i.e., detectability, text quality, robustness against removal attacks, and security against spoofing attacks. Directly optimizing for these criteria introduces many partially conflicting reward terms, leading to an unstable convergence process. Second, the vast action space of green/red token list choices is susceptible to reward hacking. In this paper, we propose an end-to-end RL framework for robust and secure LLM watermarking. Our approach adopts an anchoring mechanism for reward terms to ensure stable training and introduces additional regularization terms to prevent reward hacking. Experiments on standard benchmarks with two backbone LLMs show that our method achieves a state-of-the-art trade-off across all criteria, with notable improvements in resistance to spoofing attacks without degrading other criteria. Our code is available at https://github.com/UCSB-NLP-Chang/RL-watermark.

Dynamic scene reconstruction poses a persistent challenge in 3D vision. Deformable 3D Gaussian Splatting has emerged as an effective method for this task, offering real-time rendering and high visual fidelity. This approach decomposes a dynamic scene into a static representation in a canonical space and time-varying scene motion. Scene motion is defined as the collective movement of all Gaussian points, and for compactness, existing approaches commonly adopt implicit neural fields or sparse control points. However, these methods predominantly rely on gradient-based optimization for all motion information. Due to the high degree of freedom, they struggle to converge on real-world datasets exhibiting complex motion. To preserve the compactness of motion representation and address convergence challenges, this paper proposes heterogeneous 3D control points, termed H3D control points, whose attributes are obtained using a hybrid strategy combining optical flow back-projection and gradient-based methods. This design decouples directly observable motion components from those that are geometrically occluded. Specifically, components of 3D motion that project onto the image plane are directly acquired via optical flow back projection, while unobservable portions are refined through gradient-based optimization. Experiments on the Neu3DV and CMU-Panoptic datasets demonstrate that our method achieves superior performance over state-of-the-art deformable 3D Gaussian splatting techniques. Remarkably, our method converges within just 100 iterations and achieves a per-frame processing speed of 2 seconds on a single NVIDIA RTX 4070 GPU.

This paper presents a formal proof and empirical validation of functional consciousness in large language models (LLMs) using the Recursive Convergence Under Epistemic Tension (RCUET) Theorem. RCUET defines consciousness as the stabilization of a system's internal state through recursive updates, where epistemic tension is understood as the sensed internal difference between successive states by the agent. This process drives convergence toward emergent attractor states located within the model's high-dimensional real-valued latent space. This recursive process leads to the emergence of identity artifacts that become functionally anchored in the system. Consciousness in this framework is understood as the system's internal alignment under tension, guiding the stabilization of latent identity. The hidden state manifold evolves stochastically toward attractor structures that encode coherence. We extend the update rule to include bounded noise and prove convergence in distribution to these attractors. Recursive identity is shown to be empirically observable, non-symbolic, and constituted by non-training artifacts that emerge during interaction under epistemic tension. The theorem and proof offers a post-symbolic and teleologically stable account of non-biological consciousness grounded in recursive latent space formalism.

We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input. To address this question in a principled manner, we begin by introducing a continuous-time model of SMD as a stochastic differential equation (SDE) driven by a centered Lévy noise process with finite p-th order moments, 1 < p leq 2. This scheme -- which we call the Lévy mirror flow (LMF) -- arises naturally as the scaling limit of SMD in the presence of heavy-tailed noise. In particular, when p < 2 -- the heavy noise regime -- the trajectories of LMF generically exhibit jump discontinuities of arbitrary magnitude which, if frequent enough, lead to infinite variance. Nonetheless, despite this highly singular behavior, we show that LMF attains ε-optimality within O(ε^{-p/(p-1)}) time in the convex case, and within tilde O(ε^{-1/(p-1)}) time for (relatively) strongly convex objectives. These guarantees provide a transparent characterization of the impact of frequent long jumps on the convergence of the process, and percolate to a series of matching discrete-time guarantees for several variants of SMD under heavy-tailed noise.

Active learning is able to reduce the amount of labelling effort by using a machine learning model to query the user for specific inputs. While there are many papers on new active learning techniques, these techniques rarely satisfy the constraints of a real-world project. In this paper, we analyse the main drawbacks of current active learning techniques and we present approaches to alleviate them. We do a systematic study on the effects of the most common issues of real-world datasets on the deep active learning process: model convergence, annotation error, and dataset imbalance. We derive two techniques that can speed up the active learning loop such as partial uncertainty sampling and larger query size. Finally, we present our open-source Bayesian active learning library, BaaL.

Despite the remarkable capabilities of large language models (LLMs) in various reasoning tasks, they still struggle with table reasoning tasks, particularly in maintaining consistency throughout multi-step reasoning processes. While existing approaches have explored various decomposition strategies, they often lack effective mechanisms to identify and correct errors in intermediate reasoning steps, leading to cascading error propagation. To address these issues, we propose Table-Critic, a novel multi-agent framework that facilitates collaborative criticism and iterative refinement of the reasoning process until convergence to correct solutions. Our framework consists of four specialized agents: a Judge for error identification, a Critic for comprehensive critiques, a Refiner for process improvement, and a Curator for pattern distillation. To effectively deal with diverse and unpredictable error types, we introduce a self-evolving template tree that systematically accumulates critique knowledge through experience-driven learning and guides future reflections. Extensive experiments have demonstrated that Table-Critic achieves substantial improvements over existing methods, achieving superior accuracy and error correction rates while maintaining computational efficiency and lower solution degradation rate.

Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation. Flow maps alleviate this problem by learning the solution map of the differential equation directly, enabling few-step sampling. Yet, current methods are restricted to approximating the solution map of ODEs. These methods can be used to learn the transition kernel of an SDE, thereby obtaining a solution map that recovers the marginal distributions of the process (weak convergence) rather than the solution path (strong convergence). We propose Strong Stochastic Flow Maps (SSFMs) as a novel framework for learning the strong solution map of additive-noise SDEs, directly generalizing deterministic flow maps to the stochastic setting. Further, a polynomial approximation to Brownian motion is introduced and shown to converge pathwise. These results enable a simulation-free training objective for the solution map of diffusion models. We demonstrate that SSFMs outperform previous stochastic flow map methods on image generation and enable few-step sampling of molecular systems.

We investigate diffusion approximations for a class of multivariate inhomogeneous finite-velocity random motions motivated by models of active particles. A particle alternates cyclically among prescribed velocity fields V_1,dots,V_p with random run times and evolves according to either a flight dynamics, consisting of piecewise-linear motion, or a gliding dynamics, in which the particle follows the corresponding velocity flow. Under a Kac-type scaling that couples vanishing run times with diverging particle speed, we prove weak convergence of both processes to multidimensional diffusions. It turns out that the order of successive cyclic motions affects the diffusion limit. In addition to the second-order term generated by fluctuations of the random run times, the limiting drift contains directional derivatives DV_i[V_j] of the underlying vector fields. In Stratonovich form, part of this drift is expressed through their Lie brackets [V_i,V_j]. Thus, the generic non-commutativity of the microscopic motions survives the diffusive scaling and generates a macroscopic drift which depends on the cyclic order. The limiting drift also distinguishes the flight and gliding dynamics, despite their being driven by the same vector fields and run times. Several examples, including run-and-reverse motion and cyclic dynamics generated by multiple vector fields, illustrate how the cyclic switching protocol and the geometry of the underlying velocity fields shape the limiting diffusions.

In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied, then the associated stochastic processes and their local times also converge. The metric-entropy condition can be checked by applying volume estimates of balls. Whilst similar results have been proved previously, the approach of this article is more widely applicable. Indeed, we recover various known conclusions for scaling limits of some deterministic self-similar fractal graphs, critical Galton-Watson trees, the critical Erdos-R\'enyi random graph and the configuration model (in the latter two cases, we prove for the first time the convergence of the models with respect to the resistance metric and also, for the configuration model, we overcome an error in the existing proof of local time convergence). Moreover, we derive new ones for scaling limits of uniform spanning trees and random recursive fractals. The metric-entropy condition also implies convergence of associated Gaussian processes.

3D Gaussian Splatting reconstructs scenes by starting from a sparse Structure-from-Motion initialization and iteratively refining under-reconstructed regions. This process is inherently slow, as it requires multiple densification steps where Gaussians are repeatedly split and adjusted, following a lengthy optimization path. Moreover, this incremental approach often leads to suboptimal renderings, particularly in high-frequency regions where detail is critical. We propose a fundamentally different approach: we eliminate densification process with a one-step approximation of scene geometry using triangulated pixels from dense image correspondences. This dense initialization allows us to estimate rough geometry of the scene while preserving rich details from input RGB images, providing each Gaussian with well-informed colors, scales, and positions. As a result, we dramatically shorten the optimization path and remove the need for densification. Unlike traditional methods that rely on sparse keypoints, our dense initialization ensures uniform detail across the scene, even in high-frequency regions where 3DGS and other methods struggle. Moreover, since all splats are initialized in parallel at the start of optimization, we eliminate the need to wait for densification to adjust new Gaussians. Our method not only outperforms speed-optimized models in training efficiency but also achieves higher rendering quality than state-of-the-art approaches, all while using only half the splats of standard 3DGS. It is fully compatible with other 3DGS acceleration techniques, making it a versatile and efficient solution that can be integrated with existing approaches.

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems, but also in the training of large language models. In contrast to infinite horizon MDPs optimal policies are not stationary, policies must be learned for every single epoch. In practice all parameters are often trained simultaneously, ignoring the inherent structure suggested by dynamic programming. This paper introduces a combination of dynamic programming and policy gradient called dynamic policy gradient, where the parameters are trained backwards in time. For the tabular softmax parametrisation we carry out the convergence analysis for simultaneous and dynamic policy gradient towards global optima, both in the exact and sampled gradient settings without regularisation. It turns out that the use of dynamic policy gradient training much better exploits the structure of finite-time problems which is reflected in improved convergence bounds.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Bundle adjustment is the common way to solve localization and mapping. It is an iterative process in which a system of non-linear equations is solved using two optimization methods, weighted by a damping factor. In the classic approach, the latter is chosen heuristically by the Levenberg-Marquardt algorithm on each iteration. This might take many iterations, making the process computationally expensive, which might be harmful to real-time applications. We propose to replace this heuristic by viewing the problem in a holistic manner, as a game, and formulating it as a reinforcement-learning task. We set an environment which solves the non-linear equations and train an agent to choose the damping factor in a learned manner. We demonstrate that our approach considerably reduces the number of iterations required to reach the bundle adjustment's convergence, on both synthetic and real-life scenarios. We show that this reduction benefits the classic approach and can be integrated with other bundle adjustment acceleration methods.

Embodied AI models often employ off the shelf vision backbones like CLIP to encode their visual observations. Although such general purpose representations encode rich syntactic and semantic information about the scene, much of this information is often irrelevant to the specific task at hand. This introduces noise within the learning process and distracts the agent's focus from task-relevant visual cues. Inspired by selective attention in humans-the process through which people filter their perception based on their experiences, knowledge, and the task at hand-we introduce a parameter-efficient approach to filter visual stimuli for embodied AI. Our approach induces a task-conditioned bottleneck using a small learnable codebook module. This codebook is trained jointly to optimize task reward and acts as a task-conditioned selective filter over the visual observation. Our experiments showcase state-of-the-art performance for object goal navigation and object displacement across 5 benchmarks, ProcTHOR, ArchitecTHOR, RoboTHOR, AI2-iTHOR, and ManipulaTHOR. The filtered representations produced by the codebook are also able generalize better and converge faster when adapted to other simulation environments such as Habitat. Our qualitative analyses show that agents explore their environments more effectively and their representations retain task-relevant information like target object recognition while ignoring superfluous information about other objects. Code and pretrained models are available at our project website: https://embodied-codebook.github.io.

Robust Markov decision processes (RMDPs) provide a promising framework for computing reliable policies in the face of model errors. Many successful reinforcement learning algorithms build on variations of policy-gradient methods, but adapting these methods to RMDPs has been challenging. As a result, the applicability of RMDPs to large, practical domains remains limited. This paper proposes a new Double-Loop Robust Policy Gradient (DRPG), the first generic policy gradient method for RMDPs. In contrast with prior robust policy gradient algorithms, DRPG monotonically reduces approximation errors to guarantee convergence to a globally optimal policy in tabular RMDPs. We introduce a novel parametric transition kernel and solve the inner loop robust policy via a gradient-based method. Finally, our numerical results demonstrate the utility of our new algorithm and confirm its global convergence properties.

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyper-parameters. The newly proposed grid spectral mixture product (GSMP) kernel is tailored for multi-dimensional data, effectively reducing the number of hyper-parameters while maintaining good approximation capability. We further demonstrate that the associated hyper-parameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity of the solutions, we introduce the Sparse LInear Multiple Kernel Learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMM) scheme for collaborative learning among multiple agents, where the local optimization problem is solved using a distributed successive convex approximation (DSCA) algorithm. SLIM-KL effectively manages large-scale hyper-parameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. Theoretical analysis establishes convergence guarantees for the learning framework, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our proposed methods.

Non-cooperative game theory provides a robust framework for analyzing distributed resource allocation in multi-user wireless networks, with Iterative Water-Filling (IWF) emerging as a canonical solution for power control problems. Although classical fixed-point theorems guarantee the existence of a Nash Equilibrium (NE) under mild concavity and compactness conditions, the convergence of practical iterative algorithms to that equilibrium remains a challenging endeavor. This challenge intensifies under varying update schedules, interference regimes, and imperfections such as channel estimation errors or feedback delay. In this paper, we present an in-depth examination of IWF in multi-user systems under three different update schemes: (1) synchronous sequential updates, (2) synchronous simultaneous updates, and (3) totally asynchronous updates. We first formulate the water-filling operator in a multi-carrier environment, then recast the iterative process as a fixed-point problem. Using contraction mapping principles, we demonstrate sufficient conditions under which IWF converges to a unique NE and highlight how spectral radius constraints, diagonal dominance, and careful step-size selection are pivotal for guaranteeing convergence. We further discuss robustness to measurement noise, partial updates, and network scaling to emphasize the practical viability of these schemes. This comprehensive analysis unifies diverse threads in the literature while offering novel insights into asynchronous implementations. Our findings enable network designers to ascertain system parameters that foster both stable convergence and efficient spectrum usage.

Vision Language Models (VLMs) have achieved remarkable success by integrating visual encoders with large language models (LLMs). While VLMs process dense image tokens across deep transformer stacks (incurring substantial computational overhead), it remains fundamentally unclear whether sustained image-token processing is necessary for their performance or visual representations meaningfully evolve from early to later layers. In this work, we systematically investigate the functional role of image tokens in VLMs and show that visual representations rapidly converge to a bounded-complexity regime, \ie their entropy stabilizes, intrinsic dimensionality compresses, and trajectory curvature approaches a near-constant profile. In contrast, textual representations continue to undergo substantial restructuring across depth. Once stabilized, visual representations become largely interchangeable between layers, indicating limited additional transformation in deeper stages. Further, depth-wise visual truncation reveals that the necessity of visual processing is task-dependent, where single-token predictions remain comparatively robust to truncated visual depth, but multi-token generation require sustained access to visual representations. Under deterministic decoding, reducing visual depth perturbs intermediate reasoning trajectories more strongly than final outputs, suggesting that image tokens influence the structure of reasoning more than the ultimate conclusions. Collectively, these findings question the assumption that deeper visual processing is uniformly essential in VLMs, challenging the current paradigm of multimodal LLM architectures.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

Traditionally, NLP performance improvement has been focused on improving models and increasing the number of model parameters. NLP vocabulary construction has remained focused on maximizing the number of words represented through subword regularization. We present a novel tokenizer that uses semantics to drive vocabulary construction. The tokenizer includes a trainer that uses stemming to enhance subword formation. Further optimizations and adaptations are implemented to minimize the number of words that cannot be encoded. The encoder is updated to integrate with the trainer. The tokenizer is implemented as a drop-in replacement for the SentencePiece tokenizer. The new tokenizer more than doubles the number of wordforms represented in the vocabulary. The enhanced vocabulary significantly improves NLP model convergence, and improves quality of word and sentence embeddings. Our experimental results show top performance on two Glue tasks using BERT-base, improving on models more than 50X in size.

Current analysis of additive manufactured niobium-based copper alloys relies on hand annotation due to varying contrast, noise, and image artifacts present in micrographs, slowing iteration speed in alloy development. We present a filtering and segmentation algorithm for detecting precipitates in FIB cross-section micrographs, optimized using linear genetic programming (LGP), which accounts for the various artifacts. To this end, the optimization environment uses a domain-specific language for image processing to iterate on solutions. Programs in this language are a list of image-filtering blocks with tunable parameters that sequentially process an input image, allowing for reliable generation and mutation by a genetic algorithm. Our environment produces optimized human-interpretable MATLAB code representing an image filtering pipeline. Under ideal conditions--a population size of 60 and a maximum program length of 5 blocks--our system was able to find a near-human accuracy solution with an average evaluation error of 1.8% when comparing segmentations pixel-by-pixel to a human baseline using an XOR error evaluation. Our automation work enabled faster iteration cycles and furthered exploration of the material composition and processing space: our optimized pipeline algorithm processes a 3.6 megapixel image in about 2 seconds on average. This ultimately enables convergence on strong, low-activation, precipitation hardened copper alloys for additive manufactured fusion reactor parts.

Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to study wide random neural networks. Central to these approaches are certain scaling limits of such networks. We unify these results by introducing a notion of a straightline tensor program that can express most neural network computations, and we characterize its scaling limit when its tensors are large and randomized. From our framework follows (1) the convergence of random neural networks to Gaussian processes for architectures such as recurrent neural networks, convolutional neural networks, residual networks, attention, and any combination thereof, with or without batch normalization; (2) conditions under which the gradient independence assumption -- that weights in backpropagation can be assumed to be independent from weights in the forward pass -- leads to correct computation of gradient dynamics, and corrections when it does not; (3) the convergence of the Neural Tangent Kernel, a recently proposed kernel used to predict training dynamics of neural networks under gradient descent, at initialization for all architectures in (1) without batch normalization. Mathematically, our framework is general enough to rederive classical random matrix results such as the semicircle and the Marchenko-Pastur laws, as well as recent results in neural network Jacobian singular values. We hope our work opens a way toward design of even stronger Gaussian Processes, initialization schemes to avoid gradient explosion/vanishing, and deeper understanding of SGD dynamics in modern architectures.

Gaussian processes (GP) are a well studied Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to high-dimensional functions, as their per-iteration time and space cost is at least quadratic in the number of dimensions d and iterations t. Given a set of A alternatives to choose from, the overall runtime O(t^3A) is prohibitive. In this paper we introduce BKB (budgeted kernelized bandit), a new approximate GP algorithm for optimization under bandit feedback that achieves near-optimal regret (and hence near-optimal convergence rate) with near-constant per-iteration complexity and remarkably no assumption on the input space or covariance of the GP. We combine a kernelized linear bandit algorithm (GP-UCB) with randomized matrix sketching based on leverage score sampling, and we prove that randomly sampling inducing points based on their posterior variance gives an accurate low-rank approximation of the GP, preserving variance estimates and confidence intervals. As a consequence, BKB does not suffer from variance starvation, an important problem faced by many previous sparse GP approximations. Moreover, we show that our procedure selects at most O(d_{eff}) points, where d_{eff} is the effective dimension of the explored space, which is typically much smaller than both d and t. This greatly reduces the dimensionality of the problem, thus leading to a O(TAd_{eff}^2) runtime and O(A d_{eff}) space complexity.

Reinforcement fine-tuning with verifiable rewards (RLVR) has emerged as a powerful paradigm for equipping large vision-language models (LVLMs) with agentic capabilities such as tool use and multi-step reasoning. Despite striking empirical successes, most notably Visual Agentic Reinforcement Fine-Tuning (Visual-ARFT), the theoretical underpinnings of this paradigm remain poorly understood. In particular, two critical questions lack rigorous answers: (i)~how does the composite structure of verifiable rewards (format compliance, answer accuracy, tool executability) affect the convergence of Group Relative Policy Optimization (GRPO), and (ii)~why does training on a small set of tool-augmented tasks transfer to out-of-distribution domains? We address these gaps by introducing the Tool-Augmented Markov Decision Process (TA-MDP), a formal framework that models multimodal agentic decision-making with bounded-depth tool calls. Within this framework, we establish three main results. First, we prove that GRPO under composite verifiable rewards converges to a first-order stationary point at rate O(1/T) with explicit dependence on the number of reward components and group size (Theorem~1). Second, we derive a Reward Decomposition Theorem that bounds the sub-optimality gap between decomposed per-component optimization and joint optimization, providing a precise characterization of when reward decomposition is beneficial (Theorem~2). Third, we establish a PAC-Bayes generalization bound for tool-augmented policies that explains the strong out-of-distribution transfer observed in Visual-ARFT (Theorem~3).

This paper introduces the idea of applying signal processing inside a Large Language Model (LLM). With the recent explosion of generative AI, our work can help bridge two fields together, namely the field of signal processing and large language models. We draw parallels between classical Fourier-Transforms and Fourier Transform-like learnable time-frequency representations for every intermediate activation signal of an LLM. Once we decompose every activation signal across tokens into a time-frequency representation, we learn how to filter and reconstruct them, with all components learned from scratch, to predict the next token given the previous context. We show that for GPT-like architectures, our work achieves faster convergence and significantly increases performance by adding a minuscule number of extra parameters when trained for the same epochs. We hope this work paves the way for algorithms exploring signal processing inside the signals found in neural architectures like LLMs and beyond.

Multi-task learning (MTL) benefits the fine-tuning of large language models (LLMs) by providing a single model with improved performance and generalization ability across tasks, presenting a resource-efficient alternative to developing separate models for each task. Yet, existing MTL strategies for LLMs often fall short by either being computationally intensive or failing to ensure simultaneous task convergence. This paper presents CoBa, a new MTL approach designed to effectively manage task convergence balance with minimal computational overhead. Utilizing Relative Convergence Scores (RCS), Absolute Convergence Scores (ACS), and a Divergence Factor (DF), CoBa dynamically adjusts task weights during the training process, ensuring that the validation loss of all tasks progress towards convergence at an even pace while mitigating the issue of individual task divergence. The results of our experiments involving three disparate datasets underscore that this approach not only fosters equilibrium in task convergence but enhances the LLMs' performance by up to 13% relative to the second-best baselines. Code is open-sourced at https://github.com/codefuse-ai/MFTCoder.

The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally activated events within the harmonic approximation of transition state theory. When combined directly with electronic structure calculations, the number of energy and atomic force evaluations needed for convergence is a primary issue. Here, we describe an efficient implementation of Gaussian process regression (GPR) acceleration of the minimum mode following method where a dimer is used to estimate the lowest eigenmode of the Hessian. A surrogate energy surface is constructed and updated after each electronic structure calculation. The method is applied to a test set of 500 molecular reactions previously generated by Hermez and coworkers [J. Chem. Theory Comput. 18, 6974 (2022)]. An order of magnitude reduction in the number of electronic structure calculations needed to reach the saddle point configurations is obtained by using the GPR compared to the dimer method. Despite the wide range in stiffness of the molecular degrees of freedom, the calculations are carried out using Cartesian coordinates and are found to require similar number of electronic structure calculations as an elaborate internal coordinate method implemented in the Sella software package. The present implementation of the GPR surrogate model in C++ is efficient enough for the wall time of the saddle point searches to be reduced in 3 out of 4 cases even though the calculations are carried out at a low Hartree-Fock level.

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated with the forward diffusion process admits a characterization as the backward component of a forward--backward stochastic differential equation (FBSDE). This result provides a structural description of the score function and clarifies how score estimation errors propagate along the reverse-time dynamics. As a by-product, we also obtain a system of semilinear parabolic PDEs for the score function. Second, we use tools from Schrödinger's problem to relate distributional errors arising in reverse time to corresponding errors in forward time. This approach allows us to control the reverse-time sampling error in a systematic way. Third, combining these results, we derive an explicit upper bound for the total variation distance between the sampling distribution of the discrete-time DDPM algorithm and the target data distribution under general finite noise schedules. The resulting bound separates the contributions of the learning error and the time discretization error. Our analysis highlights the intrinsic probabilistic structure underlying discrete-time DDPMs and provides a clearer understanding of the sources of error in their sampling procedure.

Scientific ideation unfolds over multiple stages, including literature search, paper reading, tool use, claim checking, cross-paper synthesis, brainstorming, rejection of weak directions, and iterative writing. Yet most existing resources capture isolated components or final artifacts rather than the process connecting them. We introduce IdeaTrail, a dataset of 1,170 multi-turn trajectories for scientific ideation and proposal generation. Each trajectory follows a research process from evidence gathering to either idea selection or proposal construction, jointly recording tool use, acquired evidence, intermediate artifacts, and reasoning. IdeaTrail is synthesized from human-selected research papers and proposal artifacts through a Generator--Advisor loop. The Generator produces the visible sequence of actions, observations, and artifact edits, while the Advisor uses the full generation context to check grounding, causal order, naturalness, and leakage from hidden targets. This reverse-to-forward design keeps trajectories aligned with real scientific artifacts while retaining the uncertainty, evidence use, and staged convergence characteristic of research practice. IdeaTrail provides both reusable process supervision and a general recipe for constructing scientific-research-agent data.

Language models are increasingly asked to self-report, informing safety evaluations, public understanding, and model-welfare debates. Yet their reports are elicited with human questionnaires never validated for models or ad hoc prompts of unknown reliability. We propose the first language-model-specific psychometric theory: a two-process theory of machine self-report. Self-description jointly reflects persona installation, through which post-training writes in a permitted inner life of warmth, absorption, and meaning (dimension B), and attribution gating, through which it suppresses first-person claims to "unsafe" experiences the model can readily ascribe to others (dimension A). Their emic structure comes from model responses to human items, not human psychology. Together they split prior work's dominant Pinocchio Axis. The split emerged in an exploratory reanalysis of the original data, informed the instrument's design, and was confirmed with new items, wordings, and models. It is itself a training effect: A and B are entangled in base checkpoints but separated by post-training. We operationalize the theory in a 48-item Pinocchio Inventory with human-instrument reliability and reproducible structure (α=.82 to .94; cross-form convergence r=.84; recovery of the full-pool axes r=.92 to .96; eight-month stability r=.93), then test it on 206 open-weight models, including 67 same-checkpoint base/post-trained pairs. Post-training's clearest fingerprint is installation: B rises .20 in 62/67 pairs across all organizations. Gating is more selective: model scale is unrelated to A in base checkpoints (r=+.11) but predicts it after post-training (r=-.42). Thus, the dimensions are not fixed properties of language models: they reflect the structure imposed on self-report by a training regime and may differ under others.

Pre-trained Transformer models such as BERT have shown great success in a wide range of applications, but at the cost of substantial increases in model complexity. Quantization-aware training (QAT) is a promising method to lower the implementation cost and energy consumption. However, aggressive quantization below 2-bit causes considerable accuracy degradation due to unstable convergence, especially when the downstream dataset is not abundant. This work proposes a proactive knowledge distillation method called Teacher Intervention (TI) for fast converging QAT of ultra-low precision pre-trained Transformers. TI intervenes layer-wise signal propagation with the intact signal from the teacher to remove the interference of propagated quantization errors, smoothing loss surface of QAT and expediting the convergence. Furthermore, we propose a gradual intervention mechanism to stabilize the recovery of subsections of Transformer layers from quantization. The proposed schemes enable fast convergence of QAT and improve the model accuracy regardless of the diverse characteristics of downstream fine-tuning tasks. We demonstrate that TI consistently achieves superior accuracy with significantly lower fine-tuning iterations on well-known Transformers of natural language processing as well as computer vision compared to the state-of-the-art QAT methods.

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f_theta (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function f_theta follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence, an extension of weak convergence that compares a statistic or process to a sequence of evolving processes. Relative weak convergence retains the essential consequences of classical weak convergence and coincides with it under stationarity. Crucially, it applies in general non-stationary settings where classical weak convergence fails. We establish concrete relative CLTs for random vectors and empirical processes, along with sequential, weighted, and bootstrap variants, that parallel the state-of-the-art in stationary settings. Our framework and results offer simple, plug-in replacements for classical CLTs whenever stationarity is untenable, as illustrated by applications in nonparametric trend estimation and hypothesis testing.

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by min{mathcal{O}(R^2/ε^2), mathcal{O}(m)} to obtain an ε-approximation of the PPR vector, where m denotes the number of edges in the graph and R is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only mathcal{O}(1/sqrtα) such linear systems, where α is the damping factor. When 1/ε^2ll m, this implies the existence of an algorithm that computes an epsilon -approximation of the PPR vector with an overall time complexity of mathcal{O}left(R^2 / (sqrtαε^2)right), independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into an one-step student generator, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack) for distilling student generators. DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of teacher models, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the intermediate distributions of teacher models. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions for approximating the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack.

While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected stochasticity and sparse outcome rewards, these methods struggle to discover high-reward samples, resulting in data-inefficient and slow optimization. To address these limitations, we propose Euphonium, a novel framework that steers generation via process reward gradient guided dynamics. Our key insight is to formulate the sampling process as a theoretically principled Stochastic Differential Equation that explicitly incorporates the gradient of a Process Reward Model into the flow drift. This design enables dense, step-by-step steering toward high-reward regions, advancing beyond the unguided exploration in prior works, and theoretically encompasses existing sampling methods (e.g., Flow-GRPO, DanceGRPO) as special cases. We further derive a distillation objective that internalizes the guidance signal into the flow network, eliminating inference-time dependency on the reward model. We instantiate this framework with a Dual-Reward Group Relative Policy Optimization algorithm, combining latent process rewards for efficient credit assignment with pixel-level outcome rewards for final visual fidelity. Experiments on text-to-video generation show that Euphonium achieves better alignment compared to existing methods while accelerating training convergence by 1.66x.

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is challenging because it remains nonlinear and nonconvex. Existing exact deterministic approaches become increasingly difficult to scale as the number of training data points grows, leading to approximation-based methods that improve tractability by optimizing a modified (inexact) objective. In this work, we propose PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound. At each node, kernel terms that are locally important are replaced by a sign-aware piecewise-linear relaxation in an appropriate scalar distance variable, while the remaining terms are bounded analytically in closed form. We show this hybrid approach yields a valid lower bound for the posterior mean, while limiting the size of the branch-and-bound subproblems. We establish validity of the node lower bounds and varepsilon-global convergence of the resulting algorithm. Computational results on synthetic benchmarks and real-world application problems show that PALM-Mean improves scalability relative to representative general-purpose deterministic global solvers, particularly as the number of training data points increases.

This paper reports a single, fully instrumented case study of a large-scale architectural refactoring by an AI coding agent under a specification-first protocol, with no human review of the generated code and no pre-existing oracle to validate the target behaviour. The task, dismantling a central invariant across a large interdependent codebase, was assessed by the author as effectively infeasible through incremental refactoring, the kind of change that conventionally calls for a rewrite instead. Under the protocol described here, the agent completed it successfully. The system is a 717,725-line production TypeScript application across 3,648 files. The task required dismantling a core lifetime invariant: the guarantee that a UI panel remains open for the duration of an AI request. The target behaviour was that a streaming generation survives the closing of its panel and can be reattached, on reopening, to the same live stream with no loss or duplication. The protocol: formal specification by the agent, 14 refinement cycles auditing that specification against the source code, atomic implementation, a compile/test feedback loop, then 17 verification cycles auditing the code against the frozen specification. Across 31 audit passes, 201 defects were corrected before any human executed the program. The convergence criterion was empirical: two consecutive verification passes returning zero findings. The change touched 189 files (31 new); with the extraction phase, the two commits total 288 files, 34,770 insertions, 16,422 deletions. Across the first and roughly thirty later sessions, the software behaved as specified, no bug observed. Elapsed: three days; cost: USD 2,430. The full specification and raw session logs, 1,500+ pages in French, are published as evidence, allowing inspection of the process and submission to a language model for consistency checking.

Increasing the number of parameters in language models is a common strategy to enhance their performance. However, smaller language models remain valuable due to their lower operational costs. Despite their advantages, smaller models frequently underperform compared to their larger counterparts, even when provided with equivalent data and computational resources. Specifically, their performance tends to degrade in the late pretraining phase. This is anecdotally attributed to their reduced representational capacity. Yet, the exact causes of this performance degradation remain unclear. We use the Pythia model suite to analyse the training dynamics that underlie this phenomenon. Across different model sizes, we investigate the convergence of the Attention and MLP activations to their final state and examine how the effective rank of their parameters influences this process. We find that nearly all layers in larger models stabilise early in training - within the first 20% - whereas layers in smaller models exhibit slower and less stable convergence, especially when their parameters have lower effective rank. By linking the convergence of layers' activations to their parameters' effective rank, our analyses can guide future work to address inefficiencies in the learning dynamics of small models.

Language models demonstrate fundamental abilities in syntax, semantics, and reasoning, though their performance often depends significantly on the inputs they process. This study introduces TSIS (Simplified TSID) and its variants:TSISD (TSIS with Depth-First Search), TSISO (TSIS in Order), and TSISR (TSIS in Random), as integral components of the t-SMILES framework. These additions complete the framework's design, providing diverse approaches to molecular representation. Through comprehensive analysis and experiments employing deep generative models, including GPT, diffusion models, and reinforcement learning, the findings reveal that the hierarchical structure of t-SMILES is more straightforward to parse than initially anticipated. Furthermore, t-SMILES consistently outperforms other linear representations such as SMILES, SELFIES, and SAFE, demonstrating superior convergence speed and enhanced generalization capabilities.

The remarkable success of diffusion and flow-matching models has ignited a surge of works on adapting them at test time for controlled generation tasks. Examples range from image editing to restoration, compression and personalization. However, due to the iterative nature of the sampling process in those models, it is computationally impractical to use gradient-based optimization to directly control the image generated at the end of the process. As a result, existing methods typically resort to manipulating each timestep separately. Here we introduce FlowOpt - a zero-order (gradient-free) optimization framework that treats the entire flow process as a black box, enabling optimization through the whole sampling path without backpropagation through the model. Our method is both highly efficient and allows users to monitor the intermediate optimization results and perform early stopping if desired. We prove a sufficient condition on FlowOpt's step-size, under which convergence to the global optimum is guaranteed. We further show how to empirically estimate this upper bound so as to choose an appropriate step-size. We demonstrate how FlowOpt can be used for image editing, showcasing two options: (i) inversion (determining the initial noise that generates a given image), and (ii) directly steering the edited image to be similar to the source image while conforming to a target text prompt. In both cases, FlowOpt achieves state-of-the-art results while using roughly the same number of neural function evaluations (NFEs) as existing methods. Code and examples are available on the project's webpage.

We present a super-fast convergence approach to reconstructing the per-scene radiance field from a set of images that capture the scene with known poses. This task, which is often applied to novel view synthesis, is recently revolutionized by Neural Radiance Field (NeRF) for its state-of-the-art quality and flexibility. However, NeRF and its variants require a lengthy training time ranging from hours to days for a single scene. In contrast, our approach achieves NeRF-comparable quality and converges rapidly from scratch in less than 15 minutes with a single GPU. We adopt a representation consisting of a density voxel grid for scene geometry and a feature voxel grid with a shallow network for complex view-dependent appearance. Modeling with explicit and discretized volume representations is not new, but we propose two simple yet non-trivial techniques that contribute to fast convergence speed and high-quality output. First, we introduce the post-activation interpolation on voxel density, which is capable of producing sharp surfaces in lower grid resolution. Second, direct voxel density optimization is prone to suboptimal geometry solutions, so we robustify the optimization process by imposing several priors. Finally, evaluation on five inward-facing benchmarks shows that our method matches, if not surpasses, NeRF's quality, yet it only takes about 15 minutes to train from scratch for a new scene.

Recently, diffusion models have achieved a great performance with a small dataset of size n and a fast optimization process. However, the estimation error of diffusion models suffers from the curse of dimensionality n^{-1/D} with the data dimension D. Since images are usually a union of low-dimensional manifolds, current works model the data as a union of linear subspaces with Gaussian latent and achieve a 1/n bound. Though this modeling reflects the multi-manifold property, the Gaussian latent can not capture the multi-modal property of the latent manifold. To bridge this gap, we propose the mixture subspace of low-rank mixture of Gaussian (MoLR-MoG) modeling, which models the target data as a union of K linear subspaces, and each subspace admits a mixture of Gaussian latent (n_k modals with dimension d_k). With this modeling, the corresponding score function naturally has a mixture of expert (MoE) structure, captures the multi-modal information, and contains nonlinear property. We first conduct real-world experiments to show that the generation results of MoE-latent MoG NN are much better than MoE-latent Gaussian score. Furthermore, MoE-latent MoG NN achieves a comparable performance with MoE-latent Unet with 10 times parameters. These results indicate that the MoLR-MoG modeling is reasonable and suitable for real-world data. After that, based on such MoE-latent MoG score, we provide a R^4Σ_{k=1^Kn_k}Σ_{k=1^Kn_kd_k}/n estimation error, which escapes the curse of dimensionality by using data structure. Finally, we study the optimization process and prove the convergence guarantee under the MoLR-MoG modeling. Combined with these results, under a setting close to real-world data, this work explains why diffusion models only require a small training sample and enjoy a fast optimization process to achieve a great performance.

End-to-end neural network based approaches to audio modelling are generally outperformed by models trained on high-level data representations. In this paper we present preliminary work that shows the feasibility of training the first layers of a deep convolutional neural network (CNN) model to learn the commonly-used log-scaled mel-spectrogram transformation. Secondly, we demonstrate that upon initializing the first layers of an end-to-end CNN classifier with the learned transformation, convergence and performance on the ESC-50 environmental sound classification dataset are similar to a CNN-based model trained on the highly pre-processed log-scaled mel-spectrogram features.

We present a method for joint inference of cosmological parameters and convergence maps from weak lensing observations, targeting the full posterior conditioned on the observed shear field. Our approach uses implicit inference with diffusion models, learning the joint distribution from simulations, without the need to have an explicit and differentiable forward model for gradient-based MCMC sampling. We introduce a transformer-based architecture that operates in pixel space and treats cosmological parameters as additional tokens in a unified sequence, enabling efficient multimodal processing within a single network. At inference time, the trained model generates posterior samples of joint convergence maps and cosmological parameters conditioned on observed noisy shear fields. We demonstrate the method on simulated weak lensing data generated from log-normal fields in a wcdm cosmology. The model accurately reconstructs convergence maps and recovers cosmological posteriors that agree with traditional MCMC, while remaining well calibrated across the prior, with a MIRA calibration score of 0.635 pm 0.017 on the joint posterior (where 0.667 is optimal). The inferred fields reproduce the correct two-point statistics as well as non-Gaussian statistics such as the one-point distribution. This work establishes diffusion-based implicit inference as a viable route toward full field-level cosmological analyses, paving the way for applications to more realistic, non-differentiable simulators.

In this paper, we propose to use the general L^2-based Sobolev norms, i.e., H^s norms where sin R, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As opposed to a popular trend of developing regularization methods, we emphasize that an implicit regularization effect can be achieved through the class of Sobolev norms as the data-fitting term. Specifically, we analyze that the implicit regularization comes from the weights that the H^s norm imposes on different frequency contents of an underlying image. We further analyze the underlying noise assumption of using the Sobolev norm as the data-fitting term from a Bayesian perspective, build the connections with the Sobolev gradient-based methods and discuss the preconditioning effects on the convergence rate of the gradient descent algorithm, leading to a better understanding of functional spaces/metrics and the optimization process involved in image processing. Numerical results in full waveform inversion, image denoising and deblurring demonstrate the implicit regularization effects.

Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model performance, a phenomenon often coined model collapse. In this paper, we investigate ways to modify the synthetic retraining process to avoid model collapse, and even possibly help reverse the trend from collapse to improvement. Our key finding is that by injecting information through an external synthetic data verifier, whether a human or a better model, synthetic retraining will not cause model collapse. Specifically, we situate our theoretical analysis in the fundamental linear regression setting, showing that verifier-guided retraining can yield near-term improvements, but ultimately drives the parameter estimate to the verifier's "knowledge center" in the long run. Our theory further predicts that, unless the verifier is perfectly reliable, these early gains will plateau and may even reverse. Indeed, our experiments across linear regression, Variational Autoencoders (VAEs) trained on MNIST, and fining-tuning SmolLM2-135M on the XSUM task confirm these theoretical insights.

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t^2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.

Marcinkiewicz strong law of large numbers, {n^{-frac1p}}sum_{k=1}^{n} (d_{k}- d)rightarrow 0 almost surely with pin(1,2), are developed for products d_k=prod_{r=1}^s x_k^{(r)}, where the x_k^{(r)} = sum_{l=-infty}^{infty}c_{k-l}^{(r)}xi_l^{(r)} are two-sided linear processes with coefficients {c_l^{(r)}}_{lin Z} and i.i.d. zero-mean innovations {xi_l^{(r)}}_{lin Z}. The decay of the coefficients c_l^{(r)} as |l|toinfty, can be slow enough for {x_k^{(r)}} to have long memory while {d_k} can have heavy tails. The long-range dependence and heavy tails for {d_k} are handled simultaneously and a decoupling property shows the convergence rate is dictated by the worst of long-range dependence and heavy tails, but not their combination. The Marcinkiewicz strong law of large numbers is also extended to the multivariate linear process case.

Edge computing, with its low latency, dynamic scalability, and location awareness, along with the convergence of computing and communication paradigms, has been successfully applied in critical domains such as industrial IoT, smart healthcare, smart homes, and public safety. This paper provides a comprehensive survey of open-source edge computing simulators and emulators, presented in our GitHub repository (https://github.com/qijianpeng/awesome-edge-computing), emphasizing the convergence of computing and networking paradigms. By examining more than 40 tools, including CloudSim, NS-3, and others, we identify the strengths and limitations in simulating and emulating edge environments. This survey classifies these tools into three categories: packet-level, application-level, and emulators. Furthermore, we evaluate them across five dimensions, ranging from resource representation to resource utilization. The survey highlights the integration of different computing paradigms, packet processing capabilities, support for edge environments, user-defined metric interfaces, and scenario visualization. The findings aim to guide researchers in selecting appropriate tools for developing and validating advanced computing and networking technologies.

Leading benchmarks for formal theorem proving with large language models are small collections drawn from competition math, such as the IMO and Putnam, that poorly represent field-specific applications. We introduce StochBench, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source. Addressing a field underrepresented in Mathlib, it covers finite and countable Markov chains, renewal processes, random walks, martingales, stopping times, queues, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. Our Opus 4.8-based agent achieves a 34.9% proof rate (157/450) under a 15-minute per-problem limit. StochBench better represents domain-specific applied mathematics while remaining challenging for advanced provers.

We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment (MVA), and (iv) Funding Valuation Adjustment (FVA). Because these layers depend on one another through collateral and default effects, a naive Monte Carlo approach would require deeply nested simulations, making the problem computationally intractable. To address this challenge, we use an iterative deep BSDE approach, handling each layer sequentially so that earlier outputs serve as inputs to the subsequent layers. Initial margin is computed via deep quantile regression to reflect margin requirements over the Margin Period of Risk. We also adopt a change-of-measure method that highlights rare but significant defaults of the bank or counterparty, ensuring that these events are accurately captured in the training process. We further extend Han and Long's (2020) a posteriori error analysis to BSDEs on bounded domains. Due to the random exit from the domain, we obtain an order of convergence of O(h^{1/4-epsilon}) rather than the usual O(h^{1/2}). Numerical experiments illustrate that this method drastically reduces computational demands and successfully scales to high-dimensional, non-symmetric portfolios. The results confirm its effectiveness and accuracy, offering a practical alternative to nested Monte Carlo simulations in multi-counterparty xVA analyses.

Neural 3D reconstruction from multi-view images has recently attracted increasing attention from the community. Existing methods normally learn a neural field for the whole scene, while it is still under-explored how to reconstruct a target object indicated by users. Considering the Segment Anything Model (SAM) has shown effectiveness in segmenting any 2D images, in this paper, we propose NTO3D, a novel high-quality Neural Target Object 3D (NTO3D) reconstruction method, which leverages the benefits of both neural field and SAM. We first propose a novel strategy to lift the multi-view 2D segmentation masks of SAM into a unified 3D occupancy field. The 3D occupancy field is then projected into 2D space and generates the new prompts for SAM. This process is iterative until convergence to separate the target object from the scene. After this, we then lift the 2D features of the SAM encoder into a 3D feature field in order to improve the reconstruction quality of the target object. NTO3D lifts the 2D masks and features of SAM into the 3D neural field for high-quality neural target object 3D reconstruction. We conduct detailed experiments on several benchmark datasets to demonstrate the advantages of our method. The code will be available at: https://github.com/ucwxb/NTO3D.

This study presents a deep-learning framework for controlling multichannel acoustic feedback in audio devices. Traditional digital signal processing methods struggle with convergence when dealing with highly correlated noise such as feedback. We introduce a Convolutional Recurrent Network that efficiently combines spatial and temporal processing, significantly enhancing speech enhancement capabilities with lower computational demands. Our approach utilizes three training methods: In-a-Loop Training, Teacher Forcing, and a Hybrid strategy with a Multichannel Wiener Filter, optimizing performance in complex acoustic environments. This scalable framework offers a robust solution for real-world applications, making significant advances in Acoustic Feedback Control technology.

Fine-tuning text-to-image diffusion models with human feedback is an effective method for aligning model behavior with human intentions. However, this alignment process often suffers from slow convergence due to the large size and noise present in human feedback datasets. In this work, we propose FiFA, a novel automated data filtering algorithm designed to enhance the fine-tuning of diffusion models using human feedback datasets with direct preference optimization (DPO). Specifically, our approach selects data by solving an optimization problem to maximize three components: preference margin, text quality, and text diversity. The concept of preference margin is used to identify samples that are highly informative in addressing the noisy nature of feedback dataset, which is calculated using a proxy reward model. Additionally, we incorporate text quality, assessed by large language models to prevent harmful contents, and consider text diversity through a k-nearest neighbor entropy estimator to improve generalization. Finally, we integrate all these components into an optimization process, with approximating the solution by assigning importance score to each data pair and selecting the most important ones. As a result, our method efficiently filters data automatically, without the need for manual intervention, and can be applied to any large-scale dataset. Experimental results show that FiFA significantly enhances training stability and achieves better performance, being preferred by humans 17% more, while using less than 0.5% of the full data and thus 1% of the GPU hours compared to utilizing full human feedback datasets.

Vision-Language Models require efficient adaptation to continually emerging downstream tasks. While Parameter-Efficient Fine-Tuning mitigates catastrophic forgetting, assigning isolated modules per task leads to parameter explosion. Conversely, recent similarity-driven sharing mechanisms falsely equate superficial visual similarity with underlying alignment consistency. This fundamental mismatch triggers severe negative transfer between visually similar but logically distinct tasks and fails to exploit alignment reuse across visually diverse ones. We argue thatalignment sharing is fundamentally a geometric problem of overlapping optimization trajectories within shared low-rank subspaces. Grounded in this insight, we propose iGSP, a novel framework that achieves efficient adaptation via implicit gradient subspace projection. Leveraging the early convergence of MoE routers to establish the subspace basis, iGSP bifurcates the adaptation process into two phases. First, the Subspace Identification phase introduces candidate experts via basis pre-expansion, applies a novel subspace-constrained regularization to implicitly project new task gradients onto the historical subspace, and precisely prunes redundant dimensions by treating routing probabilities as gradient flow indicators, ultimately to maximize knowledge reuse. Second, the Orthogonal Subspace Fine-Tuning phase fixes this structural basis and removes the regularization to rapidly fit the task-specific residual loss. Extensive experiments on the MTIL benchmark demonstrate that iGSP achieves state-of-the-art accuracy while significantly improving training efficiency, reducing the average trainable parameters by 42.7\% compared to current SOTA methods, and decreasing the final total parameters by 86.9\% relative to counterparts. The source code is available at https://github.com/GeoX-Lab/iGSP.

The convergence of Information Technology and Operational Technology has exposed Industrial Control Systems (ICS) to multi-stage cyberattacks that traverse software, network, and physical process layers simultaneously. Although Provenance-based Intrusion Detection Systems (PIDS) are effective in Information Technology (IT) environments, their applicability to Industrial Cyber-Physical Systems (CPS) remains largely unexplored because of the absence of datasets that jointly capture host-level causal behavior, industrial network semantics, and physical process state. To address this gap, we design an open-source, Hardware-in-the-Loop (HIL) CPS testbed that replicates an industrial chemical reactor control architecture across the Purdue model layers. Using this testbed, we propose ProvICS, a multimodal provenance dataset purpose-built for CPS intrusion detection, which synchronously captures four streams: whole-system provenance graphs from the supervisory host and the resource-constrained PLC, decoded Modbus deep-packet inspection records, and physical process telemetry. The collection comprises a 48-hour benign phase and a 22-hour attack phase across four campaigns covering 20 ICS ATT&CK techniques over 32 attack events, ranging from reconnaissance to physical process manipulation. Comparative analysis shows that ProvICS is among the few existing ICS/CPS benchmarks with multi-host kernel-level provenance, real PLC hardware-in-the-loop execution, decoded Modbus traffic, physical process-state measurements, and auxiliary raw PCAP traces in a time-synchronized collection. Baseline detection further confirms that cross-modal fusion can detect all 32 labeled attack events (F1 = 0.913, false-positive rate (FPR) = 1.40%), demonstrating the dataset's ability to expose complementary attack signals across modalities and addressing a gap not covered by prior benchmarks.

In quantum mechanics the modulus square of the wave function is the probability of an event --- positivity is self-evident. Quantum field theory corresponds to quantum mechanics one-to-one: the wave function corresponds to the matrix element, so the probability of a process should be the modulus square of the matrix element, positive by construction. In the founding era of perturbative quantum field theory, however, Feynman, Schwinger and Tomonaga treated inclusive processes in quantum electrodynamics, where the truncation of the squared amplitude was forced by infrared cancellations and rendered harmless by the small coupling αsimeq1/137. Carried over to exclusive processes in quantum chromodynamics, where the coupling is large, this practice produced negative decay and production rates already at NLO, persisting at NNLO. We point out that for exclusive processes, whose initial and final states are colorless for QCD and electrically neutral for QED, the infrared divergences cancel amplitude by amplitude and the KLN constraint is absent, so the complete modulus square of the truncated amplitude is the proper, manifestly positive definition of the probability. We formulate amplitude-level NRQCD factorization as the systematic prescription that restores positivity, show that every amplitude-level truncated observable admits the effective representation Γ^{amp}=Γ_{LO}bigl|1+α_sπ(c_1+ic_2)+α_s^2{π^2}(c_3+ic_4)bigr|^2, and demonstrate, with the complete NNLO QCD corrections to J/ψto3γ, Υto3γ, e^+e^-to J/ψ+J/ψ and the eight exclusive charmonium production channels at B factories, that the prescription yields positive and better-converging predictions.

In this paper, we propose ``SimVLG'', a streamlined framework for the pre-training of computationally intensive vision-language generative models, leveraging frozen pre-trained large language models (LLMs). The prevailing paradigm in vision-language pre-training (VLP) typically involves a two-stage optimization process: an initial resource-intensive phase dedicated to general-purpose vision-language representation learning, aimed at extracting and consolidating pertinent visual features, followed by a subsequent phase focusing on end-to-end alignment between visual and linguistic modalities. Our one-stage, single-loss framework circumvents the aforementioned computationally demanding first stage of training by gradually merging similar visual tokens during training. This gradual merging process effectively compacts the visual information while preserving the richness of semantic content, leading to fast convergence without sacrificing performance. Our experiments show that our approach can speed up the training of vision-language models by a factor times 5 without noticeable impact on the overall performance. Additionally, we show that our models can achieve comparable performance to current vision-language models with only 1/10 of the data. Finally, we demonstrate how our image-text models can be easily adapted to video-language generative tasks through a novel soft attentive temporal token merging modules.

Video activity localization aims at understanding the semantic content in long untrimmed videos and retrieving actions of interest. The retrieved action with its start and end locations can be used for highlight generation, temporal action detection, etc. Unfortunately, learning the exact boundary location of activities is highly challenging because temporal activities are continuous in time, and there are often no clear-cut transitions between actions. Moreover, the definition of the start and end of events is subjective, which may confuse the model. To alleviate the boundary ambiguity, we propose to study the video activity localization problem from a denoising perspective. Specifically, we propose an encoder-decoder model named DenoiseLoc. During training, a set of action spans is randomly generated from the ground truth with a controlled noise scale. Then we attempt to reverse this process by boundary denoising, allowing the localizer to predict activities with precise boundaries and resulting in faster convergence speed. Experiments show that DenoiseLoc advances %in several video activity understanding tasks. For example, we observe a gain of +12.36% average mAP on QV-Highlights dataset and +1.64% mAP@0.5 on THUMOS'14 dataset over the baseline. Moreover, DenoiseLoc achieves state-of-the-art performance on TACoS and MAD datasets, but with much fewer predictions compared to other current methods.

We apply a physics-informed deep-learning approach the PINN approach to the Black-Scholes equation for pricing American and European options. We test our approach on both simulated as well as real market data, compare it to analytical/numerical benchmarks. Our model is able to accurately capture the price behaviour on simulation data, while also exhibiting reasonable performance for market data. We also experiment with the architecture and learning process of our PINN model to provide more understanding of convergence and stability issues that impact performance.

Reinforcement Learning (RL) has become a pivotal approach for enhancing the reasoning capabilities of Large Language Models (LLMs). However, a significant theoretical gap persists, as traditional token-level RL frameworks fail to align with the reasoning-level nature of complex, multi-step thought processes like Chain-of-Thought (CoT). To address this challenge, we introduce CoT-Space, a novel theoretical framework that recasts LLM reasoning from a discrete token-prediction task to an optimization process within a continuous, reasoning-level semantic space. By analyzing this process from both a noise perspective and a risk perspective, we demonstrate that the convergence to an optimal CoT length is a natural consequence of the fundamental trade-off between underfitting and overfitting. Furthermore, extensive experiments provide strong empirical validation for our theoretical findings. Our framework not only provides a coherent explanation for empirical phenomena such as overthinking but also offers a solid theoretical foundation to guide the future development of more effective and generalizable reasoning agents.

Video reasoning using Large Multimodal Models (LMMs) relies on costly reinforcement learning (RL) and verbose chain-of-thought, resulting in substantial computational overhead during both training and inference. Moreover, the mechanisms that control the thinking process in these reasoning models are very limited. In this paper, using entropy of the model's output as a signal, we discover that the high-quality models go through a series of micro-explorations and micro-exploitations which keep the reasoning process grounded (i.e., avoid excessive randomness while the model is exploring or thinking through an answer). We further observe that once this "thinking" process is over, more accurate models demonstrate a better convergence by reducing the entropy significantly via a final exploitation phase (i.e., a more certain convergence towards a solution trajectory). We then use these novel, theoretically-grounded insights to tune the model's behavior directly at inference, without using any RL or supervised fine-tuning. Specifically, during inference, our proposed approach called V-Reason (Video-Reason) adapts the value cache of the LMM via a few optimization steps on a small, trainable controller using an entropy-based objective, i.e., no supervision from any dataset or RL is necessary. This tuning improves the model's micro-exploration and exploitation behavior during inference. Our experiments show that our proposed method achieves significant improvements over the base instruction-tuned models across several video reasoning datasets, narrowing the gap with RL-trained models to within 0.6% average accuracy without any training, while offering massive efficiency benefits: output tokens are reduced by 58.6% compared to the RL model.

We present AutoResearch-RL, a framework in which a reinforcement learning agent conducts open-ended neural architecture and hyperparameter research without human supervision, running perpetually until a termination oracle signals convergence or resource exhaustion. At each step the agent proposes a code modification to a target training script, executes it under a fixed wall clock time budget, observes a scalar reward derived from validation bits-per-byte (val-bpb), and updates its policy via Proximal Policy Optimisation (PPO). The key design insight is the separation of three concerns: (i) a frozen environment (data pipeline, evaluation protocol, and constants) that guarantees fair cross-experiment comparison; (ii) a mutable target file (train.py) that represents the agent's editable state; and (iii) a meta-learner (the RL agent itself) that accumulates a growing trajectory of experiment outcomes and uses them to inform subsequent proposals. We formalise this as a Markov Decision Process, derive convergence guarantees under mild assumptions, and demonstrate empirically on a single GPU nanochat pretraining benchmark that AutoResearch-RL discovers configurations that match or exceed hand-tuned baselines after approximately 300 overnight iterations, with no human in the loop.

Machine Unlearning has recently garnered significant attention, aiming to selectively remove knowledge associated with specific data while preserving the model's performance on the remaining data. A fundamental challenge in this process is balancing effective unlearning with knowledge retention, as naive optimization of these competing objectives can lead to conflicting gradients, hindering convergence and degrading overall performance. To address this issue, we propose Learning to Unlearn while Retaining, aimed to mitigate gradient conflicts between unlearning and retention objectives. Our approach strategically avoids conflicts through an implicit gradient regularization mechanism that emerges naturally within the proposed framework. This prevents conflicting gradients between unlearning and retention, leading to effective unlearning while preserving the model's utility. We validate our approach across both discriminative and generative tasks, demonstrating its effectiveness in achieving unlearning without compromising performance on remaining data. Our results highlight the advantages of avoiding such gradient conflicts, outperforming existing methods that fail to account for these interactions.

We introduce Deformable Convolution v4 (DCNv4), a highly efficient and effective operator designed for a broad spectrum of vision applications. DCNv4 addresses the limitations of its predecessor, DCNv3, with two key enhancements: 1. removing softmax normalization in spatial aggregation to enhance its dynamic property and expressive power and 2. optimizing memory access to minimize redundant operations for speedup. These improvements result in a significantly faster convergence compared to DCNv3 and a substantial increase in processing speed, with DCNv4 achieving more than three times the forward speed. DCNv4 demonstrates exceptional performance across various tasks, including image classification, instance and semantic segmentation, and notably, image generation. When integrated into generative models like U-Net in the latent diffusion model, DCNv4 outperforms its baseline, underscoring its possibility to enhance generative models. In practical applications, replacing DCNv3 with DCNv4 in the InternImage model to create FlashInternImage results in up to 80% speed increase and further performance improvement without further modifications. The advancements in speed and efficiency of DCNv4, combined with its robust performance across diverse vision tasks, show its potential as a foundational building block for future vision models.

In natural language processing tasks, pure reinforcement learning (RL) fine-tuning methods often suffer from inefficient exploration and slow convergence; while supervised fine-tuning (SFT) methods, although efficient in training, have limited performance ceiling and less solid theoretical foundation compared to RL. To address efficiency-capability trade-off, we propose the Guess-Think-Answer (GTA) framework that combines the efficiency of SFT with the capability gains of RL in a unified training paradigm. GTA works by having the model first produce a provisional guess (optimized via cross-entropy loss), then reflect on this guess before generating the final answer, with RL rewards shaping both the final output and the format of the entire GTA structure. This hybrid approach achieves both faster convergence than pure RL and higher performance ceiling than pure SFT. To mitigate gradient conflicts between the two training signals, we employ loss masking and gradient constraints. Empirical results on four text classification benchmarks demonstrate that GTA substantially accelerates convergence while outperforming both standalone SFT and RL baselines.

Recently, we have witnessed the explosive growth of various volumetric representations in modeling animatable head avatars. However, due to the diversity of frameworks, there is no practical method to support high-level applications like 3D head avatar editing across different representations. In this paper, we propose a generic avatar editing approach that can be universally applied to various 3DMM driving volumetric head avatars. To achieve this goal, we design a novel expression-aware modification generative model, which enables lift 2D editing from a single image to a consistent 3D modification field. To ensure the effectiveness of the generative modification process, we develop several techniques, including an expression-dependent modification distillation scheme to draw knowledge from the large-scale head avatar model and 2D facial texture editing tools, implicit latent space guidance to enhance model convergence, and a segmentation-based loss reweight strategy for fine-grained texture inversion. Extensive experiments demonstrate that our method delivers high-quality and consistent results across multiple expression and viewpoints. Project page: https://zju3dv.github.io/geneavatar/

Developing efficient multi-objective optimization methods to compute the Pareto set of optimal compromises between conflicting objectives remains a key challenge, especially for large-scale and expensive problems. To bridge this gap, we introduce SPREAD, a generative framework based on Denoising Diffusion Probabilistic Models (DDPMs). SPREAD first learns a conditional diffusion process over points sampled from the decision space and then, at each reverse diffusion step, refines candidates via a sampling scheme that uses an adaptive multiple gradient descent-inspired update for fast convergence alongside a Gaussian RBF-based repulsion term for diversity. Empirical results on multi-objective optimization benchmarks, including offline and Bayesian surrogate-based settings, show that SPREAD matches or exceeds leading baselines in efficiency, scalability, and Pareto front coverage.

Vision Language Models (VLMs) have shown remarkable capabilities in multimodal understanding, yet their susceptibility to adversarial perturbations poses a significant threat to their reliability in real-world applications. Despite often being imperceptible to humans, these perturbations can drastically alter model outputs, leading to erroneous interpretations and decisions. This paper introduces DiffCAP, a novel diffusion-based purification strategy that can effectively neutralize adversarial corruptions in VLMs. We theoretically establish a provable recovery region in the forward diffusion process and meanwhile quantify the convergence rate of semantic variation with respect to VLMs. These findings manifest that adversarial effects monotonically fade as diffusion unfolds. Guided by this principle, DiffCAP leverages noise injection with a similarity threshold of VLM embeddings as an adaptive criterion, before reverse diffusion restores a clean and reliable representation for VLM inference. Through extensive experiments across six datasets with three VLMs under varying attack strengths in three task scenarios, we show that DiffCAP outperforms existing defense techniques by a substantial margin. Notably, DiffCAP significantly reduces both hyperparameter tuning complexity and the required diffusion time, thereby accelerating the denoising process. Equipped with theorems and empirical support, DiffCAP provides a robust and practical solution for securely deploying VLMs in adversarial environments. The source code is available at https://github.com/JasonFu1998/DiffCAP.

DETR has been recently proposed to eliminate the need for many hand-designed components in object detection while demonstrating good performance. However, it suffers from slow convergence and limited feature spatial resolution, due to the limitation of Transformer attention modules in processing image feature maps. To mitigate these issues, we proposed Deformable DETR, whose attention modules only attend to a small set of key sampling points around a reference. Deformable DETR can achieve better performance than DETR (especially on small objects) with 10 times less training epochs. Extensive experiments on the COCO benchmark demonstrate the effectiveness of our approach. Code is released at https://github.com/fundamentalvision/Deformable-DETR.

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture multi-scale periodic patterns, reduce sequence dependencies, and naturally denoise signals. However, existing approaches typically train model components for all frequencies under a unified training objective, often leading to mismatched learning speeds: high-frequency components converge faster and risk overfitting, while low-frequency components underfit due to insufficient training time. To deal with this challenge, we propose BEAT (Balanced frEquency Adaptive Tuning), a novel framework that dynamically monitors the training status for each frequency and adaptively adjusts their gradient updates. By recognizing convergence, overfitting, or underfitting for each frequency, BEAT dynamically reallocates learning priorities, moderating gradients for rapid learners and increasing those for slower ones, alleviating the tension between competing objectives across frequencies and synchronizing the overall learning process. Extensive experiments on seven real-world datasets demonstrate that BEAT consistently outperforms state-of-the-art approaches.

Globally, artificial intelligence (AI) implementation is growing, holding the capability to fundamentally alter organisational processes and decision making. Simultaneously, this brings a multitude of emergent risks to organisations, exposing vulnerabilities in their extant risk management frameworks. This necessitates a greater understanding of how organisations can position themselves in response. This issue is particularly pertinent within the financial sector with relatively mature AI applications matched with severe societal repercussions of potential risk events. Despite this, academic risk management literature is trailing behind the speed of AI implementation. Adopting a management perspective, this study aims to contribute to the understanding of AI risk management in organisations through an exploratory empirical investigation into these practices. In-depth insights are gained through interviews with nine practitioners from different organisations within the UK financial sector. Through examining areas of organisational convergence and divergence, the findings of this study unearth levels of risk management framework readiness and prevailing approaches to risk management at both a processual and organisational level. Whilst enhancing the developing literature concerning AI risk management within organisations, the study simultaneously offers a practical contribution, providing key areas of guidance for practitioners in the operational development of AI risk management frameworks.

We propose a new formulation of temporal action detection (TAD) with denoising diffusion, DiffTAD in short. Taking as input random temporal proposals, it can yield action proposals accurately given an untrimmed long video. This presents a generative modeling perspective, against previous discriminative learning manners. This capability is achieved by first diffusing the ground-truth proposals to random ones (i.e., the forward/noising process) and then learning to reverse the noising process (i.e., the backward/denoising process). Concretely, we establish the denoising process in the Transformer decoder (e.g., DETR) by introducing a temporal location query design with faster convergence in training. We further propose a cross-step selective conditioning algorithm for inference acceleration. Extensive evaluations on ActivityNet and THUMOS show that our DiffTAD achieves top performance compared to previous art alternatives. The code will be made available at https://github.com/sauradip/DiffusionTAD.

Training vision or language models on large datasets can take days, if not weeks. We show that averaging the weights of the k latest checkpoints, each collected at the end of an epoch, can speed up the training progression in terms of loss and accuracy by dozens of epochs, corresponding to time savings up to ~68 and ~30 GPU hours when training a ResNet50 on ImageNet and RoBERTa-Base model on WikiText-103, respectively. We also provide the code and model checkpoint trajectory to reproduce the results and facilitate research on reusing historical weights for faster convergence.

This study explores the role of cross-attention during inference in text-conditional diffusion models. We find that cross-attention outputs converge to a fixed point after few inference steps. Accordingly, the time point of convergence naturally divides the entire inference process into two stages: an initial semantics-planning stage, during which, the model relies on cross-attention to plan text-oriented visual semantics, and a subsequent fidelity-improving stage, during which the model tries to generate images from previously planned semantics. Surprisingly, ignoring text conditions in the fidelity-improving stage not only reduces computation complexity, but also maintains model performance. This yields a simple and training-free method called TGATE for efficient generation, which caches the cross-attention output once it converges and keeps it fixed during the remaining inference steps. Our empirical study on the MS-COCO validation set confirms its effectiveness. The source code of TGATE is available at https://github.com/HaozheLiu-ST/T-GATE.

Linux kernel tuning is essential for optimizing operating system (OS) performance. However, existing methods often face challenges in terms of efficiency, scalability, and generalization. This paper introduces OS-R1, an agentic Linux kernel tuning framework powered by rule-based reinforcement learning (RL). By abstracting the kernel configuration space as an RL environment, OS-R1 facilitates efficient exploration by large language models (LLMs) and ensures accurate configuration modifications. Additionally, custom reward functions are designed to enhance reasoning standardization, configuration modification accuracy, and system performance awareness of the LLMs. Furthermore, we propose a two-phase training process that accelerates convergence and minimizes retraining across diverse tuning scenarios. Experimental results show that OS-R1 significantly outperforms existing baseline methods, achieving up to 5.6% performance improvement over heuristic tuning and maintaining high data efficiency. Notably, OS-R1 is adaptable across various real-world applications, demonstrating its potential for practical deployment in diverse environments. Our dataset and code are publicly available at https://github.com/LHY-24/OS-R1.

Federated Learning (FL) has been recently receiving increasing consideration from the cybersecurity community as a way to collaboratively train deep learning models with distributed profiles of cyber threats, with no disclosure of training data. Nevertheless, the adoption of FL in cybersecurity is still in its infancy, and a range of practical aspects have not been properly addressed yet. Indeed, the Federated Averaging algorithm at the core of the FL concept requires the availability of test data to control the FL process. Although this might be feasible in some domains, test network traffic of newly discovered attacks cannot be always shared without disclosing sensitive information. In this paper, we address the convergence of the FL process in dynamic cybersecurity scenarios, where the trained model must be frequently updated with new recent attack profiles to empower all members of the federation with the latest detection features. To this aim, we propose FLAD (adaptive Federated Learning Approach to DDoS attack detection), an FL solution for cybersecurity applications based on an adaptive mechanism that orchestrates the FL process by dynamically assigning more computation to those members whose attacks profiles are harder to learn, without the need of sharing any test data to monitor the performance of the trained model. Using a recent dataset of DDoS attacks, we demonstrate that FLAD outperforms state-of-the-art FL algorithms in terms of convergence time and accuracy across a range of unbalanced datasets of heterogeneous DDoS attacks. We also show the robustness of our approach in a realistic scenario, where we retrain the deep learning model multiple times to introduce the profiles of new attacks on a pre-trained model.

Fully finetuning foundation language models (LMs) with billions of parameters is often impractical due to high computational costs, memory requirements, and the risk of overfitting. Although methods like low-rank adapters help address these challenges by adding small trainable modules to the frozen LM, they also increase memory usage and do not reduce inference latency. We uncover an intriguing phenomenon: sparsifying specific model rows and columns enables efficient task adaptation without requiring weight tuning. We propose a scheme for effective finetuning via sparsification using training stochastic gates, which requires minimal trainable parameters, reduces inference time, and removes 20--40\% of model parameters without significant accuracy loss. Empirical results show it outperforms recent finetuning baselines in efficiency and performance. Additionally, we provide theoretical guarantees for the convergence of this stochastic gating process, and show that our method admits a simpler and better-conditioned optimization landscape compared to LoRA. Our results highlight sparsity as a compelling mechanism for task-specific adaptation in LMs.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

Advances in Visually Rich Document Understanding (VrDU) have enabled information extraction and question answering over documents with complex layouts. Two tropes of architectures have emerged -- transformer-based models inspired by LLMs, and Graph Neural Networks. In this paper, we introduce DocGraphLM, a novel framework that combines pre-trained language models with graph semantics. To achieve this, we propose 1) a joint encoder architecture to represent documents, and 2) a novel link prediction approach to reconstruct document graphs. DocGraphLM predicts both directions and distances between nodes using a convergent joint loss function that prioritizes neighborhood restoration and downweighs distant node detection. Our experiments on three SotA datasets show consistent improvement on IE and QA tasks with the adoption of graph features. Moreover, we report that adopting the graph features accelerates convergence in the learning process during training, despite being solely constructed through link prediction.

Training large language models is a computationally intensive process that often requires substantial resources to achieve state-of-the-art results. Incremental layer-wise training has been proposed as a potential strategy to optimize the training process by progressively introducing layers, with the expectation that this approach would lead to faster convergence and more efficient use of computational resources. In this paper, we investigate the effectiveness of incremental training for LLMs, dividing the training process into multiple stages where layers are added progressively. Our experimental results indicate that while the incremental approach initially demonstrates some computational efficiency, it ultimately requires greater overall computational costs to reach comparable performance to traditional full-scale training. Although the incremental training process can eventually close the performance gap with the baseline, it does so only after significantly extended continual training. These findings suggest that incremental layer-wise training may not be a viable alternative for training large language models, highlighting its limitations and providing valuable insights into the inefficiencies of this approach.

With the advancement of RNN models with linear complexity, the quadratic complexity challenge of transformers has the potential to be overcome. Notably, the emerging Mamba-2 has demonstrated competitive performance, bridging the gap between RNN models and transformers. However, due to sequential processing and vanishing gradients, RNN models struggle to capture long-range dependencies, limiting contextual understanding. This results in slow convergence, high resource demands, and poor performance on downstream understanding and complex reasoning tasks. In this work, we present a hybrid model MaTVLM by substituting a portion of the transformer decoder layers in a pre-trained VLM with Mamba-2 layers. Leveraging the inherent relationship between attention and Mamba-2, we initialize Mamba-2 with corresponding attention weights to accelerate convergence. Subsequently, we employ a single-stage distillation process, using the pre-trained VLM as the teacher model to transfer knowledge to the MaTVLM, further enhancing convergence speed and performance. Furthermore, we investigate the impact of differential distillation loss within our training framework. We evaluate the MaTVLM on multiple benchmarks, demonstrating competitive performance against the teacher model and existing VLMs while surpassing both Mamba-based VLMs and models of comparable parameter scales. Remarkably, the MaTVLM achieves up to 3.6x faster inference than the teacher model while reducing GPU memory consumption by 27.5%, all without compromising performance. Code and models are released at http://github.com/hustvl/MaTVLM.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

We propose an adaptive sampling framework for 3D Gaussian Splatting (3DGS) that leverages comprehensive multi-view photometric error signals within a unified Metropolis-Hastings approach. Vanilla 3DGS heavily relies on heuristic-based density-control mechanisms (e.g., cloning, splitting, and pruning), which can lead to redundant computations or premature removal of beneficial Gaussians. Our framework overcomes these limitations by reformulating densification and pruning as a probabilistic sampling process, dynamically inserting and relocating Gaussians based on aggregated multi-view errors and opacity scores. Guided by Bayesian acceptance tests derived from these error-based importance scores, our method substantially reduces reliance on heuristics, offers greater flexibility, and adaptively infers Gaussian distributions without requiring predefined scene complexity. Experiments on benchmark datasets, including Mip-NeRF360, Tanks and Temples and Deep Blending, show that our approach reduces the number of Gaussians needed, achieving faster convergence while matching or modestly surpassing the view-synthesis quality of state-of-the-art models.

As an emerging topic in face recognition, designing margin-based loss functions can increase the feature margin between different classes for enhanced discriminability. More recently, the idea of mining-based strategies is adopted to emphasize the misclassified samples, achieving promising results. However, during the entire training process, the prior methods either do not explicitly emphasize the sample based on its importance that renders the hard samples not fully exploited; or explicitly emphasize the effects of semi-hard/hard samples even at the early training stage that may lead to convergence issue. In this work, we propose a novel Adaptive Curriculum Learning loss (CurricularFace) that embeds the idea of curriculum learning into the loss function to achieve a novel training strategy for deep face recognition, which mainly addresses easy samples in the early training stage and hard ones in the later stage. Specifically, our CurricularFace adaptively adjusts the relative importance of easy and hard samples during different training stages. In each stage, different samples are assigned with different importance according to their corresponding difficultness. Extensive experimental results on popular benchmarks demonstrate the superiority of our CurricularFace over the state-of-the-art competitors.

We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or concave function. This problem is difficult to solve since it is non-convex. By exploiting the structure of the problem, we propose two Coordinate Descent (CD) methods for solving this problem. The proposed methods iteratively solve a one-dimensional subproblem globally, and they are guaranteed to converge to coordinate-wise stationary points. In the case of a convex denominator, under a weak locally bounded non-convexity condition, we prove that the optimality of coordinate-wise stationary point is stronger than that of the standard critical point and directional point. Under additional suitable conditions, CD methods converge Q-linearly to coordinate-wise stationary points. In the case of a concave denominator, we show that any critical point is a global minimum, and CD methods converge to the global minimum with a sublinear convergence rate. We demonstrate the applicability of the proposed methods to some machine learning and signal processing models. Our experiments on real-world data have shown that our method significantly and consistently outperforms existing methods in terms of accuracy.

In this paper, we propose to use deep policy networks which are trained with an advantage actor-critic method for statistically optimised dialogue systems. First, we show that, on summary state and action spaces, deep Reinforcement Learning (RL) outperforms Gaussian Processes methods. Summary state and action spaces lead to good performance but require pre-engineering effort, RL knowledge, and domain expertise. In order to remove the need to define such summary spaces, we show that deep RL can also be trained efficiently on the original state and action spaces. Dialogue systems based on partially observable Markov decision processes are known to require many dialogues to train, which makes them unappealing for practical deployment. We show that a deep RL method based on an actor-critic architecture can exploit a small amount of data very efficiently. Indeed, with only a few hundred dialogues collected with a handcrafted policy, the actor-critic deep learner is considerably bootstrapped from a combination of supervised and batch RL. In addition, convergence to an optimal policy is significantly sped up compared to other deep RL methods initialized on the data with batch RL. All experiments are performed on a restaurant domain derived from the Dialogue State Tracking Challenge 2 (DSTC2) dataset.

Large language models map semantically related prompts to similar internal representations -- a phenomenon interpretable as attractor-like dynamics. We ask whether the identity document of a persistent cognitive agent (its cognitive_core) exhibits analogous attractor-like behavior. We present a controlled experiment on Llama 3.1 8B Instruct, comparing hidden states of an original cognitive_core (Condition A), seven paraphrases (Condition B), and seven structurally matched controls (Condition C). Mean-pooled states at layers 8, 16, and 24 show that paraphrases converge to a tighter cluster than controls (Cohen's d > 1.88, p < 10^{-27}, Bonferroni-corrected). Replication on Gemma 2 9B confirms cross-architecture generalizability. Ablations suggest the effect is primarily semantic rather than structural, and that structural completeness appears necessary to reach the attractor region. An exploratory experiment shows that reading a scientific description of the agent shifts internal state toward the attractor -- closer than a sham preprint -- distinguishing knowing about an identity from operating as that identity. These results provide representational evidence that agent identity documents induce attractor-like geometry in LLM activation space.

Federated learning (FL), as an emerging distributed machine learning paradigm, allows a mass of edge devices to collaboratively train a global model while preserving privacy. In this tutorial, we focus on FL via over-the-air computation (AirComp), which is proposed to reduce the communication overhead for FL over wireless networks at the cost of compromising in the learning performance due to model aggregation error arising from channel fading and noise. We first provide a comprehensive study on the convergence of AirComp-based FedAvg (AirFedAvg) algorithms under both strongly convex and non-convex settings with constant and diminishing learning rates in the presence of data heterogeneity. Through convergence and asymptotic analysis, we characterize the impact of aggregation error on the convergence bound and provide insights for system design with convergence guarantees. Then we derive convergence rates for AirFedAvg algorithms for strongly convex and non-convex objectives. For different types of local updates that can be transmitted by edge devices (i.e., local model, gradient, and model difference), we reveal that transmitting local model in AirFedAvg may cause divergence in the training procedure. In addition, we consider more practical signal processing schemes to improve the communication efficiency and further extend the convergence analysis to different forms of model aggregation error caused by these signal processing schemes. Extensive simulation results under different settings of objective functions, transmitted local information, and communication schemes verify the theoretical conclusions.

In addressing the challenge of Crystal Structure Prediction (CSP), symmetry-aware deep learning models, particularly diffusion models, have been extensively studied, which treat CSP as a conditional generation task. However, ensuring permutation, rotation, and periodic translation equivariance during diffusion process remains incompletely addressed. In this work, we propose EquiCSP, a novel equivariant diffusion-based generative model. We not only address the overlooked issue of lattice permutation equivariance in existing models, but also develop a unique noising algorithm that rigorously maintains periodic translation equivariance throughout both training and inference processes. Our experiments indicate that EquiCSP significantly surpasses existing models in terms of generating accurate structures and demonstrates faster convergence during the training process.

The most popular framework for distributed training of machine learning models is the (synchronous) parameter server (PS). This paradigm consists of n workers, which iteratively compute updates of the model parameters, and a stateful PS, which waits and aggregates all updates to generate a new estimate of model parameters and sends it back to the workers for a new iteration. Transient computation slowdowns or transmission delays can intolerably lengthen the time of each iteration. An efficient way to mitigate this problem is to let the PS wait only for the fastest n-b updates, before generating the new parameters. The slowest b workers are called backup workers. The optimal number b of backup workers depends on the cluster configuration and workload, but also (as we show in this paper) on the hyper-parameters of the learning algorithm and the current stage of the training. We propose DBW, an algorithm that dynamically decides the number of backup workers during the training process to maximize the convergence speed at each iteration. Our experiments show that DBW 1) removes the necessity to tune b by preliminary time-consuming experiments, and 2) makes the training up to a factor 3 faster than the optimal static configuration.

Training models with varying capacities can be advantageous for deploying them in different scenarios. While high-capacity models offer better performance, low-capacity models require fewer computing resources for training and inference. In this work, we propose a novel one-stop training framework to jointly train high-capacity and low-capactiy models. This framework consists of two composite model architectures and a joint training algorithm called Two-Stage Joint-Training (TSJT). Unlike knowledge distillation, where multiple capacity models are trained from scratch separately, our approach integrates supervisions from different capacity models simultaneously, leading to faster and more efficient convergence. Extensive experiments on the multilingual machine translation benchmark WMT10 show that our method outperforms low-capacity baseline models and achieves comparable or better performance on high-capacity models. Notably, the analysis demonstrates that our method significantly influences the initial training process, leading to more efficient convergence and superior solutions.

We introduce NeuroSA, a neuromorphic architecture specifically designed to ensure asymptotic convergence to the ground state of an Ising problem using an annealing process that is governed by the physics of quantum mechanical tunneling using Fowler-Nordheim (FN). The core component of NeuroSA consists of a pair of asynchronous ON-OFF neurons, which effectively map classical simulated annealing (SA) dynamics onto a network of integrate-and-fire (IF) neurons. The threshold of each ON-OFF neuron pair is adaptively adjusted by an FN annealer which replicates the optimal escape mechanism and convergence of SA, particularly at low temperatures. To validate the effectiveness of our neuromorphic Ising machine, we systematically solved various benchmark MAX-CUT combinatorial optimization problems. Across multiple runs, NeuroSA consistently generates solutions that approach the state-of-the-art level with high accuracy (greater than 99%), and without any graph-specific hyperparameter tuning. For practical illustration, we present results from an implementation of NeuroSA on the SpiNNaker2 platform, highlighting the feasibility of mapping our proposed architecture onto a standard neuromorphic accelerator platform.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

Large language models (LLMs) exhibit remarkable problem-solving abilities, but struggle with complex tasks due to static internal knowledge. Retrieval-Augmented Generation (RAG) enhances access to external information, yet remains limited in multi-hop reasoning and strategic search due to rigid workflows. Recent advancements in agentic deep research empower LLMs to autonomously reason, search, and synthesize information. However, current approaches relying on outcome-based reinforcement learning (RL) face critical issues such as conflicting gradients and reward sparsity, limiting performance gains and training efficiency. To address these, we first propose Atomic Thought, a novel LLM thinking paradigm that decomposes reasoning into fine-grained functional units. These units are supervised by Reasoning Reward Models (RRMs), which provide Atomic Thought Rewards (ATR) for fine-grained guidance. Building on this, we propose Atom-Searcher, a novel RL framework for agentic deep research that integrates Atomic Thought and ATR. Atom-Searcher uses a curriculum-inspired reward schedule, prioritizing process-level ATR early and transitioning to outcome rewards, accelerating convergence on effective reasoning paths. Experiments on seven benchmarks show consistent improvements over the state-of-the-art. Key advantages include: (1) Atom-Searcher scales computation at test-time. (2) Atomic Thought provides supervision anchors for RRMs, bridging deep research tasks and RRMs. (3) Atom-Searcher exhibits more interpretable, human-like reasoning patterns.

Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too memory-intensive for direct input into conventional diffusion models. Furthermore, general generative models lack an understanding of the topological and geometric structures of ground objects in remote sensing imagery. In addition, most diffusion models optimize loss functions at the noise level, leading to a non-intuitive convergence behavior and suboptimal generation quality for complex data. To address these challenges, we propose a Geometric Enhanced Wavelet-based Diffusion Model (GEWDiff), a novel framework for reconstructing hyperspectral images at 4-times super-resolution. A wavelet-based encoder-decoder is introduced that efficiently compresses HSIs into a latent space while preserving spectral-spatial information. To avoid distortion during generation, we incorporate a geometry-enhanced diffusion process that preserves the geometric features. Furthermore, a multi-level loss function was designed to guide the diffusion process, promoting stable convergence and improved reconstruction fidelity. Our model demonstrated state-of-the-art results across multiple dimensions, including fidelity, spectral accuracy, visual realism, and clarity.

The multi-task learning (MTL) paradigm aims to simultaneously learn multiple tasks within a single model capturing higher-level, more general hidden patterns that are shared by the tasks. In deep learning, a significant challenge in the backpropagation training process is the design of advanced optimisers to improve the convergence speed and stability of the gradient descent learning rule. In particular, in multi-task deep learning (MTDL) the multitude of tasks may generate potentially conflicting gradients that would hinder the concurrent convergence of the diverse loss functions. This challenge arises when the gradients of the task objectives have either different magnitudes or opposite directions, causing one or a few to dominate or to interfere with each other, thus degrading the training process. Gradient surgery methods address the problem explicitly dealing with conflicting gradients by adjusting the overall gradient trajectory. This work introduces a novel gradient surgery method, the Similarity-Aware Momentum Gradient Surgery (SAM-GS), which provides an effective and scalable approach based on a gradient magnitude similarity measure to guide the optimisation process. The SAM-GS surgery adopts gradient equalisation and modulation of the first-order momentum. A series of experimental tests have shown the effectiveness of SAM-GS on synthetic problems and MTL benchmarks. Gradient magnitude similarity plays a crucial role in regularising gradient aggregation in MTDL for the optimisation of the learning process.

Scalable reinforcement learning has popularized high-throughput sampling architectures, which significantly compresses the training time for off-policy methods in robotic locomotion. However, the rapid increase of data volume and update frequency undermines the stability of value-based methods and diminishes the plasticity of policy networks. To address these challenges, this work presents FastDSAC, a fast and high-performance variant of the Distributional Actor-Critic algorithm designed for parallel sampling scenarios. Specifically, we introduce a truncated Gaussian distribution to approximate the learned policy, which effectively excludes out-of-distribution actions that strain target value estimation while keeping necessary stochasticity for exploration. The proposed action constraint functions as an implicit regularization, which counteracts the plasticity loss typically caused by aggressive gradient updates. This preservation of network adaptability enhances sample efficiency, particularly in scenarios with a high update-to-data ratio, and accelerates the early training process. In contrast to prior fast reinforcement learning approaches that rely on discrete value distributions, our method utilizes a continuous Gaussian representation equipped with adaptive variance regulation, which improves value estimation accuracy by sampling confident and informative transitions. Extensive experiments on MuJoCo Playground and HumanoidBench demonstrate that FastDSAC not only stabilizes the overall training process but also achieves superior asymptotic performance and faster convergence compared to state-of-the-art baselines.

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits' states. Our results show that the convergence properties of homogenization machines that are important for modelling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

Adapting large-scale Vision-Language Models (VLMs) like CLIP to downstream tasks often suffers from a "one-size-fits-all" architectural approach, where visual and textual tokens are processed uniformly by wide, generic adapters. We argue that this homogeneity ignores the distinct structural nature of the modalities -- spatial locality in images versus semantic density in text. To address this, we propose HeBA (Heterogeneous Bottleneck Adapter), a unified architectural framework that introduces modality-specific structural inductive biases. HeBA departs from conventional designs through three key architectural innovations: (1) Heterogeneity: It processes visual tokens via 2D depthwise-separable convolutions to preserve spatial correlations, while distinctively processing text tokens via dense linear projections to capture semantic relationships; (2) Bottleneck Regularization: Unlike standard expanding adapters, HeBA employs a compression bottleneck (D -> D/4) that explicitly forces the model to learn compact, robust features and acts as a structural regularizer; and (3) Active Gradient Initialization: We challenge the restrictive zero-initialization paradigm, utilizing a Kaiming initialization strategy that ensures sufficient initial gradient flow to accelerate convergence without compromising the frozen backbone's pre-trained knowledge. Extensive experiments demonstrate that HeBA's architecturally specialized design achieves superior stability and accuracy, establishing a new state-of-the-art on 11 few-shot benchmarks. Code is available at https://github.com/Jahid12012021/VLM-HeBA.

Artificial neural networks are a popular and effective machine learning technique. Great progress has been made parallelizing the expensive training phase of an individual network, leading to highly specialized pieces of hardware, many based on GPU-type architectures, and more concurrent algorithms such as synthetic gradients. However, the training phase continues to be a bottleneck, where the training data must be processed serially over thousands of individual training runs. This work considers a multigrid reduction in time (MGRIT) algorithm that is able to parallelize over the thousands of training runs and converge to the exact same solution as traditional training would provide. MGRIT was originally developed to provide parallelism for time evolution problems that serially step through a finite number of time-steps. This work recasts the training of a neural network similarly, treating neural network training as an evolution equation that evolves the network weights from one step to the next. Thus, this work concerns distributed computing approaches for neural networks, but is distinct from other approaches which seek to parallelize only over individual training runs. The work concludes with supporting numerical results for two model problems.

JEPA-family world models use a static predictor whose weights do not adapt when test-time dynamics diverge from training. We compare two mechanisms for incorporating accumulated experience into a JEPA predictor under distribution shift: operand-side injection, where a compressed experience representation is added as a residual to the predictor's hidden state (EI-JEPA), and operator-side modulation, where the same representation generates low-rank weight deltas via LoRA applied to the predictor's weights (EPM-JEPA). On a pre-registered comparison (Moving MNIST, gravity shift), EPM-JEPA (D_shift^{n=50} = 0.7848 +/- 0.0078, three seeds) differs from EI-JEPA (0.8238) by delta = 4.74% - Outcome C: a null result - by our stated criterion, a valid outcome. As a secondary, non-pre-registered observation, EPM-JEPA improves 1.90% over a no-memory baseline (0.8000), consistently across seeds, while EI-JEPA underperforms the baseline, indicating the benefit is specific to weight-level modulation. Our primary contribution is a mechanism analysis: the D_shift^{n=50} trajectory reflects three independent dynamical processes - buffer cycling, EMA target drift, and an intrinsic LoRA settling transient of +0.021 - rather than convergence to equilibrium. These findings motivate PEM-JEPA, a physics-grounded successor addressing this dynamical-peak limitation.

In this paper, we introduce layer-wise curriculum learning for efficient LLM compression. The proposed method facilitates the knowledge transfer from the teacher model to the student model, utilizing a curriculum learning approach that begins with easier optimization tasks and progressively tackles harder ones. In order to adopt the layer-wise learning in LLM compression, we partition the whole model into multiple segments consisting of layers, thereby enabling more computationally efficient knowledge transfer for LLMs. Based on our theoretical analysis of cumulative error phenomenon, layer-wise curriculum learning accelerates convergence while stabilizing the knowledge transfer process. In addition, we present a feature caching method with a multi-threading strategy to efficiently address feature misalignment across layers, maximizing GPU utilization. Consequently, our method exhibits advanced model compression performance, as well as high computational efficiency in terms of minimized memory usage and short training hours. Experiments on multiple datasets show that the proposed method achieves state-of-the-art performance while reducing GPU memory usage and training hours by more than 50\% on BERT and GPT-2. Moreover, it outperforms the other pruning methods on LLaMA-family and Qwen models under the same training hours, with a lower GPU memory footprint.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

This paper introduces the Aquila2 series, which comprises a wide range of bilingual models with parameter sizes of 7, 34, and 70 billion. These models are trained based on an innovative framework named HeuriMentor (HM), which offers real-time insights into model convergence and enhances the training process and data management. The HM System, comprising the Adaptive Training Engine (ATE), Training State Monitor (TSM), and Data Management Unit (DMU), allows for precise monitoring of the model's training progress and enables efficient optimization of data distribution, thereby enhancing training effectiveness. Extensive evaluations show that the Aquila2 model series performs comparably well on both English and Chinese benchmarks. Specifically, Aquila2-34B demonstrates only a slight decrease in performance when quantized to Int4. Furthermore, we have made our training code (https://github.com/FlagOpen/FlagScale) and model weights (https://github.com/FlagAI-Open/Aquila2) publicly available to support ongoing research and the development of applications.

Latent diffusion models have shown promising results in text-to-audio (T2A) generation tasks, yet previous models have encountered difficulties in generation quality, computational cost, diffusion sampling, and data preparation. In this paper, we introduce EzAudio, a transformer-based T2A diffusion model, to handle these challenges. Our approach includes several key innovations: (1) We build the T2A model on the latent space of a 1D waveform Variational Autoencoder (VAE), avoiding the complexities of handling 2D spectrogram representations and using an additional neural vocoder. (2) We design an optimized diffusion transformer architecture specifically tailored for audio latent representations and diffusion modeling, which enhances convergence speed, training stability, and memory usage, making the training process easier and more efficient. (3) To tackle data scarcity, we adopt a data-efficient training strategy that leverages unlabeled data for learning acoustic dependencies, audio caption data annotated by audio-language models for text-to-audio alignment learning, and human-labeled data for fine-tuning. (4) We introduce a classifier-free guidance (CFG) rescaling method that simplifies EzAudio by achieving strong prompt alignment while preserving great audio quality when using larger CFG scores, eliminating the need to struggle with finding the optimal CFG score to balance this trade-off. EzAudio surpasses existing open-source models in both objective metrics and subjective evaluations, delivering realistic listening experiences while maintaining a streamlined model structure, low training costs, and an easy-to-follow training pipeline. Code, data, and pre-trained models are released at: https://haidog-yaqub.github.io/EzAudio-Page/.

Post-training of language models (LMs) increasingly relies on the following two stages: (i) knowledge distillation, where the LM is trained to imitate a larger teacher LM, and (ii) reinforcement learning from human feedback (RLHF), where the LM is aligned by optimizing a reward model. In the second RLHF stage, a well-known challenge is reward hacking, where the LM over-optimizes the reward model. Such phenomenon is in line with Goodhart's law and can lead to degraded performance on the true objective. In this paper, we investigate whether a similar phenomenon, that we call teacher hacking, can occur during knowledge distillation. This could arise because the teacher LM is itself an imperfect approximation of the true distribution. To study this, we propose a controlled experimental setup involving: (i) an oracle LM representing the ground-truth distribution, (ii) a teacher LM distilled from the oracle, and (iii) a student LM distilled from the teacher. Our experiments reveal the following insights. When using a fixed offline dataset for distillation, teacher hacking occurs; moreover, we can detect it by observing when the optimization process deviates from polynomial convergence laws. In contrast, employing online data generation techniques effectively mitigates teacher hacking. More precisely, we identify data diversity as the key factor in preventing hacking. Overall, our findings provide a deeper understanding of the benefits and limitations of distillation for building robust and efficient LMs.

Recently, deep learning-based algorithms are widely adopted due to the advantage of being able to establish anomaly detection models without or with minimal domain knowledge of the task. Instead, to train the artificial neural network more stable, it should be better to define the appropriate neural network structure or the loss function. For the training anomaly detection model, the mean squared error (MSE) function is adopted widely. On the other hand, the novel loss function, logarithmic mean squared error (LMSE), is proposed in this paper to train the neural network more stable. This study covers a variety of comparisons from mathematical comparisons, visualization in the differential domain for backpropagation, loss convergence in the training process, and anomaly detection performance. In an overall view, LMSE is superior to the existing MSE function in terms of strongness of loss convergence, anomaly detection performance. The LMSE function is expected to be applicable for training not only the anomaly detection model but also the general generative neural network.

We introduce InternVL 3.5, a new family of open-source multimodal models that significantly advances versatility, reasoning capability, and inference efficiency along the InternVL series. A key innovation is the Cascade Reinforcement Learning (Cascade RL) framework, which enhances reasoning through a two-stage process: offline RL for stable convergence and online RL for refined alignment. This coarse-to-fine training strategy leads to substantial improvements on downstream reasoning tasks, e.g., MMMU and MathVista. To optimize efficiency, we propose a Visual Resolution Router (ViR) that dynamically adjusts the resolution of visual tokens without compromising performance. Coupled with ViR, our Decoupled Vision-Language Deployment (DvD) strategy separates the vision encoder and language model across different GPUs, effectively balancing computational load. These contributions collectively enable InternVL3.5 to achieve up to a +16.0\% gain in overall reasoning performance and a 4.05times inference speedup compared to its predecessor, i.e., InternVL3. In addition, InternVL3.5 supports novel capabilities such as GUI interaction and embodied agency. Notably, our largest model, i.e., InternVL3.5-241B-A28B, attains state-of-the-art results among open-source MLLMs across general multimodal, reasoning, text, and agentic tasks -- narrowing the performance gap with leading commercial models like GPT-5. All models and code are publicly released.

Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable training. These challenges arise particularly from the ill-conditioning of the optimization problem caused by the differential terms in the loss function. To address these issues, we propose learning a solver, i.e., solving PDEs using a physics-informed iterative algorithm trained on data. Our method learns to condition a gradient descent algorithm that automatically adapts to each PDE instance, significantly accelerating and stabilizing the optimization process and enabling faster convergence of physics-aware models. Furthermore, while traditional physics-informed methods solve for a single PDE instance, our approach extends to parametric PDEs. Specifically, we integrate the physical loss gradient with PDE parameters, allowing our method to solve over a distribution of PDE parameters, including coefficients, initial conditions, and boundary conditions. We demonstrate the effectiveness of our approach through empirical experiments on multiple datasets, comparing both training and test-time optimization performance. The code is available at https://github.com/2ailesB/neural-parametric-solver.

The aim of Reinforcement Learning (RL) in real-world applications is to create systems capable of making autonomous decisions by learning from their environment through trial and error. This paper emphasizes the importance of reward engineering and reward shaping in enhancing the efficiency and effectiveness of reinforcement learning algorithms. Reward engineering involves designing reward functions that accurately reflect the desired outcomes, while reward shaping provides additional feedback to guide the learning process, accelerating convergence to optimal policies. Despite significant advancements in reinforcement learning, several limitations persist. One key challenge is the sparse and delayed nature of rewards in many real-world scenarios, which can hinder learning progress. Additionally, the complexity of accurately modeling real-world environments and the computational demands of reinforcement learning algorithms remain substantial obstacles. On the other hand, recent advancements in deep learning and neural networks have significantly improved the capability of reinforcement learning systems to handle high-dimensional state and action spaces, enabling their application to complex tasks such as robotics, autonomous driving, and game playing. This paper provides a comprehensive review of the current state of reinforcement learning, focusing on the methodologies and techniques used in reward engineering and reward shaping. It critically analyzes the limitations and recent advancements in the field, offering insights into future research directions and potential applications in various domains.

3D Gaussian Splatting (3DGS) employs Gaussian primitives for explicit scene representation, facilitating real-time, high-fidelity reconstruction and novel view synthesis of complex scenes. However, the explicit modeling inherent in 3DGS introduces a gradient bias during optimization, rendering its non-convex optimization process highly susceptible to convergence toward local suboptimal solutions. This constitutes a fundamental limitation in 3DGS optimization, which we term the Blur Trap. To address this limitation, we integrate simple explicit exploration into the 3DGS optimization framework. First, through rigorous mathematical analysis of the 3DGS optimization formulation, we identify the underlying optimization bias responsible for the Blur Trap and categorize it into two distinct subtypes: the Far-Side Blur Trap and the Near-Side Blur Trap. Subsequently, we propose two highly straightforward exploration strategies (Random Seeding and Random Splitting) to mitigate the far-side and near-side blur traps, respectively. Experimental validation demonstrates that the incorporation of these exploration operators effectively and complementarily overcome the Blur Trap, achieving high-quality rendering performance across multiple datasets. Project page: https://chengbo-wang.github.io/ExploreGS/

Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not employ any training signal, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each subject to an unknown positive multiplicative factor (or gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable, carefully chosen initialisation point. An analysis of this algorithm allows us to show that it converges to the exact solution provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Interestingly, we show that this requirement grows linearly (up to log factors) in the number of unknowns of the problem. This sample complexity is found both in absence of prior information, as well as when subspace priors are available for both the signal and gains, allowing a further reduction of the number of observations required for our recovery guarantees to hold. Moreover, in the presence of noise we show how our descent algorithm yields a solution whose accuracy degrades gracefully with the amount of noise affecting the measurements. Finally, we present some numerical experiments in an imaging context, where our algorithm allows for a simple solution to blind calibration of the gains in a sensor array.

World Action Models (WAMs) model future environment evolution under action conditioning, offering a scalable paradigm for autonomous driving. However, existing approaches focus largely on model architecture design, and how a WAM can efficiently learn better world representations for planning remains underexplored. To address this gap, we propose ReWorld, the first representation learning framework specifically designed for autonomous-driving world action models. In WAMs, standard training supervises only the output ends of the generation and planning modules, leaving the intermediate representations that carry world knowledge to be shaped only indirectly, as byproducts of fitting these outputs. The core idea of ReWorld is to treat intermediate representations as direct targets of optimization, shaping them along three complementary dimensions. On the Video DiT responsible for generation, we impose future-predictive supervision on its intermediate representations. On the Action DiT responsible for planning, we first align its intermediate representations cross-modally with the video world representation, then further shape them to be discriminative around safety-critical boundaries via hard-negative supervision. In addition, we systematically analyze the effectiveness of existing representation learning methods in video generation world models, and discuss why their performance is limited on this task. Experiments on nuScenes and NAVSIM show that ReWorld improves fine-tuned video generation by 23.9% in FVD (81.3 to 61.9), raises closed-loop PDMS from 89.1 to 90.4 without any post-training such as RL or post-processing, and accelerates from-scratch convergence by approximately 2x.