ICML 2026 Papers

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov–Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.

Robust signal enhancement at low SNR is fundamentally challenging because noise becomes strongly entangled with the signal and corrupts local time–frequency (TF) evidence. In this regime, fixed resolution short time Fourier transform (STFT) enhancement with purely data driven convolutional biases can become overconfident in unreliable TF regions, causing unstable suppression or residual artifacts. We propose FracKGMF, which couples Fractional Distance Decay Convolution (FracConv) with Knowledge Guided Multi-view Fusion (KGMF) for expressive TF modeling and reliability aware decisions under heavy corruption. FracConv introduces a lightweight fractional distance decay family that reshapes local interactions into long tailed receptive patterns, enabling aggregation of weak but globally consistent cues when per-bin observations are ambiguous. KGMF uses a wiener inspired reliability prior to calibrate multi-view fusion and reduce excessive suppression in uncertain regions. Experiments on speech and EM benchmarks show consistent improvements over state-of-the-art baselines, with particularly large gains under extremely low SNR, including a 33 dB average improvement on EM signals at -20 dB.

Graph Mixture-of-Experts (Graph-MoE) offers a way to scale GNNs via adaptive capacity allocation, with the goal of allowing different experts to capture diverse graph patterns. Its effectiveness heavily depends on the coordination between routing decisions and expert specialization. However, through extensive empirical study, we identify two critical phenomena. First, discrimination loss occurs on both the expert and routing sides, where GNN experts become highly homogenized and the router collapses to a small subset of experts, failing to reflect diverse graph semantics. Second, routing uncertainty is prevalent, as existing routers produce uncertain expert assignments for most nodes, and such uncertainty exhibits a strong negative correlation with model performance. To address these issues, we propose C$^2$GMoE, a novel Graph-MoE framework featuring Contrastive routing and Confidence-aware fusion. We introduce a group-wise contrastive routing strategy that provides explicit guidance for routing optimization by aligning node-level routing decisions with semantic clusters while satisfying load-balancing constraints. Moreover, through a theoretical analysis of generalization error, we develop a confidence-aware fusion mechanism that adaptively reweights expert predictions according to their confidence. Extensive experiments across multiple benchmarks demonstrate the effectiveness of our proposed C$^2$GMoE.

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, beyond graph condensation (GC) methods limited to pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose \textbf{A}nchor-guided \textbf{H}yper\textbf{G}raph \textbf{C}ondensation with \textbf{D}ual-level \textbf{D}iscrimination (\textbf{AHGCDD}), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis strategy for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Traditional hallucination detection fails on "Stubborn Hallucinations" — errors where LLMs are confidently wrong. We propose a geometric solution: Embedding-Perturbed Gradient Sensitivity (EPGS). We hypothesize that while robust facts reside in flat minima, stubborn hallucinations sit in sharp minima, supported by brittle memorization. EPGS detects this sharpness by perturbing input embeddings with Gaussian noise and measuring the resulting spike in gradient magnitude. This acts as an efficient proxy for the Hessian spectrum, differentiating stable knowledge from unstable memorization. Our experiments show that EPGS significantly outperforms entropy-based and representation-based baselines, providing a robust signal for detecting high-confidence factual errors.

We find multilayer perceptrons and transformers both universally learn an instantiation of the same divide-and-conquer algorithm that requires only a logarithmic number of neural representations to solve dihedral multiplication. Clustering neurons based on similar activation behaviour reveals remarkably clear structure: each neural representation corresponds to a Cayley graph. To our knowledge, this is the first work that fully characterizes and describes all neural representations that are learnable on a dataset, while prior work on group multiplications studied neuron-level behavior, or preliminarily investigated cluster behavior. Thus, we can understand the algorithm networks universally learn at three levels of abstraction: 1) Neurons activate on coset or approximate coset structure of the dihedral group. 2) Groups of neurons together form neural representations that act to divide the dataset into different subproblems, being Cayley graphs, where the equivalence class of the answer is computed. 3) The global algorithm then linearly combines each neural representation (subproblem) together at the logits. This work provides the community with a deep case study and a well-understood toy model for interpretability, and makes progress toward proving the conjecture that networks trained via stochastic gradient methods divide and conquer all group multiplication tasks.

In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a small representative set from the whole graph. We present the first $\tilde{O}(\log^{1.5} n)$-approximation algorithm for graph label selection under the standard budget constraint. Prior work either relies on resource augmentation, allowing substantially more than $k$ labeled vertices, or consists primarily of heuristics without provable guarantees. Finally, we demonstrate that practical heuristic variants of our algorithm scale to significantly larger graphs than previous methods, while essentially retaining their quality.

Transferring knowledge by fine-tuning large-scale pre-trained networks has become a standard paradigm for downstream tasks, yet the knowledge of a pre-trained model is tightly coupled with monolithic architecture, which restricts flexible reuse across models of varying scales. In response to this challenge, recent approaches typically resort to either parameter selection, which fails to capture the interdependent structure of this knowledge, or parameter prediction using generative models that depend on impractical access to large network collections. In this paper, we identify the low-frequency components of model weights as the concrete carrier of foundational, task-agnostic knowledge—its "learngene"—and validate this by demonstrating its efficient inheritance by downstream models and tasks. Based on this insight, we propose FRONT (FRequency dOmain kNowledge Transfer), a novel framework that uses the Discrete Cosine Transform (DCT) to isolate the low-frequency "learngene". This learngene can be seamlessly adapted to initialize models of arbitrary size via simple truncation or padding, a process that is entirely training-free. For enhanced performance, we propose an optional low-cost refinement process that introduces a spectral regularizer to further improve the learngene's transferability. Extensive experiments demonstrate that FRONT achieves the state-of-the-art performance, accelerates convergence by up to $15\times$ in vision tasks, and reduces training FLOPs by an average of 40.5\% in language tasks. Code is available at https://github.com/LUcy0505/FRONT.

Generative Graph Language Models (GLMs) must reconcile topology with causal language modeling. Linearization obscures multi-hop connectivity, while encoder-based methods bottleneck token-level reasoning during generation. Viewing context modeling as a form of message passing, we introduce **Weaver**, an encoder-free framework that extends the attention mechanism of decoder-only LLMs to enable graph reasoning. Weaver maps graph distances into rotary positional embeddings so that structurally connected nodes become proximate in attention space, propagating information over graph topology as if it were sequential context. To achieve this, we combine: 1) a masking mechanism for causal tokens with graph structures; 2) a unified geometric encoding that couples sequential position and graph distance in joint rotary embeddings (Graph-over-Tokens RoPE); and 3) a design principle to prioritize local information to resolve positional ambiguity under graph symmetries. On zero-shot benchmarks, Weaver achieves state-of-the-art performance among generative GLMs, with gains of up to 30\% over prior generative methods on heterophilic graphs, while matching specialized discriminative models on citation networks---all within a unified decoder-only framework.

Knowledge-intensive Visual Question Answering (KI-VQA) frequently suffers from severe knowledge conflicts caused by the inherent limitations of open-domain retrieval. However, existing paradigms face critical limitations, including the lack of generalizable conflict detection and intra-model constraint mechanisms to handle conflicting evidence. To address these challenges, we propose the **REAL** (**Re**asoning-Pivot **Al**ignment) framework centered on the novel concept of the **Reasoning-Pivot**. Distinct from reasoning steps that prioritize internal self-derivation, a reasoning-pivot serves as an atomic unit (node or edge) in the reasoning chain that emphasizes knowledge linkage, and it typically relies on external evidence to complete the reasoning. Supported by our constructed **REAL-VQA** dataset, our approach integrates **Reasoning-Pivot Aware SFT (RPA-SFT)** to train a generalizable discriminator by aligning conflicts with pivot extraction, and employs **Reasoning-Pivot Guided Decoding (RPGD)**, an intra-model decoding strategy that leverages these pivots for targeted conflict mitigation. Extensive experiments on diverse datasets demonstrate that REAL significantly enhances discrimination accuracy and achieves superior performance, validating our pivot-driven resolution paradigm.

Recent years have witnessed a surge of interest in federated learning. In particular, federated continual learning (FCL) emerged as an effective approach that enables clients with evolving, non-storable data to engage in collective learning. Among FCL approaches, replay-based methods excel by mitigating data storage constraints through synthetic data generation. However, existing replay-based methods overlook spatial and temporal information inherent in FCL settings, leading to suboptimal model performance. For instance, spatial variation in COVID-19 prevalence across hospitals in different states (e.g., Delta surging in Florida vs. Omicron in New York) and the temporal evolution of regional outbreaks are critical information for accurately distinguishing between COVID variants. This paper presents GFedCL to address this limitation. GFedCL is a new FCL approach that (1) constructs spatial- and temporal-aware relational graphs with attention mechanisms, and (2) uses the graphs, combined with generative adversarial learning, to generate high-quality synthetic data. GFedCL can generate synthetic data that matches the expectation of real data distribution while preserving privacy with theoretical guarantees. GFedCL consistently outperforms state-of-the-art FCL methods, gaining 27.95% improvement on TinyImageNet.

Dynamic graph learning, which focuses on modeling the merging, vanishing, and reconnection of nodes and edges, is crucial for real-world applications. In dynamic graphs, node neighborhoods often exhibit diverse and time-evolving topologies, including hierarchical, grid-like, and cyclic patterns. Existing methods typically embed graphs into a single curvature space, which limits the quality of node representations when the embedding geometry is not aligned well with the local graph topology. In this paper, we propose **DyGMoCE**, a **Dy**namic **G**raph Transformer with a **M**ixture **o**f **C**urvature-aware **E**xperts, which efficiently embeds each node at every timestamp into an adaptive curvature space. Specifically, DyGMoCE incorporates a mixture-of-experts framework to both the attention and feed-forward modules, where each expert operates on a Riemannian manifold with a distinct curvature. Then, motivated by the geometric continuity across the experts, we introduce a routing mechanism with a ranking constraint. To improve efficiency, we design a fast Riemannian attention module for DyGMoCE, achieving an average speedup of 27.5% and memory reduction of 52.6%. Notably, the fast Riemannian attention module is broadly applicable to Transformer models with sequence inputs. Extensive experimental results show that DyGMoCE significantly outperforms other state-of-the-art methods.

AI Scientists have shown promising progress across multiple stages of the research pipeline, among which automatic scientific paper writing remains a formidable challenge. The Introduction writing is especially challenging, which demands not only linguistic fluency, but logical soundness and verifiable faithfulness. Most AI-assisted methods treat the task as text generation instead of reasoning and structuring, leading to severe drawbacks, *e.g.*, hallucinating citations. To address this, we first formulate the Content-Conditional Introduction Generation (CCIG) task, which requires grounding the Introduction in the paper's core evidence. We then propose **LECTOR**, a novel **Logic-Expression Co-Reinforcement Learning** framework that can strictly follow the scientist's logic, add high-quality citations and keep structured expressions. LECTOR first constructs a logic-reasoning graph from the paper's main body to serve as a verifiable logical blueprint. Subsequently, it employs a Logic-Expression Co-Rewarding mechanism to jointly optimize for both the graph's structural fidelity and the final narrative's quality. We conduct a dataset from *Nature Communications* papers to assess our method. Extensive experiments show consistent improvements in both logic fidelity and Introduction generation quality metrics, *e.g.*, Graph Quality **(+26.7%)**, Citation Quality **(+8.6%)**, and Paper Consistency **(+3.3%)**. Code and data are available at: https://github.com/Xiao-Youth/LECTOR

We study the problem of generating structurally diverse graphs on $N$ unlabeled vertices. Given a space of such graphs $S_N$, metric $d$, and target cardinality $k$, the objective is to construct a set $\mathcal{G} \subset S_N$ that maximizes pairwise diversity under $d$. While neural generative models may appear appealing as a solution, standard approaches require samples from a target distribution that such _dispersion_ problems lack. Thus, prior work relies primarily on combinatorial or iterative search. We instead treat diversity as an explicit optimization objective, an approach we term _Neural Graph Dispersion_. An ensemble of generators is optimized under a repulsive potential, producing diverse graphs along optimization trajectories as they disperse over $(S_N,d)$, and avoiding distribution fitting and per-metric retraining entirely. Experiments show our method produces high diversity while scaling N and k an order of magnitude beyond prior work. Our source code is available at https://github.com/ryienh/neural-graph-dispersion.

Gene Regulatory Network (GRN) inference is essential for understanding complex cellular mechanisms, rendered tractable through single-cell transcriptomic data. With the emergence of single-cell Foundation Models (scFMs), enhanced transcriptomic encoding is widely expected to revolutionize GRN inference. However, we observe that their performance remains far from satisfactory. The primary reason is that the standard reconstruction-based pre-training objectives often fail to explicitly capture latent regulatory signals. To bridge this gap, we first introduce a GRN generalization benchmark designed to evaluate regulatory predictions on unseen genes and datasets, which relies on the zero-shot capabilities of scFMs and is inherently challenging for traditional methods. Furthermore, to unlock the regulatory knowledge within the foundation models, we propose two novel methods, Virtual Value Perturbation and Gradient Trajectory, to distill implicit regulatory information from scFMs into highly generalizable inter-gene features. Extensive experiments demonstrate that our approach significantly outperforms existing methods, establishing a new paradigm for leveraging the potential of scFMs in universal GRN inference.

Selecting the top $m$ from $n$ items via expensive $k$-wise comparisons is central to settings ranging from LLM-based document reranking to crowdsourced evaluation and tournament design. Existing methods either rely on heuristics that discard comparison information, or exploit it at prohibitive cost. We introduce a *tournament graph* framework that provides a principled foundation for $k$-wise ranking. Our key observation is that each $k$-item comparison reveals an induced tournament of ${k \choose 2}$ pairwise preferences; aggregating these into a global preference graph and computing its transitive closure yields many additional orderings without further oracle calls. We formalize when the current top-$m$ output is *certifiably determined* and design a greedy query schedule that maximizes information gain towards identifying the top-$m$ items. The framework also gracefully handles non-transitive preferences -- cycles induced by real-world oracles -- by collapsing them into equivalence classes that yield principled *tiered rankings*. Applied to LLM reranking across 14 benchmarks and 5 models, BlitzRank achieves Pareto dominance over existing approaches: matching or exceeding accuracy while requiring 25--40\% fewer tokens than comparable methods; against pairwise reranking, it achieves near-identical quality with 7$\times$ fewer tokens. Code available at [https://github.com/ContextualAI/BlitzRank](https://github.com/ContextualAI/BlitzRank).

Existing Cross-Tokenizer Knowledge Distillation (CTKD) methods can fail to outperform simple supervised fine-tuning when vocabulary overlap is low due to severe alignment noise. We identify this phenomenon as the **``Low-Overlap negative transfer regime''**. To overcome this, we propose **Entropy-aware Span-Constrained Optimal Transport (E-SCOT)**, a robust framework that treats distillation as a sparse transport problem built upon a vocabulary-agnostic ground metric. Unlike prior OT approaches that incur quadratic costs via dense sequence-level optimization, E-SCOT employs span-anchored lexical alignment to construct a deterministic, locality-preserving support set in linear time with respect to sequence length. Furthermore, we introduce R\'enyi-entropy adaptive reweighting to dynamically concentrate the distillation budget on informative positions exhibiting significant uncertainty-profile gaps. Extensive experiments demonstrate that E-SCOT achieves state-of-the-art performance across diverse model families, effectively eliminating negative transfer even in challenging low-overlap scenarios.

Instruction tuning (IT) is a central mechanism for aligning large language models (LLMs) with user intent. In practice, randomly shuffling the training set is a simple yet surprisingly strong baseline. However, it overlooks latent structure, such as domain and reasoning depth, and thus interleaves heterogeneous objectives, which can induce gradient conflicts and diminish effective optimization progress. To this end, we propose **EP-Order**, an embedding-proximity-based data-ordering paradigm for IT of LLMs. Unlike previous paradigms that derive order from **per-example** scores, EP-Order explicitly accounts for **inter-sample** correlations by operating in representation space. EP-Order trains a warm-up model on a small subset of data (*e.g.*, 10%), embeds all training samples for clustering, and ranks these clusters according to embedding proximity. To handle sharp gradient changes at cluster transitions and alleviate catastrophic forgetting under cluster-based training, we introduce mixed regions that interleave samples from the previous, current, and next clusters, thereby stabilizing learning. Extensive experiments on 14 benchmarks spanning vision-language, text-only, and hybrid thinking/no-thinking scenarios show that EP-Order achieves broadly consistent improvements over random shuffling. These results suggest that exploiting embedding-level data structure offers an effective and general direction for improving IT on complex, high-conflict training data.

Graph Contrastive Learning (GCL) has significantly advanced self-supervised representation learning on graphs, yet its practical efficacy remains hindered by random augmentations that induce semantic distortion and rigid one-to-one sampling strategy that amplifies inter-class entanglement and intra-class dispersion. To address these limitations, we develop CL-GCL, a Comprehensive and Lightweight Graph Contrastive Learning framework. Specifically, we exploit graph coarsening‌ to preserve structural semantics through community-level representations and manifold learning‌ to capture local geometric relations without costly pairwise distance computations. This design naturally aligns with the neighborhood aggregation principle of Graph Convolutional Networks, enhancing structural consistency while eliminating negative sampling bias. We theoretically prove that CL-GCL approximates node-level contrastive loss under mild conditions. Extensive experiments demonstrate consistent superiority in both accuracy and efficiency over state-of-the-art GCL methods.