Ziang Chen, Guannan Li, Fanlin Ji, Yipeng Kang, Jiaqi Li, Muhan Zhang, Yangtao Zhang, Li Tianjiao, Jiannan Wang, Xin Guo, Song-Chun Zhu, Bin Ling. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Recent advancements in large language models (LLMs) have significantly enhanced their reasoning capabilities.However, they continue to struggle with basic character-level tasks, such as counting letters in words-a problem rooted in their tokenization process.While existing benchmarks have highlighted this weakness through basic character operations, such failures are often dismissed due to lacking practical relevance.Yet, many real-world applications, such as navigating text-based maps or interpreting structured tables, rely heavily on precise sub-token understanding.In this regard, we introduce SUBTOKENTEST, a comprehensive benchmark that assesses sub-token understanding through practical, utility-driven tasks.Our benchmark includes ten tasks across four domains and isolates tokenization-related failures by decoupling performance from complex reasoning.We provide a comprehensive evaluation of nine advanced LLMs.Additionally, we investigate the impact of test-time scaling on sub-token reasoning, explore how characterlevel information is encoded within the hidden states.

Yi Hu, Jiaqi Gu, Ruxin Wang, Zijun Yao, Hao Peng, Xiaobao Wu, Jianhui Chen, Muhan Zhang, Liangming Pan. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Large Language Models (LLMs) face the "knowledge cutoff" challenge, where their frozen parametric memory prevents direct internalization of new information.While Supervised Fine-Tuning (SFT) is commonly used to update model knowledge, it often updates factual content without reliably improving the model's ability to use the newly incorporated information for question answering or decisionmaking.Reinforcement Learning (RL) is essential for acquiring reasoning skills; however, its high computational cost makes it impractical for efficient online adaptation.We empirically observe that the parameter updates induced by SFT and RL are nearly orthogonal.Based on this observation, we propose Parametric Skill Transfer (PaST), a framework that supports modular skill transfer for efficient and effective knowledge adaptation.By extracting a domain-agnostic Skill Vector from a source domain, we can linearly inject knowledge manipulation skills into a target model after it has undergone lightweight SFT on new data.Experiments on knowledge-incorporation QA (SQuAD, LooGLE) and agentic tool-use benchmarks (ToolBench) demonstrate the effectiveness of our method.On SQuAD, PaST outperforms the state-of-the-art self-editing SFT baseline by up to 9.9 points.PaST further scales to long-context QA on LooGLE with an 8.0-point absolute accuracy gain, and improves zero-shot ToolBench success rates by +10.3 points on average with consistent gains across tool categories, indicating strong scalability and crossdomain transferability of the Skill Vector. Motivation: Functional Disconnect between Knowledge and ReasoningI'm trying to download a post and a reel from Instagram.Can you provide me with the download links for the post and reel?The post link is [post link] and the reel link is [reel link]. Standard SFT (Knowledge Only)Thought: I should call the 'posts_for_instagram_ reels_and_post_downloader' function with the argument 'link' set to [post link]… Action: posts_for_instagram_reels_and_post_ downloader Action Input: {"

Multi-Head Latent Attention (MLA), introduced in DeepSeek-V2, compresses key–value states into a low-rank latent vector cKV, caching only this vector to reduce memory. In tensor parallelism (TP), however, attention heads are computed across multiple devices, and each device must load the full cKV, eroding the advantage of MLA over Grouped Query Attention (GQA). We present TPLA, a scheme that partitions both the latent representation and each head's input dimension across devices, performs attention independently on each shard, and aggregates the results with an all-reduce. Unlike GLA, every attention head in TPLA still attends to the full latent space, preserving MLA's representational capacity while reducing the per-device KV cache. To make TPLA drop-in compatible with MLA checkpoints, we further derive orthogonal reparameterizations of RMSNorm and softmax---instantiated with Hadamard and PCA transforms---that mitigate cross-shard discrepancies when slicing latent vectors across devices. Finally, we introduce a prefill-decode separation scheme that keeps the MLA form during compute-bound prefilling and switches to TPLA during memory-bound decoding, minimizing conversion-induced error. By reducing the per-device KV cache for DeepSeek-V3 and Kimi-K2, we achieve 1.79x) and 1.93) speedups respectively, at a 32K-token context length while maintaining accuracy on commonsense and LongBench benchmarks. TPLA can be further implemented on top of FlashAttention-3, enabling practical end-to-end acceleration.

Recent advancements in graph neural networks (GNNs) for link prediction have introduced sophisticated training techniques and model architectures. However, reliance on outdated baselines may exaggerate the benefits of these new approaches. To tackle this issue, we systematically explore Graph Autoencoders (GAEs) by applying model-agnostic tricks in recent methods and tuning hyperparameters. We find that a well-tuned GAE can match the performance of recent sophisticated models while offering superior computational efficiency on widely used link prediction benchmarks. Our approach delivers substantial performance gains on datasets where structural information dominates and feature data is limited. Specifically, our GAE achieves a state-of-the-art (SOTA) Hits@100 score of 78.41% on the ogbl-ppa dataset. Furthermore, we examine the impact of various tricks to uncover the reasons behind our success and to guide the design of future methods. Our study emphasizes the critical need to update baselines for a more accurate assessment of progress in GNNs for link prediction. Our code is available at https://github.com/GraphPKU/Refined-GAE.

Subgraph Graph Neural Networks (GNNs) are emerging as a promising approach to enhance GNN expressiveness, but their more complex graph structures with numerous independent and irregular subgraphs pose significant hardware deployment challenges. In this work, we propose 3D-SubG, a 3D stacked hybrid processing-near/in-memory accelerator for subgraph GNNs. With hybrid bonding packaging technology, a logic die is 3D stacked with a DRAM die for highly parallel memory accesses. The logic die employs digital SRAM-based processing-in-memory (PIM) macros to boost computation density and minimize data transfer. We further propose a bit-level non-zero gathering method to exploit graph sparsity for PIM, a workloadbalanced mapping strategy for subgraph allocation onto different logic-to-DRAM blocks, and a distributed global pooling approach to reduce inter-block data movements. Experimental results show that 3D-SubG achieves average improvements of $146.11 \times$ in performance, $934.18 \times$ in area efficiency, and $1171.80 \times$ in energy efficiency compared to RTX 3090Ti.

Existing parameter-efficient fine-tuning (PEFT) methods for large language models (LLMs), such as LoRA and PiSSA, constrain model updates to low-rank subspaces, limiting their expressiveness and leading to suboptimal performance on complex tasks.To address this, we introduce High-rank Distributed PiSSA (HD-PiSSA 1 ), a distributed PEFT approach that initializes orthogonal adapters across different devices and aggregates their delta updates collectively on W for fine-tuning.Unlike Data Parallel LoRA or PiSSA, which maintain identical adapters across all devices, HD-PiSSA assigns different principal components of the pre-trained weights to each GPU, significantly expanding the range of update directions.This results in over 16× higher effective updated ranks than data-parallel LoRA or PiSSA when fine-tuning on 8 GPUs with the same per-device adapter rank.Empirically, we evaluate HD-PiSSA across various challenging downstream tasks, including mathematics, code generation, and multi-task learning.In the multi-task setting, HD-PiSSA achieves average gains of 10.0 absolute points (14.63%) over LoRA and 4.98 points (6.60%) over PiSSA across 12 benchmarks, demonstrating its benefits from the extra optimization flexibility.

Foundation models, such as Large Language Models (LLMs) or Large Vision Models (LVMs), have emerged as one of the most powerful tools in the respective fields. However, unlike text and image data, graph data do not have a definitive structure, posing great challenges to developing a Graph Foundation Model (GFM). For example, current attempts at designing general graph models either transform graph data into a language format for LLM-based prediction or still train a GNN model with LLM as an assistant. The former can handle unlimited tasks, while the latter captures graph structure much better---yet, no existing work can achieve both simultaneously. In this paper, we first identify three key desirable properties of a GFM: self-supervised pretraining, fluidity in tasks, and graph awareness. To account for these properties, we extend the conventional language modeling to the graph domain and propose a novel generative graph language model GOFA. The model interleaves randomly initialized GNN layers into a frozen pre-trained LLM so that the semantic and structural modeling abilities are organically combined. GOFA is pre-trained on newly proposed graph-level next-word prediction, question-answering, structural understanding, and information retrieval tasks to obtain the above GFM properties. The pre-trained model is further instruction fine-tuned to obtain the task-solving ability. Our GOFA model is evaluated on various downstream datasets unseen during the pre-training and fine-tuning phases, demonstrating a strong ability to solve structural and contextual problems in zero-shot scenarios. The code is available at https://github.com/JiaruiFeng/GOFA.

Invariant models, one important class of geometric deep learning models, are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. These models are characterized by their simplicity, good experimental results and computational efficiency. However, their theoretical expressive power still remains unclear, restricting a deeper understanding of the potential of such models. In this work, we concentrate on characterizing the theoretical expressiveness of a wide range of invariant models under *fully-connected* conditions. We first rigorously characterize the expressiveness of the most classic invariant model, message-passing neural networks incorporating distance (DisGNN), restricting its unidentifiable cases to be only highly symmetric point clouds. We then prove that GeoNGNN, the geometric counterpart of one of the simplest subgraph graph neural networks, can effectively break these corner cases' symmetry and thus achieve E(3)-completeness. By leveraging GeoNGNN as a theoretical tool, we further prove that: 1) most subgraph GNNs developed in traditional graph learning can be seamlessly extended to geometric scenarios with E(3)-completeness; 2) DimeNet, GemNet and SphereNet, three well-established invariant models, are also all capable of achieving E(3)-completeness. Our theoretical results fill the gap in the expressive power of invariant models, contributing to a rigorous and comprehensive understanding of their capabilities.

Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as $9.11 > 9.9$). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs.

Recent advances in molecular generative models have demonstrated great promise for accelerating scientific discovery, particularly in drug design. However, these models often struggle to generate high-quality molecules, especially in conditional scenarios where specific molecular properties must be satisfied. In this work, we introduce GeoRCG, a general framework to improve molecular generative models by integrating geometric representation conditions with provable theoretical guarantees. We decompose the generation process into two stages: first, generating an informative geometric representation; second, generating a molecule conditioned on the representation. Compared with single-stage generation, the easy-to-generate representation in the first stage guides the second stage generation toward a high-quality molecule in a goal-oriented way. Leveraging EDM and SemlaFlow as base generators, we observe significant quality improvements in unconditional molecule generation on the widely used QM9 and GEOM-DRUG datasets. More notably, in the challenging conditional molecular generation task, our framework achieves an average 50% performance improvement over state-of-the-art approaches, highlighting the superiority of conditioning on semantically rich geometric representations. Furthermore, with such representation guidance, the number of diffusion steps can be reduced to as small as 100 while largely preserving the generation quality achieved with 1,000 steps, thereby significantly reducing the generation iterations needed.

Decoder-only models generate tokens autoregressively by caching key/value vectors, but as the cache grows, inference becomes memory-bounded. To address this challenge, we introduce CLOVER (Cross-Layer Orthogonal Vectors) pruning, a novel approach that treats pairs of components of the attention mechanism as low-rank decompositions. CLOVER applies Singular Value Decomposition (SVD) to the Q-K and V-O pairs within each attention head. The resulting singular values, in turn, guide pruning and further serve as trainable parameters for efficient fine-tuning, ultimately enabling the model to recover its performance to the level before pruning.After pruning and fine-tuning, these values are reintegrated into the model without increasing its parameter count. Visualizations across various models show that CLOVER effectively removes linear redundancies within attention heads, greatly improving pruning efficiency. For example, pruning 70% of the Q-K head dimension in GPT-2 XL results in a perplexity comparable to that of pruning just 8% using vanilla pruning. The combination of CLOVER and TransMLA achieves a speedup of up to 11.1$\times$ over LLaMA-2-7B.

We introduce Griffin, the first foundation model attemptation designed specifically for Relational Databases (RDBs). Unlike previous smaller models focused on single RDB tasks, Griffin unifies the data encoder and task decoder to handle diverse tasks. Additionally, we enhance the architecture by incorporating a cross-attention module and a novel aggregator. Griffin utilizes pretraining on both single-table and RDB datasets, employing advanced encoders for categorical, numerical, and metadata features, along with innovative components such as cross-attention modules and enhanced message-passing neural networks (MPNNs) to capture the complexities of relational data. Evaluated on large-scale, heterogeneous, and temporal graphs extracted from RDBs across various domains (spanning over 150 million nodes), Griffin demonstrates superior or comparable performance to individually trained models, excels in low-data scenarios, and shows strong transferability with similarity and diversity in pretraining across new datasets and tasks, highlighting its potential as a universally applicable foundation model for RDBs. Code available at https://github.com/yanxwb/Griffin.

Large language models (LLMs) are equipped with increasingly extended context windows recently, yet their long context understanding capabilities over long dependency tasks remain fundamentally limited and underexplored. This gap is especially significant in many real-world long-context applications that were rarely benchmarked. In this paper, we introduce $\textbf{LooGLE v2}$, a novel benchmark designed to evaluate LLMs' long context ability in real-world applications and scenarios. Our benchmark consists of automatically collected real-world long texts, ranging from 16k to 2M tokens, encompassing domains in law, finance, game and code. Accordingly, we delicately design 10 types of domain-specific long-dependency tasks and generate 1,934 QA instances with various diversity and complexity in a scalable data curation pipeline for further practical needs. We conduct a comprehensive assessment of 6 locally deployed and 4 API-based LLMs. The evaluation results show that even the best-performing model achieves only a 59.2\% overall score on our benchmark. Despite the extensive context windows, popular LLMs are only capable of understanding a much shorter length of context than they claim to be, revealing significant limitations in their ability to handle real-world tasks with long dependencies and highlighting substantial room for model improvement in practical long-context understanding.

Length generalization—the ability to solve problems longer than those seen during training—remains a critical challenge for large language models (LLMs). Previous work modifies positional encodings (PEs) and data formats to improve length generalization on specific symbolic tasks such as addition and sorting. However, these approaches are fundamentally limited to special tasks, often degrading general language performance. Furthermore, they are typically evaluated on small transformers trained from scratch on single tasks and can cause performance drop when applied during post-training stage of practical LLMs with general capabilities. Hu et al., (2024) proposed Rule-Following Fine-Tuning (RFFT) to improve length generalization in the post-training stage of LLMs. Despite its compatibility with practical models and strong performance, RFFT is proposed for single tasks too, requiring re-training for each individual task with extensive examples. In this paper, we study length generalization in multi-task settings and propose *Meta Rule-Following Fine-Tuning (Meta-RFFT)*, the first framework enabling robust *cross-task* length generalization. As our first contribution, we construct a large length generalization dataset containing **86 tasks** spanning code execution, number processing, symbolic and logical reasoning tasks, beyond the common addition or multiplication tasks. Secondly, we show that cross-task length generalization is possible with Meta-RFFT—after training on a large number of tasks and instances, the models achieve remarkable length generalization ability on *unseen* tasks with *minimal fine-tuning or one-shot prompting*. For example, after fine-tuning on 1 to 5 digit addition, our 32B model **achieves 95% accuracy on 30 digit addition**, significantly outperforming the state-of-the-art reasoning models (DeepSeek-R1-671B: 72%; QwQ-32B: 32%), despite never seeing this task during RF-pretraining.

As Large Language Models (LLMs) are frequently updated, LoRA weights trained on earlier versions quickly become obsolete. The conventional practice of retraining LoRA weights from scratch on the latest model is costly, time-consuming, and environmentally detrimental, particularly as the diversity of LLMs and downstream tasks expands. This motivates a critical question: "How can we efficiently leverage existing LoRA weights to adapt to newer model versions?" To address this, we propose LoRASuite, a modular approach tailored specifically to various types of LLM updates. First, we compute a transfer matrix utilizing known parameters from both old and new LLMs. Next, we allocate corresponding layers and attention heads based on centered kernel alignment and cosine similarity metrics, respectively. A subsequent small-scale, skillful fine-tuning step ensures numerical stability. Experimental evaluations demonstrate that LoRASuite consistently surpasses small-scale vanilla LoRA methods. Notably, on backbone LLMs such as MiniCPM and Qwen, LoRASuite even exceeds the performance of full-scale LoRA retraining, with average improvements of +1.4 and +6.6 points on math tasks, respectively. Additionally, LoRASuite significantly reduces memory consumption by 5.5 GB and computational time by 78.23%.

Modern large-language models often face communication bottlenecks on current hardware rather than computational limitations. *Multi-head latent attention (MLA)* addresses this by compressing the key-value cache using low-rank matrices, while the Absorb operation prevents the KV cache from reverting to its original size, significantly boosting both training and inference speed. Despite the success of DeepSeek V2/V3/R1, most model providers have heavily invested in optimizing GQA-based models and, therefore, lack strong incentives to retrain MLA-based models from scratch. This paper demonstrates that MLA provides superior expressive power compared to GQA with the same KV cache overhead, thereby offering a rationale for transitioning from GQA to MLA. In addition, we introduce TransMLA, a framework that seamlessly converts any GQA-based pre-trained model (e.g., LLaMA, Qwen, Gemma, Mistral/Mixtral) into an MLA-based model. For the first time, our method enables *direct conversion of these models into a format compatible with DeepSeek's codebase*, allowing them to fully leverage the existing, highly-optimized support for the DeepSeek architecture within inference engines like vLLM and SGlang. By compressing 93\% of the KV cache in LLaMA-2-7B, we achieve a **10x speedup** with an 8K context length while maintaining meaningful output. Moreover, the model requires only **6B tokens** for fine-tuning to recover comparable performance across multiple benchmarks. TransMLA provides a practical path for migrating GQA-based models to the MLA structure, and when combined with DeepSeek’s advanced optimizations—such as FP8 quantization and Multi-Token Prediction—further inference acceleration can be achieved.

Current benchmarks for evaluating the reasoning capabilities of Large Language Models (LLMs) face significant limitations: task oversimplification, data contamination, and flawed evaluation items. These deficiencies necessitate more rigorous assessment methods. To address these limitations, we introduce PHYBench, a benchmark of 500 original physics problems ranging from high school to Physics Olympiad difficulty. PHYBench addresses data contamination through original content and employs a systematic curation pipeline to eliminate flawed items. Evaluations show that PHYBench activates more tokens and provides stronger differentiation between reasoning models compared to other baselines like AIME 2024, OlympiadBench and GPQA. Even the best-performing model, Gemini 2.5 Pro, achieves only 36.9\% accuracy compared to human experts' 61.9\%. To further enhance evaluation precision, we introduce the Expression Edit Distance (EED) Score for mathematical expression assessment, which improves sample efficiency by 204\% over binary scoring. Moreover, PHYBench effectively elicits multi-step and multi-condition reasoning, providing a platform for examining models' reasoning robustness, preferences, and deficiencies. The benchmark results and dataset are publicly available at https://www.phybench.cn/.

Common Neighbors (CNs) and their higher-order variants are important pairwise features widely used in state-of-the-art link prediction methods. However, existing methods often struggle with the repetition across different orders of CNs and fail to fully leverage their potential. We identify that these limitations stem from two key issues: redundancy and over-smoothing in high-order common neighbors. To address these challenges, we design orthogonalization to eliminate redundancy between different-order CNs and normalization to mitigate over-smoothing. By combining these two techniques, we propose Orthogonal Common Neighbor (OCN), a novel approach that significantly outperforms the strongest baselines by an average of 7.7\% on popular link prediction benchmarks. A thorough theoretical analysis is provided to support our method. Ablation studies also verify the effectiveness of our orthogonalization and normalization techniques.

In this paper, we study using graph neural networks (GNNs) for multi-node representation learning, where a representation for a set of more than one node (such as a link) is to be learned. Existing GNNs are mainly designed to learn single-node representations. When used for multi-node representation learning, a common practice is to directly aggregate the single-node representations obtained by a GNN. In this paper, we show a fundamental limitation of such an approach, namely the inability to capture the dependence among multiple nodes in the node set. A straightforward solution is to distinguish target nodes from others. Formalizing this idea, we propose \text{labeling trick}, which first labels nodes in the graph according to their relationships with the target node set before applying a GNN and then aggregates node representations obtained in the labeled graph for multi-node representations. Besides node sets in graphs, we also extend labeling tricks to posets, subsets and hypergraphs. Experiments verify that the labeling trick technique can boost GNNs on various tasks, including undirected link prediction, directed link prediction, hyperedge prediction, and subgraph prediction. Our work explains the superior performance of previous node-labeling-based methods and establishes a theoretical foundation for using GNNs for multi-node representation learning.

This paper explores the potential role of AI, e.g., large language models (LLMs), in supporting theme development in thematic analysis. While prior applications of AI in qualitative data analysis have focused on supporting coding, we investigate whether LLMs can effectively contribute as collaborators in the more abstract and conceptual phases of qualitative analysis, specifically theme development. Despite growing interest in AI as a collaborator in theme development, there is limited empirical evidence on designing AI-assisted tools while supporting user autonomy and understanding researcher interaction with AI-assisted theme development. To address this gap, we designed ThemeViz, an interactive system that uses GPT-4 to generate and visualize multiple versions of themes based on user input while allowing researchers to maintain control through manual coding and theme development. Our study examines the effectiveness of this human-AI collaboration approach in iterative theme development and its implications for future designs.

Large language models (LLMs) are typically limited to processing texts within contextwindow size, which has spurred significant research efforts into enhancing LLMs' longcontext understanding as well as developing high-quality benchmarks to evaluate the ability.However, prior datasets suffer from shortcomings like short length compared to the context window of modern LLMs; outdated documents that might have data leakage problems; and an emphasis on short dependency tasks only.In this paper, we present ooGLE , a Long Context Generic Language Evaluation benchmark.It features documents post-2022, with over 24,000 tokens per document and 6,000 newly generated questions spanning varying dependency ranges in diverse domains.Human annotators meticulously crafted over 1,100 high-quality question-answer (QA) pairs with thorough cross-validation for a most precise assessment of LLMs' long dependency capabilities.We conduct a comprehensive evaluation of representative LLMs on ooGLE .The results indicate that most LLMs have shockingly bad long context ability and fail to capture long dependencies in the context, even when their context window size is enough to fit the entire document.Our results shed light on enhancing the "true long-context understanding" ability of LLMs instead of merely enlarging their context window.

GNN-to-MLP distillation aims to utilize knowledge distillation (KD) to learn computationally-efficient multi-layer perceptron (student MLP) on graph data by mimicking the output representations of teacher GNN. Existing methods mainly make the MLP to mimic the GNN predictions over a few class labels. However, the class space may not be expressive enough for covering numerous diverse local graph structures, thus limiting the performance of knowledge transfer from GNN to MLP. To address this issue, we propose to learn a new powerful graph representation space by directly labeling nodes' diverse local structures for GNN-to-MLP distillation. Specifically, we propose a variant of VQ-VAE to learn a structure-aware tokenizer on graph data that can encode each node's local substructure as a discrete code. The discrete codes constitute a codebook as a new graph representation space that is able to identify different local graph structures of nodes with the corresponding code indices. Then, based on the learned codebook, we propose a new distillation target, namely soft code assignments, to directly transfer the structural knowledge of each node from GNN to MLP. The resulting framework VQGraph achieves new state-of-the-art performance on GNN-to-MLP distillation in both transductive and inductive settings across seven graph datasets. We show that VQGraph with better performance infers faster than GNNs by 828×, and also achieves accuracy improvement over GNNs and stand-alone MLPs by 3.90% and 28.05% on average, respectively. Our code is available at https://github.com/YangLing0818/VQGraph

Designing a single model to address multiple tasks has been a long-standing objective in artificial intelligence. Recently, large language models have demonstrated exceptional capability in solving different tasks within the language domain. However, a unified model for various graph tasks remains underexplored, primarily due to the challenges unique to the graph learning domain. First, graph data from different areas carry distinct attributes and follow different distributions. Such discrepancy makes it hard to represent graphs in a single representation space. Second, tasks on graphs diversify into node, link, and graph tasks, requiring distinct embedding strategies. Finally, an appropriate graph prompting paradigm for in-context learning is unclear. We propose **One for All (OFA)**, the first general framework that can use a single graph model to address the above challenges. Specifically, OFA proposes text-attributed graphs to unify different graph data by describing nodes and edges with natural language and uses language models to encode the diverse and possibly cross-domain text attributes to feature vectors in the same embedding space. Furthermore, OFA introduces the concept of nodes-of-interest to standardize different tasks with a single task representation. For in-context learning on graphs, OFA introduces a novel graph prompting paradigm that appends prompting substructures to the input graph, which enables it to address varied tasks without fine-tuning. We train the OFA model using graph data from multiple domains (including citation networks, molecular graphs, knowledge graphs, etc.) simultaneously and evaluate its ability in supervised, few-shot, and zero-shot learning scenarios. OFA performs well across different tasks, making it the first general-purpose across-domains classification model on graphs.

The expressivity of Graph Neural Networks (GNNs) has been studied broadly in recent years to reveal the design principles for more powerful GNNs. Graph canonization is known as a typical approach to distinguish non-isomorphic graphs, yet rarely adopted when developing expressive GNNs. This paper proposes to maximize the expressivity of GNNs by graph canonization, then the power of such GNNs is studies from the perspective of model stability. A stable GNN will map similar graphs to close graph representations in the vectorial space, and the stability of GNNs is critical to generalize their performance to unseen graphs. We theoretically reveal the trade-off of expressivity and stability in graph-canonization-enhanced GNNs. Then we introduce a notion of universal graph canonization as the general solution to address the trade-off and characterize a widely applicable sufficient condition to solve the universal graph canonization. A comprehensive set of experiments demonstrates the effectiveness of the proposed method. In many popular graph benchmark datasets, graph canonization successfully enhances GNNs and provides highly competitive performance, indicating the capability and great potential of proposed method in general graph representation learning. In graph datasets where the sufficient condition holds, GNNs enhanced by universal graph canonization consistently outperform GNN baselines and successfully improve the SOTA performance up to $31$%, providing the optimal solution to numerous challenging real-world graph analytical tasks like gene network representation learning in bioinformatics.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) *Non-uniqueness*: there are many different eigendecompositions of the same Laplacian, and (2) *Instability*: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be the use of "hard partition'' of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to ``softly partition'' eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods. Our code is available at https://github.com/Graph-COM/SPE.

In this work, we propose a novel link prediction model and further boost it by studying graph incompleteness. First, We introduce MPNN-then-SF, an innovative architecture leveraging structural feature (SF) to guide MPNN's representation pooling, with its implementation, namely Neural Common Neighbor (NCN). NCN exhibits superior expressiveness and scalability compared with existing models, which can be classified into two categories: SF-then-MPNN, augmenting MPNN's input with SF, and SF-and-MPNN, decoupling SF and MPNN. Second, we investigate the impact of graph incompleteness---the phenomenon that some links are unobserved in the input graph---on SF, like the common neighbor. Through dataset visualization, we observe that incompleteness reduces common neighbors and induces distribution shifts, significantly affecting model performance. To address this issue, we propose to use a link prediction model to complete the common neighbor structure. Combining this method with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins, and NCNC further surpasses state-of-the-art models in standard link prediction benchmarks.

Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn basic *rules* of addition and apply them to new problems of any length, LLMs struggle to do the same. Instead, they may rely on similar *cases* seen in the training corpus for help. We define these two different reasoning mechanisms as "*rule-based reasoning*" and "*case-based reasoning*". Since rule-based reasoning is essential for acquiring systematic generalization ability, we aim to explore exactly whether transformers use rule-based or case-based reasoning for math problems. Through carefully designed intervention experiments on five math tasks, we confirm that transformers are performing case-based reasoning, no matter whether scratchpad is used, which aligns with the previous observations that transformers use subgraph matching/shortcut learning to reason. To mitigate such problems, we propose a Rule-Following Fine-Tuning (RFFT) technique to teach transformers to perform rule-based reasoning. Specifically, we provide explicit rules in the input and then instruct transformers to recite and follow the rules step by step. Through RFFT, we successfully enable LLMs fine-tuned on 1-5 digit addition to generalize to up to 12-digit addition with over 95% accuracy, which is over 40% higher than scratchpad. The significant improvement demonstrates that teaching LLMs to use rules explicitly helps them learn rule-based reasoning and generalize better in length. Code is available at https://github.com/GraphPKU/Case_or_Rule.

Graph is a fundamental data structure to model interconnections between entities. Set, on the contrary, stores independent elements. To learn graph representations, current Graph Neural Networks (GNNs) primarily use message passing to encode the interconnections. In contrast, this paper introduces a novel graph-to-set conversion method that bijectively transforms interconnected nodes into a set of independent points and then uses a set encoder to learn the graph representation. This conversion method holds dual significance. Firstly, it enables using set encoders to learn from graphs, thereby significantly expanding the design space of GNNs. Secondly, for Transformer, a specific set encoder, we provide a novel and principled approach to inject graph information losslessly, different from all the heuristic structural/positional encoding methods adopted in previous graph transformers. To demonstrate the effectiveness of our approach, we introduce Point Set Transformer (PST), a transformer architecture that accepts a point set converted from a graph as input. Theoretically, PST exhibits superior expressivity for both short-range substructure counting and long-range shortest path distance tasks compared to existing GNNs. Extensive experiments further validate PST’s outstanding real-world performance. Besides Transformer, we also devise a Deepset-based set encoder, which achieves performance comparable to representative GNNs, affirming the versatility of our graph-to-set method.

Research on the theoretical expressiveness of Graph Neural Networks (GNNs) has developed rapidly, and many methods have been proposed to enhance the expressiveness. However, most methods do not have a uniform expressiveness measure except for a few that strictly follow the $k$-dimensional Weisfeiler-Lehman ($k$-WL) test hierarchy, leading to difficulties in quantitatively comparing their expressiveness. Previous research has attempted to use datasets for measurement, but facing problems with difficulty (any model surpassing 1-WL has nearly 100% accuracy), granularity (models tend to be either 100% correct or near random guess), and scale (only several essentially different graphs involved). To address these limitations, we study the realized expressive power that a practical model instance can achieve using a novel expressiveness dataset, BREC, which poses greater difficulty (with up to 4-WL-indistinguishable graphs), finer granularity (enabling comparison of models between 1-WL and 3-WL), a larger scale (consisting of 800 1-WL-indistinguishable graphs that are non-isomorphic to each other). We synthetically test 23 models with higher-than-1-WL expressiveness on BREC. Our experiment gives the first thorough measurement of the realized expressiveness of those state-of-the-art beyond-1-WL GNN models and reveals the gap between theoretical and realized expressiveness. Dataset and evaluation codes are released at: https://github.com/GraphPKU/BREC.

We investigate the enhancement of graph neural networks' (GNNs) representation power through their ability in substructure counting. Recent advances have seen the adoption of subgraph GNNs, which partition an input graph into numerous subgraphs, subsequently applying GNNs to each to augment the graph's overall representation. Despite their ability to identify various substructures, subgraph GNNs are hindered by significant computational and memory costs. In this paper, we tackle a critical question: Is it possible for GNNs to count substructures both efficiently and provably? Our approach begins with a theoretical demonstration that the distance to rooted nodes in subgraphs is key to boosting the counting power of subgraph GNNs. To avoid the need for repetitively applying GNN across all subgraphs, we introduce precomputed structural embeddings that encapsulate this crucial distance information. Experiments validate that our proposed model retains the counting power of subgraph GNNs while achieving significantly faster performance.

To parameter-efficiently fine-tune (PEFT) large language models (LLMs), the low-rank adaptation (LoRA) method approximates the model changes $\Delta W \in \mathbb{R}^{m \times n}$ through the product of two matrices $A \in \mathbb{R}^{m \times r}$ and $B \in \mathbb{R}^{r \times n}$, where $r \ll \min(m, n)$, $A$ is initialized with Gaussian noise, and $B$ with zeros. LoRA **freezes the original model $W$** and **updates the "Noise \& Zero" adapter**, which may lead to slow convergence. To overcome this limitation, we introduce **P**r**i**ncipal **S**ingular values and **S**ingular vectors **A**daptation (PiSSA). PiSSA shares the same architecture as LoRA, but initializes the adaptor matrices $A$ and $B$ with the principal components of the original matrix $W$, and put the remaining components into a residual matrix $W^{res} \in \mathbb{R}^{m \times n}$ which is frozen during fine-tuning. Compared to LoRA, PiSSA **updates the principal components** while **freezing the "residual" parts**, allowing faster convergence and enhanced performance. Comparative experiments of PiSSA and LoRA across 11 different models, ranging from 184M to 70B, encompassing 5 NLG and 8 NLU tasks, reveal that PiSSA consistently outperforms LoRA under identical experimental setups. On the GSM8K benchmark, Gemma-7B fine-tuned with PiSSA achieves an accuracy of 77.7\%, surpassing LoRA's 74.53\% by 3.25\%. Due to the same architecture, PiSSA is also compatible with quantization to further reduce the memory requirement of fine-tuning. Compared to QLoRA, QPiSSA (PiSSA with 4-bit quantization) exhibits smaller quantization errors in the initial stages. Fine-tuning LLaMA-3-70B on GSM8K, QPiSSA attains an accuracy of 86.05\%, exceeding the performances of QLoRA at 81.73\%. Leveraging a fast SVD technique, PiSSA can be initialized in only a few seconds, presenting a negligible cost for transitioning from LoRA to PiSSA.

Large Language Models (LLMs) trained on massive corpora have shown remarkable success in knowledge-intensive tasks. Yet, most of them rely on pre-stored knowledge. Inducing new general knowledge from a specific environment andperforming reasoning with the acquired knowledge—situated inductive reasoning, is crucial and challenging for machine intelligence. In this paper, we design Mars, an interactive environment devised for situated inductive reasoning. It introduces counter-commonsense game mechanisms by modifying terrain, survival setting and task dependency while adhering to certain principles. In Mars, agents need to actively interact with their surroundings, derive useful rules and perform decision-making tasks in specific contexts. We conduct experiments on various RL-based and LLM-based methods, finding that they all struggle on this challenging situated inductive reasoning benchmark. Furthermore, we explore Induction from Reflection, where we instruct agents to perform inductive reasoning from history trajectory. The superior performance underscores the importance of inductive reasoning in Mars. Through Mars, we aim to galvanize advancements in situated inductive reasoning and set the stage for developing the next generation of AI systems that can reason in an adaptive and context-sensitive way.

Given a relational database (RDB), how can we predict missing column values in some target table of interest? Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks. From a delivery standpoint, we operationalize the above four dimensions (4D) of exploration within a unified, scalable open-source toolbox called 4DBInfer; please see https://github.com/awslabs/multi-table-benchmark .

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) using one formulation. We first formulate prediction tasks including regression and classification into a generic (conditional) generation framework, which enables diffusion models to perform deterministic tasks with provable guarantees. We then propose Latent Graph Diffusion (LGD), a generative model that can generate node, edge, and graph-level features of all categories simultaneously. We achieve this goal by embedding the graph structures and features into a latent space leveraging a powerful encoder and decoder, then training a diffusion model in the latent space. LGD is also capable of conditional generation through a specifically designed cross-attention mechanism. Leveraging LGD and the ``all tasks as generation'' formulation, our framework is capable of solving graph tasks of various levels and types. We verify the effectiveness of our framework with extensive experiments, where our models achieve state-of-the-art or highly competitive results across a wide range of generation and regression tasks.

Many graph neural networks (GNNs) are inapplicable when the graph structure representing the node relations is unavailable. Recent studies have shown that this problem can be effectively solved by jointly learning the graph structure and the parameters of GNNs. However, most of these methods learn graphs by using either a Euclidean or hyperbolic metric, which means that the space curvature is assumed to be either constant zero or constant negative. Graph embedding spaces usually have nonconstant curvatures, and thus, such an assumption may produce some obfuscatory nodes, which are improperly embedded and close to multiple categories. In this article, we propose a joint-space graph learning (JSGL) method for GNNs. JSGL learns a graph based on Euclidean embeddings and identifies Euclidean obfuscatory nodes. Then, the graph topology near the identified obfuscatory nodes is refined in hyperbolic space. We also present a theoretical justification of our method for identifying obfuscatory nodes and conduct a series of experiments to test the performance of JSGL. The results show that JSGL outperforms many baseline methods. To obtain more insights, we analyze potential reasons for this superior performance.

Modern large-scale designs make extensive use of heterogeneous macros, which can significantly affect routability. Predicting the final routing quality in the early macro placement stage can filter out poor solutions and speed up design closure. By observing that routing is correlated with the relative positions between instances, we propose MacroRank, a macro placement ranking framework leveraging translation equivariance and a Learning to Rank technique. The framework is able to learn the relative order of macro placement solutions and rank them based on routing quality metrics like wirelength, number of vias, and number of shorts. The experimental results show that compared with the most recent baseline, our framework can improve the Kendall rank correlation coefficient by 49.5% and the average performance of top-30 prediction by 8.1%, 2.3%, and 10.6% on wirelength, vias, and shorts, respectively.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler-Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve graph isomorphism distinguishing power of message passing neural networks. The method is then extended to higher-dimensional WL, leading to a novel $k,l$-WL algorithm, a more general framework than $k$-WL. We further introduce the subgraph concept into our hierarchy and propose a localized $k,l$-WL framework, incorporating a wide range of existing work, including many subgraph GNNs. Theoretically, we analyze the expressivity of $k,l$-WL w.r.t. $k$ and $l$ and compare it with the traditional $k$-WL. Complexity reduction methods are also systematically discussed to build powerful and practical $k,l$-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our $k,l$-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

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 $k \geq 2$) 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.

While Graph Neural Networks (GNNs) recently became powerful tools in graph learning tasks, considerable efforts have been spent on improving GNNs' structural encoding ability. A particular line of work proposed subgraph GNNs that use subgraph information to improve GNNs' expressivity and achieved great success. However, such effectivity sacrifices the efficiency of GNNs by enumerating all possible subgraphs. In this paper, we analyze the necessity of complete subgraph enumeration and show that a model can achieve a comparable level of expressivity by considering a small subset of the subgraphs. We then formulate the identification of the optimal subset as a combinatorial optimization problem and propose Magnetic Graph Neural Network (MAG-GNN), a reinforcement learning (RL) boosted GNN, to solve the problem. Starting with a candidate subgraph set, MAG-GNN employs an RL agent to iteratively update the subgraphs to locate the most expressive set for prediction. This reduces the exponential complexity of subgraph enumeration to the constant complexity of a subgraph search algorithm while keeping good expressivity. We conduct extensive experiments on many datasets, showing that MAG-GNN achieves competitive performance to state-of-the-art methods and even outperforms many subgraph GNNs. We also demonstrate that MAG-GNN effectively reduces the running time of subgraph GNNs.

Graph Neural Networks (GNNs) are often used for tasks involving the 3D geometry of a given graph, such as molecular dynamics simulation. While incorporating Euclidean distance into Message Passing Neural Networks (referred to as Vanilla DisGNN) is a straightforward way to learn the geometry, it has been demonstrated that Vanilla DisGNN is geometrically incomplete. In this work, we first construct families of novel and symmetric geometric graphs that Vanilla DisGNN cannot distinguish even when considering all-pair distances, which greatly expands the existing counterexample families. Our counterexamples show the inherent limitation of Vanilla DisGNN to capture symmetric geometric structures. We then propose $k$-DisGNNs, which can effectively exploit the rich geometry contained in the distance matrix. We demonstrate the high expressive power of $k$-DisGNNs from three perspectives: 1. They can learn high-order geometric information that cannot be captured by Vanilla DisGNN. 2. They can unify some existing well-designed geometric models. 3. They are universal function approximators from geometric graphs to scalars (when $k\geq 2$) and vectors (when $k\geq 3$). Most importantly, we establish a connection between geometric deep learning (GDL) and traditional graph representation learning (GRL), showing that those highly expressive GNN models originally designed for GRL can also be applied to GDL with impressive performance, and that existing complicated, equivariant models are not the only solution. Experiments verify our theory. Our $k$-DisGNNs achieve many new state-of-the-art results on MD17.

The ability of graph neural networks (GNNs) to count certain graph substructures, especially cycles, is important for the success of GNNs on a wide range of tasks. It has been recently used as a popular metric for evaluating the expressive power of GNNs. Many of the proposed GNN models with provable cycle counting power are based on subgraph GNNs, i.e., extracting a bag of subgraphs from the input graph, generating representations for each subgraph, and using them to augment the representation of the input graph. However, those methods require heavy preprocessing, and suffer from high time and memory costs. In this paper, we overcome the aforementioned limitations of subgraph GNNs by proposing a novel class of GNNs---$d$-Distance-Restricted FWL(2) GNNs, or $d$-DRFWL(2) GNNs, based on the well-known FWL(2) algorithm. As a heuristic method for graph isomorphism testing, FWL(2) colors all node pairs in a graph and performs message passing among those node pairs. In order to balance the expressive power and complexity, $d$-DRFWL(2) GNNs simplify FWL(2) by restricting the range of message passing to node pairs whose mutual distances are at most $d$. This way, $d$-DRFWL(2) GNNs exploit graph sparsity while avoiding the expensive subgraph extraction operations in subgraph GNNs, making both the time and space complexity lower. We theoretically investigate both the discriminative power and the cycle counting power of $d$-DRFWL(2) GNNs. Our most important finding is that $d$-DRFWL(2) GNNs have provably strong cycle counting power even with $d=2$: they can count all 3, 4, 5, 6-cycles. Since 6-cycles (e.g., benzene rings) are ubiquitous in organic molecules, being able to detect and count them is crucial for achieving robust and generalizable performance on molecular tasks. Experiments on both synthetic datasets and molecular datasets verify our theory. To the best of our knowledge, 2-DRFWL(2) GNN is the most efficient GNN model to date (both theoretically and empirically) that can count up to 6-cycles.

Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.

Subgraph-based graph representation learning (SGRL) has recently emerged as a powerful tool in many prediction tasks on graphs due to its advantages in model expressiveness and generalization ability. Most previous SGRL models face computational issues related to the high cost of extracting subgraphs for each training or testing query. Recently, SUREL was proposed to accelerate SGRL, which samples random walks offline and joins these walks online as a proxy of subgraphs for prediction. Thanks to the reusability of sampled walks across different queries, SUREL achieves state-of-the-art performance in terms of scalability and prediction accuracy. However, SUREL still suffers from high computational overhead caused by node redundancy in sampled walks. In this work, we propose a novel framework SUREL+ that upgrades SUREL by using node sets instead of walks to represent subgraphs. By definition, such set-based representations avoid repeated nodes, but node sets can be irregular in size. To solve this issue, we design a dedicated sparse data structure to efficiently store and access node sets, and provide a specialized operator to join them in parallel batches. SUREL+ is modularized to support multiple types of set samplers, structural features, and neural encoders to complement the loss of structural information after the reduction from walks to sets. Extensive experiments have been performed to verify the effectiveness of SUREL+ in the prediction tasks of links, relation types, and higher-order patterns. SUREL+ achieves 3--11× speedups of SUREL while maintaining comparable or even better prediction performance; compared to other SGRL baselines, SUREL+ achieves ~20× speedups and significantly improves the prediction accuracy.

Optimization of directed acyclic graph (DAG) structures has many applications, such as neural architecture search (NAS) and probabilistic graphical model learning. Encoding DAGs into real vectors is a dominant component in most neural-network-based DAG optimization frameworks. Currently, most popular DAG encoders use an asynchronous message passing scheme which sequentially processes nodes according to the dependency between nodes in a DAG. That is, a node must not be processed until all its predecessors are processed. As a result, they are inherently not parallelizable. In this work, we propose a Parallelizable Attention-based Computation structure Encoder (PACE) that processes nodes simultaneously and encodes DAGs in parallel. We demonstrate the superiority of PACE through encoder-dependent optimization subroutines that search the optimal DAG structure based on the learned DAG embeddings. Experiments show that PACE not only improves the effectiveness over previous sequential DAG encoders with a significantly boosted training and inference speed, but also generates smooth latent (DAG encoding) spaces that are beneficial to downstream optimization subroutines.

Deep learning has achieved tremendous success in designing novel chemical compounds with desirable pharmaceutical properties. In this work, we focus on a new type of drug design problem — generating a small “linker” to physically attach two independent molecules with their distinct functions. The main computational challenges include: 1) the generation of linkers is conditional on the two given molecules, in contrast to generating complete molecules from scratch in previous works; 2) linkers heavily depend on the anchor atoms of the two molecules to be connected, which are not known beforehand; 3) 3D structures and orientations of the molecules need to be considered to avoid atom clashes, for which equivariance to E(3) group are necessary. To address these problems, we propose a conditional generative model, named 3DLinker, which is able to predict anchor atoms and jointly generate linker graphs and their 3D structures based on an E(3) equivariant graph variational autoencoder. So far as we know, no previous models could achieve this task. We compare our model with multiple conditional generative models modified from other molecular design tasks and find that our model has a significantly higher rate in recovering molecular graphs, and more importantly, accurately predicting the 3D coordinates of all the atoms.

Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral GNNs. This paper studies spectral GNNs’ expressive power theoretically. We first prove that even spectral GNNs without nonlinearity can produce arbitrary graph signals and give two conditions for reaching universality. They are: 1) no multiple eigenvalues of graph Laplacian, and 2) no missing frequency components in node features. We also establish a connection between the expressive power of spectral GNNs and Graph Isomorphism (GI) testing, the latter of which is often used to characterize spatial GNNs’ expressive power. Moreover, we study the difference in empirical performance among different spectral GNNs with the same expressive power from an optimization perspective, and motivate the use of an orthogonal basis whose weight function corresponds to the graph signal density in the spectrum. Inspired by the analysis, we propose JacobiConv, which uses Jacobi basis due to its orthogonality and flexibility to adapt to a wide range of weight functions. JacobiConv deserts nonlinearity while outperforming all baselines on both synthetic and real-world datasets.

The most popular design paradigm for Graph Neural Networks (GNNs) is 1-hop message passing---aggregating information from 1-hop neighbors repeatedly. However, the expressive power of 1-hop message passing is bounded by the Weisfeiler-Lehman (1-WL) test. Recently, researchers extended 1-hop message passing to $K$-hop message passing by aggregating information from $K$-hop neighbors of nodes simultaneously. However, there is no work on analyzing the expressive power of $K$-hop message passing. In this work, we theoretically characterize the expressive power of $K$-hop message passing. Specifically, we first formally differentiate two different kernels of $K$-hop message passing which are often misused in previous works. We then characterize the expressive power of $K$-hop message passing by showing that it is more powerful than 1-WL and can distinguish almost all regular graphs. Despite the higher expressive power, we show that $K$-hop message passing still cannot distinguish some simple regular graphs and its expressive power is bounded by 3-WL. To further enhance its expressive power, we introduce a KP-GNN framework, which improves $K$-hop message passing by leveraging the peripheral subgraph information in each hop. We show that KP-GNN can distinguish many distance regular graphs which could not be distinguished by previous distance encoding or 3-WL methods. Experimental results verify the expressive power and effectiveness of KP-GNN. KP-GNN achieves competitive results across all benchmark datasets.

Graph Neural Networks (GNNs) have recently been applied to graph learning tasks and achieved state-of-the-art (SOTA) results. However, many competitive methods run GNNs multiple times with subgraph extraction and customized labeling to capture information that is hard for normal GNNs to learn. Such operations are time-consuming and do not scale to large graphs. In this paper, we propose an efficient GNN framework called Geodesic GNN (GDGNN) that requires only one GNN run and injects conditional relationships between nodes into the model without labeling. This strategy effectively reduces the runtime of subgraph methods. Specifically, we view the shortest paths between two nodes as the spatial graph context of the neighborhood around them. The GNN embeddings of nodes on the shortest paths are used to generate geodesic representations. Conditioned on the geodesic representations, GDGNN can generate node, link, and graph representations that carry much richer structural information than plain GNNs. We theoretically prove that GDGNN is more powerful than plain GNNs. We present experimental results to show that GDGNN achieves highly competitive performance with SOTA GNN models on various graph learning tasks while taking significantly less time.

Most knowledge graphs (KGs) are incomplete, which motivates one important research topic on automatically complementing knowledge graphs. However, evaluation of knowledge graph completion (KGC) models often ignores the incompleteness---facts in the test set are ranked against all unknown triplets which may contain a large number of missing facts not included in the KG yet. Treating all unknown triplets as false is called the closed-world assumption. This closed-world assumption might negatively affect the fairness and consistency of the evaluation metrics. In this paper, we study KGC evaluation under a more realistic setting, namely the open-world assumption, where unknown triplets are considered to include many missing facts not included in the training or test sets. For the currently most used metrics such as mean reciprocal rank (MRR) and Hits@K, we point out that their behavior may be unexpected under the open-world assumption. Specifically, with not many missing facts, their numbers show a logarithmic trend with respect to the true strength of the model, and thus, the metric increase could be insignificant in terms of reflecting the true model improvement. Further, considering the variance, we show that the degradation in the reported numbers may result in incorrect comparisons between different models, where stronger models may have lower metric numbers. We validate the phenomenon both theoretically and experimentally. Finally, we suggest possible causes and solutions for this problem. Our code and data are available at https://github.com/GraphPKU/Open-World-KG .

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from scalability issues since they require extracting subgraphs for each training or test query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over six homogeneous, heterogeneous and higher-order graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10X speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50% prediction accuracy improvement.

State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond just a few layers, two fundamental challenges emerge: 1. degraded expressivity due to oversmoothing, and 2. expensive computation due to neighborhood explosion. We propose a design principle to decouple the depth and scope of GNNs – to generate representation of a target entity (i.e., a node or an edge), we first extract a localized subgraph as the bounded-size scope, and then apply a GNN of arbitrary depth on top of the subgraph. A properly extracted subgraph consists of a small number of critical neighbors, while excluding irrelevant ones. The GNN, no matter how deep it is, smooths the local neighborhood into informative representation rather than oversmoothing the global graph into “white noise”. Theoretically, decoupling improves the GNN expressive power from the perspectives of graph signal processing (GCN), function approximation (GraphSAGE) and topological learning (GIN). Empirically, on seven graphs (with up to 110M nodes) and six backbone GNN architectures, our design achieves significant accuracy improvement with orders of magnitude reduction in computation and hardware cost.

Graph neural network (GNN)'s success in graph classification is closely related to the Weisfeiler-Lehman (1-WL) algorithm. By iteratively aggregating neighboring node features to a center node, both 1-WL and GNN obtain a node representation that encodes a rooted subtree around the center node. These rooted subtree representations are then pooled into a single representation to represent the whole graph. However, rooted subtrees are of limited expressiveness to represent a non-tree graph. To address it, we propose Nested Graph Neural Networks (NGNNs). NGNN represents a graph with rooted subgraphs instead of rooted subtrees, so that two graphs sharing many identical subgraphs (rather than subtrees) tend to have similar representations. The key is to make each node representation encode a subgraph around it more than a subtree. To achieve this, NGNN extracts a local subgraph around each node and applies a base GNN to each subgraph to learn a subgraph representation. The whole-graph representation is then obtained by pooling these subgraph representations. We provide a rigorous theoretical analysis showing that NGNN is strictly more powerful than 1-WL. In particular, we proved that NGNN can discriminate almost all r-regular graphs, where 1-WL always fails. Moreover, unlike other more powerful GNNs, NGNN only introduces a constant-factor higher time complexity than standard GNNs. NGNN is a plug-and-play framework that can be combined with various base GNNs. We test NGNN with different base GNNs on several benchmark datasets. NGNN uniformly improves their performance and shows highly competitive performance on all datasets.

In this paper, we provide a theory of using graph neural networks (GNNs) for multi-node representation learning (where we are interested in learning a representation for a set of more than one node, such as link). We know that GNN is designed to learn single-node representations. When we want to learn a node set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN into a joint node set representation. In this paper, we show a fundamental constraint of such an approach, namely the inability to capture the dependence between nodes in the node set, and argue that directly aggregating individual node representations does not lead to an effective joint representation for multiple nodes. Then, we notice that a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, and ID-GNN, all used node labeling. These methods first label nodes in the graph according to their relationships with the target node set before applying a GNN. Then, the node representations obtained in the labeled graph are aggregated into a node set representation. By investigating their inner mechanisms, we unify these node labeling techniques into a single and most general form---labeling trick. We prove that with labeling trick a sufficiently expressive GNN learns the most expressive node set representations, thus in principle solves any joint learning tasks over node sets. Experiments on one important two-node representation learning task, link prediction, verified our theory. Our work explains the superior performance of previous node-labeling-based methods, and establishes a theoretical foundation of using GNNs for multi-node representation learning.

Medical ontologies are widely used to represent and organize medical terminologies. Examples include ICD-9, ICD-10, UMLS etc. The ontologies are often constructed in hierarchical structures, encoding the multi-level subclass relationships among different medical concepts, allowing very fine distinctions between concepts. Medical ontologies provide a great source for incorporating domain knowledge into a healthcare prediction system, which might alleviate the data insufficiency problem and improve predictive performance with rare categories. To incorporate such domain knowledge, Gram, a recent graph attention model, represents a medical concept as a weighted sum of its ancestors' embeddings in the ontology using an attention mechanism. Although showing improved performance, Gram only considers the unordered ancestors of a concept, which does not fully leverage the hierarchy thus having limited expressibility. In this paper, we propose Hierarchical Attention Propagation (HAP), a novel medical ontology embedding model that hierarchically propagate attention across the entire ontology structure, where a medical concept adaptively learns its embedding from all other concepts in the hierarchy instead of only its ancestors. We prove that HAP learns more expressive medical concept embeddings -- from any medical concept embedding we are able to fully recover the entire ontology structure. Experimental results on two sequential procedure/diagnosis prediction tasks demonstrate HAP's better embedding quality than Gram and other baselines. Furthermore, we find that it is not always best to use the full ontology. Sometimes using only lower levels of the hierarchy outperforms using all levels.

Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.

This paper addresses the hyperlink prediction problem in hypernetworks. Different from the traditional link prediction problem where only pairwise relations are considered as links, our task here is to predict the linkage of multiple nodes, i.e., hyperlink. Each hyperlink is a set of an arbitrary number of nodes which together form a multiway relationship. Hyperlink prediction is challenging---since the cardinality of a hyperlink is variable, existing classifiers based on a fixed number of input features become infeasible. Heuristic methods, such as the common neighbors and Katz index, do not work for hyperlink prediction, since they are restricted to pairwise similarities. In this paper, we formally define the hyperlink prediction problem, and propose a new algorithm called Coordinated Matrix Minimization (CMM), which alternately performs nonnegative matrix factorization and least square matching in the vertex adjacency space of the hypernetwork, in order to infer a subset of candidate hyperlinks that are most suitable to fill the training hypernetwork. We evaluate CMM on two novel tasks: predicting recipes of Chinese food, and finding missing reactions of metabolic networks. Experimental results demonstrate the superior performance of our method over many seemingly promising baselines.

Neural networks are typically designed to deal with data in tensor forms. In this paper, we propose a novel neural network architecture accepting graphs of arbitrary structure. Given a dataset containing graphs in the form of (G,y) where G is a graph and y is its class, we aim to develop neural networks that read the graphs directly and learn a classification function. There are two main challenges: 1) how to extract useful features characterizing the rich information encoded in a graph for classification purpose, and 2) how to sequentially read a graph in a meaningful and consistent order. To address the first challenge, we design a localized graph convolution model and show its connection with two graph kernels. To address the second challenge, we design a novel SortPooling layer which sorts graph vertices in a consistent order so that traditional neural networks can be trained on the graphs. Experiments on benchmark graph classification datasets demonstrate that the proposed architecture achieves highly competitive performance with state-of-the-art graph kernels and other graph neural network methods. Moreover, the architecture allows end-to-end gradient-based training with original graphs, without the need to first transform graphs into vectors.

Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to their simplicity, interpretability, and for some of them, scalability. However, every heuristic has a strong assumption on when two nodes are likely to link, which limits their effectiveness on networks where these assumptions fail. In this regard, a more reasonable way should be learning a suitable heuristic from a given network instead of using predefined ones. By extracting a local subgraph around each target link, we aim to learn a function mapping the subgraph patterns to link existence, thus automatically learning a ``heuristic'' that suits the current network. In this paper, we study this heuristic learning paradigm for link prediction. First, we develop a novel $\gamma$-decaying heuristic theory. The theory unifies a wide range of heuristics in a single framework, and proves that all these heuristics can be well approximated from local subgraphs. Our results show that local subgraphs reserve rich information related to link existence. Second, based on the $\gamma$-decaying theory, we propose a new method to learn heuristics from local subgraphs using a graph neural network (GNN). Its experimental results show unprecedented performance, working consistently well on a wide range of problems.

In this paper, we propose a next-generation link prediction method, Weisfeiler-Lehman Neural Machine (WLNM), which learns topological features in the form of graph patterns that promote the formation of links. WLNM has unmatched advantages including higher performance than state-of-the-art methods and universal applicability over various kinds of networks. WLNM extracts an enclosing subgraph of each target link and encodes the subgraph as an adjacency matrix. The key novelty of the encoding comes from a fast hashing-based Weisfeiler-Lehman (WL) algorithm that labels the vertices according to their structural roles in the subgraph while preserving the subgraph's intrinsic directionality. After that, a neural network is trained on these adjacency matrices to learn a predictive model. Compared with traditional link prediction methods, WLNM does not assume a particular link formation mechanism (such as common neighbors), but learns this mechanism from the graph itself. We conduct comprehensive experiments to show that WLNM not only outperforms a great number of state-of-the-art link prediction methods, but also consistently performs well across networks with different characteristics.

Motivation: Metabolic network reconstructions are often incomplete. Constraint-based and pattern-based methodologies have been used for automated gap filling of these networks, each with its own strengths and weaknesses. Moreover, since validation of hypotheses made by gap filling tools require experimentation, it is challenging to benchmark performance and make improvements other than that related to speed and scalability. Results: We present BoostGAPFILL, an open source tool that leverages both constraint-based and machine learning methodologies for hypotheses generation in gap filling and metabolic model refinement. BoostGAPFILL uses metabolite patterns in the incomplete network captured using a matrix factorization formulation to constrain the set of reactions used to fill gaps in a metabolic network. We formulate a testing framework based on the available metabolic reconstructions and demonstrate the superiority of BoostGAPFILL to state-of-the-art gap filling tools. We randomly delete a number of reactions from a metabolic network and rate the different algorithms on their ability to both predict the deleted reactions from a universal set and to fill gaps. For most metabolic network reconstructions tested, BoostGAPFILL shows above 60% precision and recall, which is more than twice that of other existing tools. Availability and Implementation: MATLAB open source implementation ( https://github.com/Tolutola/BoostGAPFILL ). Contacts: [email protected] or [email protected] . Supplementary information: Supplementary data are available at Bioinformatics online.

While active learning (AL) has been widely studied for classification problems, limited efforts have been done on AL for regression. In this paper, we introduce a new AL framework for regression, expected model change maximization (EMCM), which aims at choosing the unlabeled data instances that result in the maximum change of the current model once labeled. The model change is quantified as the difference between the current model parameters and the updated parameters after the inclusion of the newly selected examples. In light of the stochastic gradient descent learning rule, we approximate the change as the gradient of the loss function with respect to each single candidate instance. Under the EMCM framework, we propose novel AL algorithms for the linear and nonlinear regression models. In addition, by simulating the behavior of the sequential AL policy when applied for k iterations, we further extend the algorithms to batch mode AL to simultaneously choose a set of k most informative instances at each query time. Extensive experimental results on both UCI and StatLib benchmark data sets have demonstrated that the proposed algorithms are highly effective and efficient.

Abstract Background Flux analyses, including flux balance analysis (FBA) and 13C-metabolic flux analysis (13C-MFA), offer direct insights into cell metabolism, and have been widely used to characterize model and non-model microbial species. Nonetheless, constructing the 13C-MFA model and performing flux calculation are demanding for new learners, because they require knowledge of metabolic networks, carbon transitions, and computer programming. To facilitate and standardize the 13C-MFA modeling work, we set out to publish a user-friendly and programming-free platform (WUFlux) for flux calculations in MATLAB®. Results We constructed an open-source platform for steady-state 13C-MFA. Using GUIDE (graphical user interface design environment) in MATLAB, we built a user interface that allows users to modify models based on their own experimental conditions. WUFlux is capable of directly correcting mass spectrum data of TBDMS (N-tert-butyldimethylsilyl-N-methyltrifluoroacetamide)-derivatized proteinogenic amino acids by removing background noise. To simplify 13C-MFA of different prokaryotic species, the software provides several metabolic network templates, including those for chemoheterotrophic bacteria and mixotrophic cyanobacteria. Users can modify the network and constraints, and then analyze the microbial carbon and energy metabolisms of various carbon substrates (e.g., glucose, pyruvate/lactate, acetate, xylose, and glycerol). WUFlux also offers several ways of visualizing the flux results with respect to the constructed network. To validate our model’s applicability, we have compared and discussed the flux results obtained from WUFlux and other MFA software. We have also illustrated how model constraints of cofactor and ATP balances influence fluxome results. Conclusion Open-source software for 13C-MFA, WUFlux, with a user-friendly interface and easy-to-modify templates, is now available at http://www.13cmfa.org /or ( http://tang.eece.wustl.edu/ToolDevelopment.htm ). We will continue documenting curated models of non-model microbial species and improving WUFlux performance.

Learning to rank has become increasingly important for many information retrieval applications. To reduce the labeling cost at training data preparation, many active sampling algorithms have been proposed. In this article, we propose a novel active learning-for-ranking strategy called ranking-based sensitivity sampling (RSS), which is tailored for Gradient Boosting Decision Tree (GBDT), a machine-learned ranking method widely used in practice by major commercial search engines for ranking. We leverage the property of GBDT that samples close to the decision boundary tend to be sensitive to perturbations and design the active learning strategy accordingly. We further theoretically analyze the proposed strategy by exploring the connection between the sensitivity used for sample selection and model regularization to provide a potentially theoretical guarantee w.r.t. the generalization capability. Considering that the performance metrics of ranking overweight the top-ranked items, item rank is incorporated into the selection function. In addition, we generalize the proposed technique to several other base learners to show its potential applicability in a wide variety of applications. Substantial experimental results on both the benchmark dataset and a real-world dataset have demonstrated that our proposed active learning strategy is highly effective in selecting the most informative examples.