ICML 2025 Papers

Inductive knowledge graph completion aims to predict missing triplets in an incomplete knowledge graph that differs from the one observed during training. While subgraph reasoning models have demonstrated empirical success in this task, their theoretical properties, such as stability and generalization capability, remain unexplored. In this work, we present the first theoretical analysis of the relationship between the stability and the generalization capability for subgraph reasoning models. Specifically, we define stability as the degree of consistency in a subgraph reasoning model's outputs in response to differences in input subgraphs and introduce the Relational Tree Mover’s Distance as a metric to quantify the differences between the subgraphs. We then show that the generalization capability of subgraph reasoning models, defined as the discrepancy between the performance on training data and test data, is proportional to their stability. Furthermore, we empirically analyze the impact of stability on generalization capability using real-world datasets, validating our theoretical findings.

Generalized Category Discovery (GCD) aims to identify both known and novel categories in unlabeled data by leveraging knowledge from old classes. However, existing methods are limited to non-graph data; lack theoretical foundations to answer *When and how known classes can help GCD*. We introduce the Graph GCD task; provide the first rigorous theoretical analysis of *parametric GCD*. By quantifying the relationship between old and new classes in the embedding space using the Wasserstein distance W, we derive the first provable GCD loss bound based on W. This analysis highlights two necessary conditions for effective GCD. However, we uncover, through a Pairwise Markov Random Field perspective, that popular graph contrastive learning (GCL) methods inherently violate these conditions. To address this limitation, we propose SWIRL, a novel GCL method for GCD. Experimental results validate our (theoretical) findings and demonstrate SWIRL's effectiveness.

Graph-based data structures have become powerful and ubiquitous tools for scalable approximate nearest-neighbor (ANN) search over the past decade. In spite of their apparent practical performance, there has only recently been progress on the **worst-case** performance of these data structures. Indeed, the influential work of Indyx and Xu (2023) introduced the key concept of $\alpha$-reachable graphs, showing that graphs constructed by the DiskANN algorithm (Subramanya, et. al. 2023) produce an $\left(\frac{\alpha+1}{\alpha-1}\right)$-approximate solution with a simple best-first search that runs in poly-logarithmic query time. In our work, we improve and generalize this analysis as follows: - We introduce **sorted** $\alpha$-reachable graphs, and use this notion to obtain a stronger approximation factor of $\frac{\alpha}{\alpha-1}$ for the DiskANN algorithm on Euclidean metrics. - We present the **first** worst-case theoretical analysis for the popular **beam-search** algorithm, which is used in practice to search these graphs for $k > 1$ candidate nearest neighbors. We also present empirical results validating the significance of sorted $\alpha$-reachable graphs, which aligns with our theoretical findings.

Spectral graph learning builds upon two foundations: Graph Fourier basis as its theoretical cornerstone,with polynomial approximation to enable practical implementation. While this framework has led to numerous successful designs, we argue that its effectiveness might stem from mechanisms different from its theoretical foundations. In this paper, we identify two fundamental issues that challenge our current understanding: (1) The graph Fourier basis $\mathbf{U}$ (eigenvectors of the normalized graph Laplacian) faces too many questions to truly serve its intended role, particularly in preserving its semantic properties of Fourier analysis; (2) The limitations preventing expressive filters are not merely practical constraints, but fundamental barriers that naturally protect stability and generalization. Importantly, the two issues entangle with each other. The second obscured the first: the natural avoidance of complex filters has prevented us from fully confronting the questions about $\mathbf{U}$'s role as a Fourier basis. This observation leads to our position: the effectiveness of spectral GNNs relies less on Graph Fourier basis than originally conceived, or, in other words, **spectral GNNs might not be so spectral**. The position leads us to at least two potential research interests: to incorporate a more semantically meaningful graph dictionary except for $\mathbf{U}$, and to re-examine the theoretical role of the introduced polynomial techniques.

We formalize a new concept for LLMs, **context-enhanced learning**. It involves standard gradient-based learning on text except that the context is enhanced with additional data on which no auto-regressive gradients are computed. This setting is a gradient-based analog of usual in-context learning (ICL) and appears in some recent works. Using a multi-step reasoning task, we prove in a simplified setting that context-enhanced learning can be **exponentially more sample-efficient** than standard learning when the model is capable of ICL. At a mechanistic level, we find that the benefit of context-enhancement arises from a more accurate gradient learning signal. We also experimentally demonstrate that it appears hard to detect or recover learning materials that were used in the context during training. This may have implications for data security as well as copyright.

Knowledge graphs (KGs) are ubiquitous in numerous real-world applications, and watermarking facilitates protecting intellectual property and preventing potential harm from AI-generated content. Existing watermarking methods mainly focus on static plain text or image data, while they can hardly be applied to dynamic graphs due to spatial and temporal variations of structured data. This motivates us to propose KGMark, the first graph watermarking framework that aims to generate robust, detectable, and transparent diffusion fingerprints for dynamic KG data. Specifically, we propose a novel clustering-based alignment method to adapt the watermark to spatial variations. Meanwhile, we present a redundant embedding strategy to harden the diffusion watermark against various attacks, facilitating the robustness of the watermark to the temporal variations. Additionally, we introduce a novel learnable mask matrix to improve the transparency of diffusion fingerprints. By doing so, our KGMark properly tackles the variation challenges of structured data. Experiments on various public benchmarks show the effectiveness of our proposed KGMark.

Modern sequence models (e.g., Transformers and linear RNNs) emerged as dominant backbones of recent deep learning frameworks, mainly due to their efficiency, representational power, and/or ability to capture long-range dependencies. Recently, adopting these sequence models for graph-structured data has gained popularity as the alternative to Message Passing Neural Networks (MPNNs). There is, however, a lack of a common foundation about what constitutes a good graph sequence model, and a mathematical description of the benefits and deficiencies in adopting different sequence models for learning on graphs. To this end, we introduce the Graph Sequence Model (GSM), a unifying framework for applying sequence models to graph data. The GSM framework allows us to understand, evaluate, and compare the power of different sequence model backbones in graph tasks. Building on this insight, we propose GSM++, a fast hybrid model that hierarchically tokenizes the graph using Hierarchical Affinity Clustering (HAC) and then encodes these sequences via a hybrid architecture. The theoretical and experimental findings confirm that GSM++ outperforms baseline models on most benchmarks.

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic perspective and developing a suitable analog to data processing inequality to quantify information throughout the model's layers. In contrast to non-graph domains, information about the node-level prediction target can *increase* with model depth if a node's features are semantically different from its neighbors. Therefore, on heterophilic graphs, the latent embeddings of an MPNN each provide different information about the data distribution - different from homophilic settings. This reveals that considering all node representations simultaneously is a key design principle for epistemic uncertainty estimation on graphs beyond homophily. We empirically confirm this with a simple post-hoc density estimator on the joint node embedding space that provides state-of-the-art uncertainty on heterophilic graphs. At the same time, it matches prior work on homophilic graphs without explicitly exploiting homophily through post-processing.

Large language models (LLMs) have demonstrated impressive reasoning abilities, but they still struggle with faithful reasoning due to knowledge gaps and hallucinations. To address these issues, knowledge graphs (KGs) have been utilized to enhance LLM reasoning through their structured knowledge. However, existing KG-enhanced methods, either retrieval-based or agent-based, encounter difficulties in accurately retrieving knowledge and efficiently traversing KGs at scale. In this work, we introduce graph-constrained reasoning (GCR), a novel framework that bridges structured knowledge in KGs with unstructured reasoning in LLMs. To eliminate hallucinations, GCR ensures faithful KG-grounded reasoning by integrating KG structure into the LLM decoding process through KG-Trie, a trie-based index that encodes KG reasoning paths. KG-Trie constrains the decoding process, allowing LLMs to directly reason on graphs and generate faithful reasoning paths grounded in KGs. Additionally, GCR leverages a lightweight KG-specialized LLM for graph-constrained reasoning alongside a powerful general LLM for inductive reasoning over multiple reasoning paths, resulting in accurate reasoning with zero reasoning hallucination. Extensive experiments on several KGQA benchmarks demonstrate that GCR achieves state-of-the-art performance and exhibits strong zero-shot generalizability to unseen KGs without additional training.

Temporal Graph Neural Networks (TGNNs) are widely used to model dynamic systems where relationships and features evolve over time. Although TGNNs demonstrate strong predictive capabilities in these domains, their complex architectures pose significant challenges for explainability. Counterfactual explanation methods provide a promising solution by illustrating how modifications to input graphs can influence model predictions. To address this challenge, we present CoDy—Counterfactual Explainer for Dynamic Graphs—a model-agnostic, instance-level explanation approach that identifies counterfactual subgraphs to interpret TGNN predictions. CoDy employs a search algorithm that combines Monte Carlo Tree Search with heuristic selection policies, efficiently exploring a vast search space of potential explanatory subgraphs by leveraging spatial, temporal, and local event impact information. Extensive experiments against state-of-the-art factual and counterfactual baselines demonstrate CoDy's effectiveness, with improvements of 16% in AUFSC+ over the strongest baseline. Our code is available at: https://github.com/daniel-gomm/CoDy

Complex query answering (CQA) on knowledge graphs (KGs) is gaining momentum as a challenging reasoning task. In this paper, we show that the current benchmarks for CQA might not be as *complex* as we think, as the way they are built distorts our perception of progress in this field. For example, we find that in these benchmarks most queries (up to 98% for some query types) can be reduced to simpler problems, e.g., link prediction, where only one link needs to be predicted. The performance of state-of-the-art CQA models decreses significantly when such models are evaluated on queries that cannot be reduced to easier types. Thus, we propose a set of more challenging benchmarks composed of queries that *require* models to reason over multiple hops and better reflect the construction of real-world KGs. In a systematic empirical investigation, the new benchmarks show that current methods leave much to be desired from current CQA methods.

While Multi-modal Large Language Models (MLLMs) demonstrate impressive abilities over high-level perception and reasoning, their robustness in the wild remains limited, often falling short on tasks that are intuitive and effortless for humans. We examine the hypothesis that these deficiencies stem from the absence of core knowledge—rudimentary cognitive abilities innate to humans from early childhood. To explore the core knowledge representation in MLLMs, we introduce CoreCognition, a large-scale benchmark encompassing 12 core knowledge concepts grounded in developmental cognitive science. We evaluate 230 models with 11 different prompts, leading to a total of 2,530 data points for analysis. Our experiments uncover four key findings, collectively demonstrating core knowledge deficits in MLLMs: they consistently underperform and show reduced, or even absent, scalability on low-level abilities relative to high-level ones. Finally, we propose Concept Hacking, a novel controlled evaluation method that reveals MLLMs fail to progress toward genuine core knowledge understanding, but instead rely on shortcut learning as they scale.

We study the offline active learning problem on graphs. In this problem, one seeks to select k vertices whose labels are best suited for predicting the labels of all the other vertices in the graph. Guillory and Bilmes (Guillory & Bilmes, 2009) introduced a natural theoretical model motivated by a label smoothness assumption. Prior to our work, algorithms with theoretical guarantees were only known for restricted graph types such as trees (Cesa-Bianchi et al., 2010) despite the models simplicity. We present the first O(log n)-resource augmented algorithm for general weighted graphs. To complement our algorithm, we show constant hardness of approximation.

We propose DRAGO, a novel approach for continual model-based reinforcement learning aimed at improving the incremental development of world models across a sequence of tasks that differ in their reward functions but not the state space or dynamics. DRAGO comprises two key components: *Synthetic Experience Rehearsal*, which leverages generative models to create synthetic experiences from past tasks, allowing the agent to reinforce previously learned dynamics without storing data, and *Regaining Memories Through Exploration*, which introduces an intrinsic reward mechanism to guide the agent toward revisiting relevant states from prior tasks. Together, these components enable the agent to maintain a comprehensive and continually developing world model, facilitating more effective learning and adaptation across diverse environments. Empirical evaluations demonstrate that DRAGO is able to preserve knowledge across tasks, achieving superior performance in various continual learning scenarios.

With the increasing size of datasets used for training neural networks, data pruning has gained traction in recent years. However, most current data pruning algorithms are limited in their ability to preserve accuracy compared to models trained on the full data, especially in high pruning regimes. In this paper we explore the application of data pruning while incorporating knowledge distillation (KD) when training on a pruned subset. That is, rather than relying solely on ground-truth labels, we also use the soft predictions from a teacher network pre-trained on the complete data. By integrating KD into training, we demonstrate significant improvement across datasets, pruning methods, and on all pruning fractions. We first establish a theoretical motivation for employing self-distillation to improve training on pruned data. Then, we empirically make a compelling and highly practical observation: using KD, simple random pruning is comparable or superior to sophisticated pruning methods across all pruning regimes. On ImageNet for example, we achieve superior accuracy despite training on a random subset of only 50% of the data. Additionally, we demonstrate a crucial connection between the pruning factor and the optimal knowledge distillation weight. This helps mitigate the impact of samples with noisy labels and low-quality images retained by typical pruning algorithms. Finally, we make an intriguing observation: when using lower pruning fractions, larger teachers lead to accuracy degradation, while surprisingly, employing teachers with a smaller capacity than the student's may improve results. Our code will be made available.

Shallow node embeddings like node2vec (N2V) can be used for nodes without features or to supplement existing features with structure-based information. Embedding methods like N2V are limited in their application on new nodes, which restricts them to the transductive setting where the entire graph, including the test nodes, is available during training. We propose inductive node2vec (iN2V), which combines a post-hoc procedure to compute embeddings for nodes unseen during training and modifications to the original N2V training procedure to prepare the embeddings for this post-hoc procedure. We conduct experiments on several benchmark datasets and demonstrate that iN2V is an effective approach to bringing transductive embeddings to an inductive setting. Using iN2V embeddings improves node classification by 1 point on average, with up to 6 points of improvement depending on the dataset and the number of unseen nodes. Our iN2V is a plug-in approach to create new or enrich existing embeddings. It can also be combined with other embedding methods, making it a versatile approach for inductive node representation learning. Code to reproduce the results is available at https://github.com/Foisunt/iN2V.

Foundation models are pretrained on large-scale corpora to learn generalizable patterns across domains and tasks---such as contours, textures, and edges in images, or tokens and sentences in text. In contrast, discovering such generalities in graph-structured data, especially across heterogeneous graph tasks, remains an open challenge. To address this, we propose a novel approach to cross-task generalization in graphs via task-trees, which serve as unified learning instances aligning node-, edge-, and graph-level tasks. We theoretically analyze the stability, transferability, and generalization properties of task-trees, showing that pretraining a graph neural network (GNN) on diverse task-trees with a reconstruction objective induces transferable knowledge. This enables efficient adaptation to downstream tasks with minimal fine-tuning. To validate our framework, we introduce Graph Generality Identifier on Task-Trees (GIT), a graph foundation model that demonstrates strong performance on over 30 graphs across five domains via fine-tuning, in-context learning, and zero-shot generalization. Code and data are available at https://github.com/Zehong-Wang/GIT.

Node classification is a key task in temporal graph learning (TGL). Real-life temporal graphs often introduce new node classes over time, but existing TGL methods assume a fixed set of classes. This assumption brings limitations, as updating models with full data is costly, while focusing only on new classes results in forgetting old ones. Graph continual learning (GCL) methods mitigate forgetting using old-class subsets but fail to account for their evolution. We define this novel problem as temporal graph continual learning (TGCL), which focuses on efficiently maintaining up-to-date knowledge of old classes. To tackle TGCL, we propose a selective learning framework that substitutes the old-class data with its subsets, Learning Towards the Future (LTF). We derive an upper bound on the error caused by such replacement and transform it into objectives for selecting and learning subsets that minimize classification error while preserving the distribution of the full old-class data. Experiments on three real-world datasets show that LTF effectively addresses the TGCL challenge.

Knowledge Editing (KE) algorithms alter models' weights to perform targeted updates to incorrect, outdated, or otherwise unwanted factual associations. However, recent work has shown that applying KE can adversely affect models' broader factual recall accuracy and diminish their reasoning abilities. Although these studies give insights into the potential harms of KE algorithms, e.g., performance evaluations on benchmarks, little is understood about why such destructive failures occur. Motivated by this, we define a novel synthetic task in which a Transformer is trained from scratch to internalize a "structured" knowledge graph. The structure enforces relationships between entities of the graph, such that editing a factual association has "trickling effects" on other entities (e.g., altering X's parent is Y to Z affects who X's siblings' parent is). Through evaluations of edited models on this task, we show that KE inadvertently affects representations of entities beyond the targeted one, distorting relevant structures that allow a model to infer unseen knowledge about an entity. We call this phenomenon representation shattering and demonstrate that it degrades models' factual recall and reasoning performance. We further corroborate our findings in naturalistic settings with pre-trained Llama and Mamba models as well. Overall, our work yields a precise mechanistic hypothesis to explain why KE has adverse effects on model abilities.