ICLR 2026 论文列表

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between the pre-trained model and target domains. In this paper, we propose a fresh differential geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then “glues” the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue’s geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold.

Federated Graph-level Clustering (FGC) offers a promising framework for analyzing distributed graph data while ensuring privacy protection. However, existing methods fail to simultaneously consider knowledge heterogeneity across intra- and inter-client, and still attempt to share as much knowledge as possible, resulting in consensus failure in the server. To solve these issues, we propose a novel **F**ederated **G**raph-level **C**lustering **N**etwork with **D**ual **K**nowledge **S**eparation (FGCN-DKS). The core idea is to decouple differentiated subgraph patterns and optimize them separately on the client, and then leverage cluster-oriented patterns to guide personalized knowledge aggregation on the server. Specifically, on the client, we separate personalized variant subgraphs and cluster-oriented invariant subgraphs for each graph. Then the former are retained locally for further refinement of the clustering process, while pattern digests are extracted from the latter for uploading to the server. On the server, we calculate the relation of inter-cluster patterns to adaptively aggregate cluster-oriented prototypes and parameters. Finally, the server generates personalized guidance signals for each cluster of clients, which are then fed back to local clients to enhance overall clustering performance. Extensive experiments on multiple graph benchmark datasets have proven the superiority of the proposed FGCN-DKS over the SOTA methods.

The pretrain-finetuning paradigm has achieved notable success in graph learning. Moreover, merging models fine-tuned on different tasks to enable a parameter-efficient model with multi-task capabilities is gaining increasing attention for its practicality. However, existing model merging methods, such as weight averaging and task arithmetic, struggle to generalize well to graph structures and Graph Neural Network (GNN) models due to the unique structural heterogeneity of graph data. In this paper, we propose an innovative graph model merging framework called G-Merging for merging multiple task-specific fine-tuned GNN models. G-Merging first employs task arithmetic to coarsely merge graph models, capturing shared cross-task knowledge. Second, it introduces a Topology-aware Wasserstein Distance (TWD) loss to train lightweight task adapters, preserving domain-specific graph patterns via aligning the embeddings of merged and fine-tuned models. Third, G-Merging integrates the adapters into a training-free, topology-aware router within a mixture-of-experts (MoE) architecture, dynamically routing input graphs to task-specific adapters based on structural similarity, thereby mitigating conflicts and enhancing knowledge sharing. Extensive experiments on 8 graph downstream datasets demonstrate the effectiveness of G-Merging, showing impressive performance close to or exceeding individual finetuned models while improving parameters and training efficiency. Our code is available at https://anonymous.4open.science/r/G-Merging-D515

One of the most challenging problems in graph machine learning is generalizing across graphs with diverse properties. Graph neural networks (GNNs) face a fundamental limitation: they require separate training for each new graph, preventing universal generalization across diverse graph datasets. A critical challenge facing GNNs lies in their reliance on labeled training data for each individual graph, a requirement that hinders the capacity for universal node classification due to the heterogeneity inherent in graphs --- differences in homophily levels, community structures, and feature distributions across datasets. Inspired by the success of large language models (LLMs) that achieve in-context learning through massive-scale pre-training on diverse datasets, we introduce NodePFN. This universal node classification method generalizes to arbitrary graphs without graph-specific training. NodePFN learns posterior predictive distributions (PPDs) by training only on thousands of synthetic graphs generated from carefully designed priors. Our synthetic graph generation covers real-world graphs through the use of random networks with controllable homophily levels and structural causal models for complex feature-label relationships. We develop a dual-branch architecture combining context-query attention mechanisms with local message passing to enable graph-aware in-context learning. Extensive evaluation on 23 benchmarks demonstrates that a single pre-trained NodePFN achieves 71.27% average accuracy. These results validate that universal graph learning patterns can be effectively learned from synthetic priors, establishing a new paradigm for generalization in node classification.

Even a slight perturbation in the graph structure can cause a significant drop in the accuracy of graph neural networks (GNNs). Most existing attacks leverage gradient information to perturb edges. This relaxes the attack's optimization problem from a discrete to a continuous space, resulting in solutions far from optimal. It also prevents the adaptability of the attack to non-differentiable objectives. Instead, we introduce a few simple, yet effective, enhancements of an evolutionary-based algorithm to solve the discrete optimization problem directly. Our Evolutionary Attack EvA works with any black-box model and objective, eliminating the need for a differentiable proxy loss. This allows us to design two novel attacks that reduce the effectiveness of robustness certificates and break conformal sets. EvA uses sparse representations to significantly reduce memory requirements and scale to larger graphs. We also introduce a divide and conquer strategy that improves both EvA and existing gradient-based attacks. Among our experiments, EvA shows $\sim$11\% additional drop in accuracy on average compared to the best previous attack, revealing significant untapped potential in designing attacks.

We investigate whether large language models (LLMs) can predict whether they will succeed on a given task and whether their predictions improve as they progress through multi-step tasks. We also investigate whether LLMs can learn from in-context experiences to make better decisions about whether to pursue a task in scenarios where failure is costly. All LLMs we tested are overconfident, but most predict their success with better-than-random discriminatory power. We find that newer and larger LLMs generally do not have greater discriminatory power, though Claude models do show such a trend. On multi-step agentic tasks, the overconfidence of several frontier LLMs worsens as they progress through the tasks, and reasoning LLMs perform comparable to or worse than non-reasoning LLMs. With in-context experiences of failure, some LLMs reduce their overconfidence leading to significantly improved decision making, while others do not. Interestingly, all LLMs’ decisions are approximately rational given their estimated probabilities of success, yet their overly-optimistic estimates result in poor decision making. These results suggest that current LLM agents are hindered by their lack of awareness of their own capabilities. We discuss the implications of LLMs' awareness of their capabilities for AI misuse and misalignment risks.

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the Anti de Sitter space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. In particular, we employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF is a complete invariant of (non-hierarchical) sequences of partitions and can be interpreted as a higher-order extension of Sankey diagrams, which reduce to dendrograms for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We then demonstrate through experiments the use of MCbiF Hilbert functions as interpretable topological feature maps for downstream machine learning tasks, and show that MCbiF feature maps outperform both baseline features and representation learning methods on regression and classification tasks for non-hierarchical sequences of partitions. We also showcase an application of MCbiF to real-world data of non-hierarchical wild mice social grouping patterns across time.

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs but is challenged by complex, multi-faceted distributional shifts. Existing methods attempt to reduce distributional shifts by aligning manually selected graph elements (e.g., node attributes or structural statistics), which typically require manually designed graph filters to extract relevant features before alignment. However, such approaches are inflexible: they rely on scenario-specific heuristics, and struggle when dominant discrepancies vary across transfer scenarios. To address these limitations, we propose \textbf{ADAlign}, an Adaptive Distribution Alignment framework for GDA. Unlike heuristic methods, ADAlign requires no manual specification of alignment criteria. It automatically identifies the most relevant discrepancies in each transfer and aligns them jointly, capturing the interplay between attributes, structures, and their dependencies. This makes ADAlign flexible, scenario-aware, and robust to diverse and dynamically evolving shifts. To enable this adaptivity, we introduce the Neural Spectral Discrepancy (NSD), a theoretically principled parametric distance that provides a unified view of cross-graph shifts. NSD leverages neural characteristic function in the spectral domain to encode feature-structure dependencies of all orders, while a learnable frequency sampler adaptively emphasizes the most informative spectral components for each task via minimax paradigm. Extensive experiments on 10 datasets and 16 transfer tasks show that ADAlign not only outperforms state-of-the-art baselines but also achieves efficiency gains with lower memory usage and faster training.

Data-centric distillation, including data augmentation, selection, and mixing, offers a promising path to creating smaller, more efficient student Large Language Models (LLMs) that retain strong reasoning abilities. However, there still lacks a comprehensive benchmark to systematically assess the effect of each distillation approach. This paper introduces DC-CoT, the first data-centric benchmark that investigates data manipulation in chain-of-thought (CoT) distillation from method, model and data perspectives. Utilizing various teacher models (e.g., o4-mini, Gemini-Pro, Claude-3.5) and student architectures (e.g., 3B, 7B parameters), we rigorously evaluate the impact of these data manipulations on student model performance across multiple reasoning datasets, with a focus on in-distribution (IID) and out-of-distribution (OOD) generalization, and cross-domain transfer. Our findings aim to provide actionable insights and establish best practices for optimizing CoT distillation through data-centric techniques, ultimately facilitating the development of more accessible and capable reasoning models. The nonymous codebase can be accessed https://anonymous.4open.science/r/DC-COT-FF4C/

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.

Knowledge distillation has become a crucial technique to transfer the capacities of large language models (LLMs) to smaller, more efficient models for practical deployment. While recent work exploits rich information from intermediate states of the teacher model for more effective knowledge transfer, imperfect knowledge from the teacher can also mislead student learning, restricting the student’s generalization capacity. In this work, we propose a two-stage distillation framework that is effective for diverse knowledge distillation scenarios. In the first stage, we pretrain projectors to extract and compress teacher knowledge into a low-dimensional vector space via self-reconstruction. In the second stage, we perform distillation with a hybrid objective that combines learning from the compressed teacher representations with standard supervised fine-tuning on ground-truth data. Our key innovation is residual learning for LLM distillation, where the student learns to make predictions based on the differential between its representations and projected states from the teacher. This approach encourages the student to further improve its representations beyond potentially erroneous teacher knowledge. For Mixture-of-Experts (MoE) teacher models, we further fuse the experts’ outputs using a self-attention mechanism for better utilizing the teacher knowledge. Moreover, to support the cross-tokenizer distillation setting, where the teacher and student models have different vocabularies, we adopt a cross-model attention mechanism that eliminates the need for explicit token alignment rules. Experimental results show the superior performance of our proposed framework under both same- and cross-tokenizer settings, demonstrating the effectiveness in preserving teacher knowledge and improving student generalization capability.

Trustworthy language models should provide both correct and verifiable answers. However, citations generated directly by standalone LLMs are often unreliable due to hallucinations. As a result, current systems insert citations by querying an external retriever at inference time, introducing latency, infrastructure dependence, and vulnerability to retrieval noise. We explore whether LLMs can be made to reliably attribute to the documents seen during (continual) pretraining, without test‑time retrieval, by revising the training process. To study this, we construct **CitePretrainBench**, a benchmark that mixes real‑world corpora (Wikipedia, Common Crawl, arXiv) with novel, unseen documents and probes both short‑form (single fact) and long‑form (multi‑fact) citation tasks. Our approach follows a two-stage process: (1) Continual-pretraining to index factual knowledge by binding it to persistent document identifiers; (2) Instruction tuning to elicit citation behavior. We introduce **Active Indexing** for the first stage, which creates generalizable, source-anchored bindings by augmenting training with synthetic data that (i) restate each fact in diverse, compositional forms and (ii) enforce bidirectional training (source$\to$fact and fact$\to$source). This equips the model to both generate content from a cited source and attribute its own answers, improving robustness to paraphrase and composition. Experiments with Qwen‑2.5‑7B and 3B show that Active Indexing consistently outperforms a Passive Indexing baseline, which simply appends an identifier to each document, achieving citation precision gains of up to 30.2\% across all tasks and models. Our ablation studies reveal that performance continues to improve as we scale the amount of augmented data, showing a clear upward trend even at 16× the original token count. Finally, we show that internal citations complement external ones by making the model more robust to retrieval noise.

Current Chain-of-Thought (CoT) verification methods predict reasoning correctness based on outputs (black-box) or activations (gray-box), but offer limited insight into \textit{why} a computation fails. We introduce a white-box method: \textbf{Circuit-based Reasoning Verification (CRV)}. We hypothesize that attribution graphs of correct CoT steps, viewed as \textit{execution traces} of the model's latent reasoning circuits, possess distinct structural fingerprints from those of incorrect steps. By training a classifier on structural features of these graphs, we show that these traces contain a powerful signal of reasoning errors. Our white-box approach yields novel scientific insights unattainable by other methods. (1) We demonstrate that structural signatures of error are highly predictive, establishing the viability of verifying reasoning directly via its computational graph. (2) We find these signatures to be highly domain-specific, revealing that failures in different reasoning tasks manifest as distinct computational patterns. (3) We provide evidence that these signatures are not merely correlational; by using our analysis to guide targeted interventions on individual transcoder features, we successfully correct the model's faulty reasoning. Our work shows that, by scrutinizing a model's computational process, we can move from simple error detection to a deeper, causal understanding of LLM reasoning.

The transcriptional response to genetic perturbation reveals fundamental insights into complex cellular systems. While current approaches have made progress in predicting genetic perturbation responses, they provide limited biological understanding and cannot systematically refine existing knowledge. Overcoming these limitations requires an end-to-end integration of data-driven learning and existing knowledge. However, this integration is challenging due to inconsistencies between data and knowledge bases, such as noise, misannotation, and incompleteness. To address this challenge, we propose ALIGNED (Adaptive aLignment for Inconsistent Genetic kNowledgE and Data), a neuro-symbolic framework based on the Abductive Learning (ABL) paradigm. This end-to-end framework aligns neural and symbolic components and performs systematic knowledge refinement. We introduce a balanced consistency metric to evaluate the predictions' consistency against both data and knowledge. Our results show that ALIGNED outperforms state-of-the-art methods by achieving the highest balanced consistency, while also re-discovering biologically meaningful knowledge. Our work advances beyond existing methods to enable both the transparency and the evolution of mechanistic biological understanding.

Frontier language models appear strong at solving reasoning problems, but their performance is often inflated by shortcuts such as memorisation and knowledge. We introduce LingOLY-TOO, a challenging reasoning benchmark of 6,995 questions that counters these shortcuts by applying expert-designed obfuscations to Linguistics Olympiad problems. These obfuscations preserve the underlying solution logic while removing orthographic clues that could trigger patterns from memorisation or knowledge. Our experiments show that models exploit shortcuts on the original questions as performance markedly drop upon obfuscation. Even the best reasoning models remain highly sensitive, with scores dropping from around $0.60$ on original problems to $0.48$ after obfuscation. LingOLY-TOO disentangles reasoning from knowledge, offering a clear measure of true reasoning capabilities.

Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of pseudometrics that capture different degrees of structural similarity between graphs and relate these similarities to generalization, and consequently, the performance of expressive GNNs. By considering a setting where graph labels are correlated with structural features, we derive generalization bounds that depend on the distance between training and test graphs, model complexity, and training set size. These bounds reveal that more expressive GNNs may generalize worse unless their increased complexity is balanced by a sufficiently large training set or reduced distance between training and test graphs. Our findings relate expressivity and generalization, offering theoretical insights supported by empirical results.

Knowledge distillation from Large Language Models (LLMs) to smaller models has emerged as a critical technique for deploying efficient AI systems. However, current methods for distillation via synthetic data lack pedagogical awareness, treating knowledge transfer as a one-off data synthesis and training task rather than a systematic learning process. In this paper, we propose a novel pedagogically-inspired framework for LLM knowledge distillation that draws from fundamental educational principles. Our approach introduces a three-stage pipeline—**Knowledge Identifier**, **Organizer**, and **Adapter** (**IOA**)—that systematically identifies knowledge deficiencies in student models, organizes knowledge delivery through progressive curricula, and adapts representations to match the cognitive capacity of student models. We integrate Bloom's Mastery Learning Principles and Vygotsky's Zone of Proximal Development to create a dynamic distillation process where student models approach teacher model's performance on prerequisite knowledge before advancing, and new knowledge is introduced with controlled, gradual difficulty increments. Extensive experiments using LLaMA-3.1/3.2 and Qwen2.5 as student models demonstrate that IOA achieves significant improvements over baseline distillation methods, with student models retaining 94.7\% of teacher performance on DollyEval while using less than 1/10th of the parameters. Our framework particularly excels in complex reasoning tasks, showing 19.2\% improvement on MATH and 22.3\% on HumanEval compared with state-of-the-art baselines.

We present a systematic study of medical-domain interpretability in Large Language Models (LLMs). We study how the LLMs both represent and process medical knowledge through four different interpretability techniques: (1) UMAP projections of intermediate activations, (2) gradient-based saliency with respect to the model weights, (3) layer lesioning/removal and (4) activation patching. We present knowledge maps of five LLMs which show, at a coarse-resolution, where knowledge about patient's ages, medical symptoms, diseases and drugs is stored in the models. In particular for Llama3.3-70B, we find that most medical knowledge is processed in the first half of the model's layers. In addition, we find several interesting phenomena: (i) age is often encoded in a non-linear and sometimes discontinuous manner at intermediate layers in the models, (ii) the disease progression representation is non-monotonic and circular at certain layers of the model, (iii) in Llama, drugs cluster better by medical specialty rather than mechanism of action, especially for Llama and (iv) Gemma-27B and MedGemma-27B have activations that collapse at intermediate layers but recover by the final layers. These results can guide future research on fine-tuning, un-learning or de-biasing LLMs for medical tasks by suggesting at which layers in the model these techniques should be applied. We attached our source code to the paper for reproducibility.