Daily Papers

It has been shown that a message passing neural networks (MPNNs), a popular family of neural networks for graph-structured data, are at most as expressive as the first-order Weisfeiler-Leman (1-WL) graph isomorphism test, which has motivated the development of more expressive architectures. In this work, we analyze if the limited expressiveness is actually a limiting factor for MPNNs and other WL-based models in standard graph datasets. Interestingly, we find that the expressiveness of WL is sufficient to identify almost all graphs in most datasets. Moreover, we find that the classification accuracy upper bounds are often close to 100\%. Furthermore, we find that simple WL-based neural networks and several MPNNs can be fitted to several datasets. In sum, we conclude that the performance of WL/MPNNs is not limited by their expressiveness in practice.

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the 1-dimensional Weisfeiler--Leman algorithm (1-WL). Here, the 1-WL is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik--Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the 1-WL. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the 1-WL and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically -- showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the 1-dimensional Weisfeiler-Leman graph isomorphism heuristic (1-WL). We show that GNNs have the same expressiveness as the 1-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are limited in their expressive power. These models are no more powerful than the 1-dimensional Weisfeiler-Leman (1-WL) algorithm in terms of distinguishing non-isomorphic graphs. In this paper, we propose Path Neural Networks (PathNNs), a model that updates node representations by aggregating paths emanating from nodes. We derive three different variants of the PathNN model that aggregate single shortest paths, all shortest paths and all simple paths of length up to K. We prove that two of these variants are strictly more powerful than the 1-WL algorithm, and we experimentally validate our theoretical results. We find that PathNNs can distinguish pairs of non-isomorphic graphs that are indistinguishable by 1-WL, while our most expressive PathNN variant can even distinguish between 3-WL indistinguishable graphs. The different PathNN variants are also evaluated on graph classification and graph regression datasets, where in most cases, they outperform the baseline methods.

Graph similarity computation (GSC) is to calculate the similarity between one pair of graphs, which is a fundamental problem with fruitful applications in the graph community. In GSC, graph edit distance (GED) and maximum common subgraph (MCS) are two important similarity metrics, both of which are NP-hard to compute. Instead of calculating the exact values, recent solutions resort to leveraging graph neural networks (GNNs) to learn data-driven models for the estimation of GED and MCS. Most of them are built on components involving node-level interactions crossing graphs, which engender vast computation overhead but are of little avail in effectiveness. In the paper, we present GraSP, a simple yet effective GSC approach for GED and MCS prediction. GraSP achieves high result efficacy through several key instruments: enhanced node features via positional encoding and a GNN model augmented by a gating mechanism, residual connections, as well as multi-scale pooling. Theoretically, GraSP can surpass the 1-WL test, indicating its high expressiveness. Empirically, extensive experiments comparing GraSP against 10 competitors on multiple widely adopted benchmark datasets showcase the superiority of GraSP over prior arts in terms of both effectiveness and efficiency. The code is available at https://github.com/HaoranZ99/GraSP.

Message passing neural networks (MPNNs) have emerged as the most popular framework of graph neural networks (GNNs) in recent years. However, their expressive power is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test. Some works are inspired by k-WL/FWL (Folklore WL) and design the corresponding neural versions. Despite the high expressive power, there are serious limitations in this line of research. In particular, (1) k-WL/FWL requires at least O(n^k) space complexity, which is impractical for large graphs even when k=3; (2) The design space of k-WL/FWL is rigid, with the only adjustable hyper-parameter being k. To tackle the first limitation, we propose an extension, (k,t)-FWL. We theoretically prove that even if we fix the space complexity to O(n^k) (for any kgeq 2) in (k,t)-FWL, we can construct an expressiveness hierarchy up to solving the graph isomorphism problem. To tackle the second problem, we propose k-FWL+, which considers any equivariant set as neighbors instead of all nodes, thereby greatly expanding the design space of k-FWL. Combining these two modifications results in a flexible and powerful framework (k,t)-FWL+. We demonstrate (k,t)-FWL+ can implement most existing models with matching expressiveness. We then introduce an instance of (k,t)-FWL+ called Neighborhood^2-FWL (N^2-FWL), which is practically and theoretically sound. We prove that N^2-FWL is no less powerful than 3-WL, and can encode many substructures while only requiring O(n^2) space. Finally, we design its neural version named N^2-GNN and evaluate its performance on various tasks. N^2-GNN achieves record-breaking results on ZINC-Subset (0.059), outperforming previous SOTA results by 10.6%. Moreover, N^2-GNN achieves new SOTA results on the BREC dataset (71.8%) among all existing high-expressive GNN methods.

It was demonstrated recently that the W_{1+infty} algebra contains commutative subalgebras associated with all integer slope rays (including the vertical one). In this paper, we realize that every element of such a ray is associated with a generalized widetilde W algebra. In particular, the simplest commutative subalgebra associated with the rational Calogero Hamiltonians is associated with the widetilde W algebras studied earlier. We suggest a definition of the generalized widetilde W algebra as differential operators in variables p_k basing on the matrix realization of the W_{1+infty} algebra, and also suggest an unambiguous recursive definition, which, however, involves more elements of the W_{1+infty} algebra than is contained in its commutative subalgebras. The positive integer rays are associated with widetilde W algebras that form sets of Ward identities for the WLZZ matrix models, while the vertical ray associated with the trigonometric Calogero-Sutherland model describes the hypergeometric tau-functions corresponding to the completed cycles.

Text representations using neural word embeddings have proven effective in many NLP applications. Recent researches adapt the traditional word embedding models to learn vectors of multiword expressions (concepts/entities). However, these methods are limited to textual knowledge bases (e.g., Wikipedia). In this paper, we propose a novel and simple technique for integrating the knowledge about concepts from two large scale knowledge bases of different structure (Wikipedia and Probase) in order to learn concept representations. We adapt the efficient skip-gram model to seamlessly learn from the knowledge in Wikipedia text and Probase concept graph. We evaluate our concept embedding models on two tasks: (1) analogical reasoning, where we achieve a state-of-the-art performance of 91% on semantic analogies, (2) concept categorization, where we achieve a state-of-the-art performance on two benchmark datasets achieving categorization accuracy of 100% on one and 98% on the other. Additionally, we present a case study to evaluate our model on unsupervised argument type identification for neural semantic parsing. We demonstrate the competitive accuracy of our unsupervised method and its ability to better generalize to out of vocabulary entity mentions compared to the tedious and error prone methods which depend on gazetteers and regular expressions.

We present a preview version of DeepSeek-V4 series, including two strong Mixture-of-Experts (MoE) language models -- DeepSeek-V4-Pro with 1.6T parameters (49B activated) and DeepSeek-V4-Flash with 284B parameters (13B activated) -- both supporting a context length of one million tokens. DeepSeek-V4 series incorporate several key upgrades in architecture and optimization: (1) a hybrid attention architecture that combines Compressed Sparse Attention (CSA) and Heavily Compressed Attention (HCA) to improve long-context efficiency; (2) Manifold-Constrained Hyper-Connections (mHC) that enhance conventional residual connections; (3) and the Muon optimizer for faster convergence and greater training stability. We pre-train both models on more than 32T diverse and high-quality tokens, followed by a comprehensive post-training pipeline that unlocks and further enhances their capabilities. DeepSeek-V4-Pro-Max, the maximum reasoning effort mode of DeepSeek-V4-Pro, redefines the state-of-the-art for open models, outperforming its predecessors in core tasks. Meanwhile, DeepSeek-V4 series are highly efficient in long-context scenarios. In the one-million-token context setting, DeepSeek-V4-Pro requires only 27% of single-token inference FLOPs and 10% of KV cache compared with DeepSeek-V3.2. This enables us to routinely support one-million-token contexts, thereby making long-horizon tasks and further test-time scaling more feasible. The model checkpoints are available at https://huggingface.co/collections/deepseek-ai/deepseek-v4.

Subtle hand differences make sign language recognition challenging, yet many existing methods rely on encoders pretrained on generic action datasets that poorly capture such fine-grained cues. We propose a self-supervised pretraining method for sign language recognition that uses segmentation-based masking to adapt to the presence and motion of key body parts, rather than treating hand poses as static visual tokens. The resulting mask-and-reconstruct objective improves fine-grained sign representation learning. On WLASL, NMFs-CSL, and Slovo, our encoder achieves state-of-the-art performance, improving per-instance and per-class Top-1 accuracy while using fewer input frames and modalities than comparable encoders.

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of least squares (LS) problems min_x|b-Ax|_2, where A in R^{mtimes n}, arise in numerous application areas. Overdetermined standard least squares problems can be solved by using mixed precision within the iterative refinement method of Björck, which transforms the least squares problem into an (m+n)times(m+n) ''augmented'' system. It has recently been shown that mixed precision GMRES-based iterative refinement can also be used, in an approach termed GMRES-LSIR. In practice, we often encounter types of least squares problems beyond standard least squares, including weighted least squares (WLS), min_x|D^{1/2}(b-Ax)|_2, where D^{1/2} is a diagonal matrix of weights. In this paper, we discuss a mixed precision FGMRES-WLSIR algorithm for solving WLS problems using two different preconditioners.