ICLR 2026 论文列表

Data heterogeneity in Federated Learning (FL) leads to significant bias in local training. While recent efforts to introduce distributional statistics as priors have shown progress, they universally rely on a flawed global linearity assumption, failing to capture the nonlinear manifold structures prevalent in real-world data. This model-reality mismatch causes the calibration process to generate out-of-distribution (OOD) samples, which fundamentally misleads the model. To address this, we introduce a paradigm shift. We propose Federated Manifold Calibration (FedMC), a novel framework that learns and leverages the local, nonlinear geometry of data. FedMC employs local kernel PCA on the client side to learn fine-grained local geometries, and constructs a global "geometry dictionary" on the server side to aggregate and distribute this knowledge. Clients then utilize this dictionary to perform context-aware, on-manifold calibration. We validate our proposed method by integrating it with a wide range of existing FL algorithms. Experimental results show that by explicitly modeling nonlinear manifolds, FedMC consistently and significantly enhances the performance of these state-of-the-art methods across multiple benchmarks.

Distilling robust reasoning capabilities from large language models (LLMs) into smaller, computationally efficient student models remains an unresolved challenge. Despite recent advances, distilled models frequently suffer from superficial pattern memorization and subpar generalization. To overcome these limitations, we introduce a novel distillation framework that moves beyond simple mimicry to instill a deeper conceptual understanding. Our framework features two key innovations. \underline{\textit{First}}, to address pattern memorization, Explanatory Inversion (EI) generates targeted ``explanatory probes'' that compel the student to articulate the underlying logic behind an answer, rather than just memorizing it. \underline{\textit{Second}}, to improve generalization, Explanatory GRPO (\texttt{EXGRPO}) uses a reinforcement learning algorithm with a novel Dialogue Structure Utility Bonus, which explicitly rewards the student for maintaining a coherent reasoning process across these probes. Extensive evaluations on 12 datasets demonstrate significant improvements. Using Gemma-7b as the student model, our method yields an average \textbf{20.39\%} increase over zero-shot performance and a \textbf{6.02\%} improvement over the state-of-the-art distillation baselines. Moreover, models distilled with our method show remarkable training efficiency (e.g., surpassing vanilla fine-tuning with \textbf{10-25\%} training data) and strong generalization to out-of-distribution tasks.

Large language models (LLMs) exhibit strong abilities in multi-document reasoning, yet their evidence identification is highly sensitive to input order. We trace this limitation to attention mechanisms, where many heads overemphasize sequence boundaries and neglect central content. We systematically analyze attention distributions under document permutations and discover a small subset of heads that consistently prioritize task-relevant documents regardless of position. We formalize these as Expert Heads, identified via activation frequency and stability across permutations. Experiments on LLaMA, Mistral, and Qwen reveal architecture-specific patterns: mid-layer heads in LLaMA and Mistral dominate semantic integration, while deeper-layer heads in Qwen specialize in evidence selection. Moreover, Expert Heads exhibit concentrated focus during understanding and more distributed engagement during generation. Their activation strongly correlates with answer correctness, providing diagnostic signals for hallucination detection. Leveraging Expert Heads for document voting significantly improves retrieval and ranking on HotpotQA, 2WikiMultiHopQA, and MuSiQue, outperforming dense retrievers and LLM-based ranking with minimal overhead. Ablations confirm that even a small subset achieves robust gains. Our findings establish Expert Heads as a stable and interpretable mechanism for evidence integration, offering new directions for context pruning, hallucination mitigation, and head-guided training of LLMs

Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as the Dirichlet energy. We argue that these metrics have critical limitations and fail to reliably capture oversmoothing in realistic scenarios. For instance, they provide meaningful insights only for very deep networks, while typical GNNs show a performance drop already with as few as 10 layers. As an alternative, we propose measuring oversmoothing by examining the numerical or effective rank of the feature representations. We provide extensive numerical evaluation across diverse graph architectures and datasets to show that rank-based metrics consistently capture oversmoothing, whereas energy-based metrics often fail. Notably, we reveal that drops in the rank align closely with performance degradation, even in scenarios where energy metrics remain unchanged. Along with the experimental evaluation, we provide theoretical support for this approach, clarifying why Dirichlet-like measures may fail to capture performance drop and proving that the numerical rank of feature representations collapses to one for a broad family of GNN architectures.

Knowledge editing aims to efficiently correct factual errors in Language Models (LMs). The popular locate-then-edit approach modifies an MLP layer by finding an optimal mapping between its input vector (key) and output vector (value) that leads to the expression of the edited knowledge. However, existing methods without any constraints on the key and value vectors cause significant perturbations to the edited model. To address this, we propose Subspace Knowledge Edit (SUIT), a method that identifies and modifies only the subspace of critical features relevant to the edit. Our empirical results on LLaMA-3-8B, GPT-J-6B, and Qwen2.5-7B models show that SUIT dramatically improves knowledge preservation over strong baselines while maintaining high edit efficacy. This effectiveness confirms that SUIT successfully identifies the critical subspace for the edit. Further analyses provide additional validation for our approach. The source code and data will be released to the public upon publication of the paper.

Interventional causal discovery seeks to identify causal relations by leveraging distributional changes introduced by interventions, even in the presence of latent confounders. Beyond the spurious dependencies induced by latent confounders, we highlight a common yet often overlooked challenge in the problem due to post-treatment selection, in which samples are selectively included in datasets after interventions. This fundamental challenge widely exists in biological studies; for example, in gene expression analysis, both observational and interventional samples are retained only if they meet quality control criteria (e.g., highly active cells). Neglecting post-treatment selection may introduce spurious dependencies and distributional changes under interventions, which can mimic causal responses, thereby distorting causal discovery results and challenging existing causal formulations. To address this, we introduce a novel causal formulation that explicitly models post-treatment selection and reveals how its differential reactions to interventions can distinguish causal relations from selection patterns, allowing us to go beyond traditional equivalence classes toward the underlying true causal structure. We then characterize its Markov properties and propose a $\mathcal{F}$ine-grained $\mathcal{I}$nterventional equivalence class, named $\mathcal{FI}$-Markov equivalence, represented by a new graphical diagram, $\mathcal{F}$-PAG. Finally, we develop a provably sound and complete algorithm, $\mathcal{F}$-FCI, to identify causal relations, latent confounders, and post-treatment selection up to $\mathcal{FI}$-Markov equivalence, using both observational and interventional data. Experimental results on synthetic and real-world datasets demonstrate that our method recovers causal relations despite the presence of both selection and latent confounders.

Large Language Models (LLMs) have demonstrated impressive generalization ability by learning from extensive unlabeled text. However, they still exhibit reasoning mistakes, which can affect their trustworthiness and reliability. Although users can interact with LLMs and provide diverse and comprehensive queries to expose the flaws of LLMs, obtaining sufficient and effective feedback is demanding. Furthermore, comprehensively evaluating LLMs with limited labeled samples is difficult. These make it a challenge to diagnose and remedy the deficiencies in LLMs through rich label-free user queries. To tackle this challenge and considersing that LLMs' reasoning mistakes often stem from knowledge deficiencies, we propose label-free curricular meaningful learning (LaMer), which first employs relative entropy to diagnose and quantify knowledge deficiencies of LLMs in a label-free setting. Then, LaMer adaptively synthesizes augmentation data based on deficiency severity and progressively remedies them with a curricular remedy strategy. Experiments show that LaMer effectively diagnoses and remedies knowledge deficiencies in LLMs, improving various LLMs across seven out-of-distribution (OOD) reasoning benchmarks, achieving comparable results to baselines with only 40% training data. LaMer even surpasses methods that rely on labeled data for deficiency diagnosis. In application, LaMer offers a diagnostic tool for efficient LLM development.

Scaled post‑training now drives many of the largest capability gains in language models (LMs), yet its effect on pretrained knowledge remains poorly understood. Not all forgetting is equal: Forgetting one fact (e.g., a U.S. president or an API call) does not “average out” by recalling another. Hence, we propose a sample-wise paradigm to measure what is forgotten and when backward transfer occurs. Our metric counts 1→0 transitions (correct before post‑training, incorrect after) to quantify forgetting and 0→1 transitions to quantify backward transfer. Traditional task averages conflate these effects and obscure large changes. For multiple‑choice benchmarks, we add chance‑adjusted variants that subtract the expected contribution of random guessing from pre‑ and post‑training accuracies. We apply this framework across post‑training stages, model sizes, and data scales. Our large‑scale analysis across nearly 30 model pairs and 100 sub-benchmarks with up to 32,768 generated tokens per sample shows that: (1) Domain-continual pretraining induces moderate forgetting with low backward backward transfer; (2) RL/SFT post-training applied to base models and Instruction tuning yield substantial backward transfer with minimal forgetting; (3) Applying RL/SFT to instruction‑tuned models is sensitive on data scale: at small scales, both forgetting and backward transfer are small; at larger scales, effects are mixed and warrant further study with better controls; (4) Model merging does not reliably mitigate forgetting. Overall, our framework offers a practical yardstick for mapping how post‑training alters pretrained knowledge at scale -- enabling progress towards generally capable AI systems.

Dynamic graph representation learning under distribution shifts has drawn an increasing amount of attention in the research community, given its wide applicability in real-world scenarios. Existing methods typically employ a fixed-architecture design to extract invariant patterns. However, there may exist evolving distribution shifts in dynamic graphs, leading to suboptimal performance of fixed-architecture designs. To address this issue, we propose a novel adaptive-architecture design to handle evolving distribution shifts over time, to the best of our knowledge, for the first time. The proposed adaptive-architecture design introduces an adaptive mixture of architecture experts to capture invariant patterns under evolving distribution shifts, which imposes three challenges: 1) How to detect and characterize evolving distribution shifts to inform architectural decisions; 2) How to dynamically route different expert architectures to handle varying distribution characteristics; 3) How to ensure that the adaptive mixture of experts effectively discovers invariant patterns. To solve these challenges, we propose a novel \underline{\textbf{Ada}}ptive \underline{\textbf{Mix}}ture of Disentangled Experts (AdaMix) model to adaptively route architecture experts to varying distribution shifts and jointly learn spatio-temporal invariant patterns. Specifically, we propose a spatio-temporal distribution detector to infer evolving distribution shifts by jointly leveraging historical and current information. Building upon this, we develop a prototype-guided mixture of disentangled experts that adaptively routes experts with disentangled factors to different distribution shifts. Finally, we design a distribution-aware intervention mechanism that discovers invariant patterns based on expert selection of nodes. Extensive experiments on both synthetic and real-world datasets demonstrate that our proposed (AdaMix) model significantly outperforms state-of-the-art baselines.

Dynamic Text-Attribute Graphs (DyTAGs), characterized by time-evolving graph interactions and associated text attributes, are prevalent in real-world applications. Existing methods, such as Graph Neural Networks (GNNs) and Large Language Models (LLMs), mostly focus on static TAGs. Extending these existing methods to DyTAGs is challenging as they largely neglect the *recent-global temporal semantics*: the recent semantic dependencies among interaction texts and the global semantic evolution of nodes over time. Furthermore, applying LLMs to the abundant and evolving text in DyTAGs faces efficiency issues. To tackle these challenges, we propose $\underline{Dy}$namic $\underline{G}$lobal-$\underline{R}$ecent $\underline{A}$daptive $\underline{S}$emantic $\underline{P}$rocessing (DyGRASP), a novel method that leverages LLMs and temporal GNNs to efficiently and effectively reason on DyTAGs. Specifically, we first design a node-centric implicit reasoning method together with a sliding window mechanism to efficiently capture recent temporal semantics. In addition, to capture global semantic dynamics of nodes, we leverage explicit reasoning with tailored prompts and an RNN-like chain structure to infer long-term semantics. Lastly, we intricately integrate the recent and global temporal semantics as well as the dynamic graph structural information using updating and merging layers. Extensive experiments on DyTAG benchmarks demonstrate DyGRASP's superiority, achieving up to 34\% improvement in Hit@10 for destination node retrieval task. Besides, DyGRASP exhibits strong generalization across different temporal GNNs and LLMs.

The reversal curse---a language model's (LM) inability to infer an unseen fact ``B is A'' from a learned factA is B''---is widely considered a fundamental limitation. We show that this is not an inherent failure but an artifact of how models encode knowledge. By training LMs from scratch on a synthetic dataset of relational knowledge graphs, we demonstrate that bilinear relational structure emerges in their hidden representations. This structure is associated with alleviating the reversal curse, facilitating the inference of unseen reverse facts. Crucially, we also find that this bilinear structure plays a key role in consistent model editing. When a fact is updated in a LM with this structure, the edit correctly propagates to its reverse and other logically dependent facts. In contrast, models lacking this representation not only suffer from the reversal curse but also fail to generalize edits, further introducing logical inconsistencies. Our results establish that training on a relational knowledge dataset induces the emergence of bilinear internal representations, which in turn support LMs in behaving in a logically consistent manner after editing. This implies that the success of model editing may be tied not just to editing algorithms but to the underlying representational geometry of the knowledge being modified.

Continuous-time graph representation (CTGR) is a widely-used methodology in machine learning, physics, bioinformatics, and social networks. The sequential survival process in a latent space with the squared $\ell_2$ distance is an important ultra-low-dimensional embedding for CTGR. However, the squared $\ell_2$ distance violates the triangle inequality, which may cause distortion of the relative node positions in the latent space and thus deteriorates in social, contact, and collaboration networks. Reverting to the $\ell_2$ distance is infeasible because the corresponding integral computation is intractable. To solve these problems, we propose a theoretically-sound $\ell_1$ latent distance based continuous-time graph representation ($\ell_1$LD-CTGR). It facilitates a true latent metric space for the sequential survival process. Moreover, the integral of the hazard function is found to be a closed-form piece-wise exponential integral, which well fits the ultra-low-dimensional embedding. To handle the non-differentiable $\ell_1$ norm, we successfully find a descent direction of the hazard function to replace the gradient, enabling mainstream learning architectures to learn the parameters. Extensive experiments using both synthetic and real-world data show the competitive performance of $\ell_1$LD-CTGR.

Graph neural networks (GNNs) have emerged as a powerful tool for modeling graph-structured data, demonstrating remarkable success in many real-world applications such as complex biological network analysis, neuroscientific analysis, and social network analysis. However, existing GNNs often struggle with heterophilic graphs, where connected nodes tend to have dissimilar features or labels. While numerous methods have been proposed to address this challenge, they primarily focus on architectural designs without directly targeting the root cause of the heterophily problem. These approaches still perform even worse than the simplest MLPs on challenging heterophilic datasets. For instance, our experiments show that 23 latest GNNs still fall behind the MLP on the Actor dataset. This critical challenge calls for an innovative approach to addressing graph heterophily beyond architectural designs. To bridge this gap, we propose and study a new and unexplored paradigm: directly increasing the graph homophily via a carefully designed graph transformation. In this work, we present a simple yet effective framework called Graph Homophily Booster (GRAPHITE) to address graph heterophily. To the best of our knowledge, this work is the first method that explicitly transforms the graph to directly improve the graph homophily. Stemmed from the exact definition of homophily, our proposed GRAPHITE creates feature nodes to facilitate homophilic message passing between nodes that share similar features. Furthermore, we both theoretically and empirically show that our proposed GRAPHITE significantly increases the homophily of originally heterophilic graphs, with only a slight increase in the graph size. Extensive experiments on challenging datasets demonstrate that our proposed GRAPHITE significantly outperforms state-of-the-art methods on heterophilic graphs while achieving comparable accuracy with state-of-the-art methods on homophilic graphs. Furthermore, our proposed graph transformation alone can already enhance the performance of homophilic GNNs on heterophilic graphs, even though they were not originally designed for heterophilic graphs. Our code is publicly available at https://github.com/q-rz/ICLR26-GRAPHITE .

State-of-the-art models for code representation, such as GraphCodeBERT, embed the hierarchical structure of source code into Euclidean space. This approach can lead to significant representation distortion, especially when embedding deep or highly branched hierarchies,limiting the models' ability to capture deep program semantics. We argue that the natural geometry for code is hyperbolic, as its exponential volume growth perfectly matches the tree-like structure of a code's Abstract Syntax Tree (AST), enabling low-distortion hierarchical embeddings. We introduce {HypeCodeNet}, a geometric deep learning framework that operates natively in hyperbolic space. Formulated in the numerically stable Lorentz model, its manifold-aware components include a hyperbolic embedding layer, a tangent space message-passing mechanism, and a geodesic-based attention module. On code clone detection, code completion, and link prediction, HypeCodeNet significantly outperforms existing Euclidean models, especially on tasks requiring deep structural understanding. Our work suggests that hyperbolic geometry offers a geometrically sound foundation for code representation, establishing hyperbolic geometry as a key to unlocking the structured semantics of code.

Abductive reasoning in knowledge graphs aims to generate plausible logical hypotheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to a lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis reward oversensitivity. To address these challenges, we propose **CtrlHGen**, a **C**on**tr**ollable **l**ogcial **H**ypothesis **Gen**eration framework for abductive reasoning over knowledge graphs, trained in a two-stage paradigm including supervised learning and subsequent reinforcement learning. To mitigate hypothesis space collapse, we design a dataset augmentation strategy based on sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components. To address hypothesis reward oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a condition-adherence reward to guide the generation toward user-specified control constraints. Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines. Our code is available at https://github.com/HKUST-KnowComp/CtrlHGen.

Retrieval-Augmented Generation (RAG) aims to mitigate hallucinations in large language models (LLMs) by grounding responses in retrieved documents. Yet, RAG-based LLMs still hallucinate even when provided with correct and sufficient context. A growing line of work suggests that this stems from an imbalance between how models use external context and their internal knowledge, and several approaches have attempted to quantify these signals for hallucination detection. However, existing methods require extensive hyperparameter tuning, limiting their generalizability. We propose LUMINA, a novel framework that detects hallucinations in RAG systems through context--knowledge signals: external context utilization is quantified via distributional distance, while internal knowledge utilization is measured by tracking how predicted tokens evolve across transformer layers. We further introduce a framework for statistically validating these measurements. Experiments on common RAG hallucination benchmarks and four open-source LLMs show that LUMINA achieves consistently high AUROC and AUPRC scores, outperforming prior utilization-based methods by up to +13% AUROC on HalluRAG. Moreover, LUMINA remains robust under relaxed assumptions about retrieval quality and model matching, offering both effectiveness and practicality. LUMINA: https://github.com/deeplearning-wisc/LUMINA

Reasoning on Temporal Knowledge Graphs (TKGs) is essential for predicting future events and time-aware facts. While existing methods are effective at capturing relational dynamics, their performance is limited by a closed-world assumption, which fails to account for emerging entities not present in the training. Notably, these entities continuously join the network without historical interactions. Empirical study reveals that emerging entities are widespread in TKGs, comprising roughly 25\% of all entities. The absence of historical interactions of these entities leads to significant performance degradation in reasoning tasks. Whereas, we observe that entities with semantic similarities often exhibit comparable interaction histories, suggesting the presence of transferable temporal patterns. Inspired by this insight, we propose TransFIR (Transferable Inductive Reasoning), a novel framework that leverages historical interaction sequences from semantically similar known entities to support inductive reasoning. Specifically, we propose a codebook-based classifier that categorizes emerging entities into latent semantic clusters, allowing them to adopt reasoning patterns from similar entities. Experimental results demonstrate that TransFIR outperforms all baselines in reasoning on emerging entities, achieving an average improvement of 28.6\% in Mean Reciprocal Rank (MRR) across multiple datasets. The implementations are available at https://anonymous.4open.science/r/TransFIR-C72F.

Graph-based Retrieval-Augmented Generation (RAG) systems leverage interconnected knowledge structures to capture complex relationships that flat retrieval struggles with, enabling multi-hop reasoning. Yet most existing graph-based methods suffer from (i) heuristic designs lacking theoretical guarantees for subgraph quality or relevance and/or (ii) the use of static exploration strategies that ignore the query's holistic meaning, retrieving neighborhoods or communities regardless of intent. We propose *Query-Aware Flow Diffusion RAG* (QAFD-RAG), a training-free framework that dynamically adapts graph traversal to each query's holistic semantics. The central innovation is *query-aware traversal*: during graph exploration, edges are dynamically weighted by how well their endpoints align with the query's embedding, guiding flow along semantically relevant paths while avoiding structurally connected but irrelevant regions. These query-specific reasoning subgraphs enable the first statistical guarantees for query-aware graph retrieval, showing that QAFD-RAG recovers relevant subgraphs with high probability under mild signal-to-noise conditions. The algorithm converges exponentially fast, with complexity scaling with the retrieved subgraph size rather than the full graph. Experiments on question answering and text-to-SQL tasks demonstrate consistent improvements over state-of-the-art graph-based RAG methods.

Knowledge Distillation (KD) has emerged as a powerful technique for model compression, enabling lightweight student networks to benefit from the performance of redundant teacher networks. However, the inherent capacity gap often limits the performance of student networks. Inspired by the expressiveness of pretrained teacher networks, a compelling research question arises: is there a type of network that can not only inherit the teacher’s structure but also maximize the inheritance of its knowledge? Furthermore, how does the performance of such an inheriting network compare to that of student networks, all benefiting from the same teacher network? To further explore this question, we propose InherNet, a neural network inheritance method that performs asymmetric low-rank decomposition on the teacher’s weights and reconstructs a lightweight yet expressive network without significant architectural disruption. By leveraging Singular Value Decomposition (SVD) for initialization to ensure the inheritance of principal knowledge, InherNet effectively balances depth, width, and compression efficiency. Experimental results across unimodal and multimodal tasks demonstrate that InherNet achieves higher performance compared to student networks of similar parameter sizes. Our findings reveal a promising direction for future research in efficient model compression beyond traditional distillation.