ICLR 2026 论文列表

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (\textit{RoPE}) encode positions through \textit{fixed-angle} rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce \textit{Selective RoPE}, an \textit{input-dependent} rotary embedding mechanism, that generalizes \textit{RoPE}, and enables rotation in \textit{arbitrary angles} for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with \textit{Selective RoPE}, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.

Sheaf neural networks (SNNs) leverage cellular sheaves to induce flexible diffusion processes on graphs, generalizing the diffusion mechanism of classical graph neural networks. While SNNs have been shown to cope well with heterophilic tasks and alleviate oversmoothing, we argue that there is further room for improving sheaf diffusion. More specifically, we show that SNNs do not allow nodes to independently choose how they cooperate with their neighbors, i.e., whether they convey and/or gather information to/from their neighbors. To address this issue, we first introduce the notion of cellular sheaves over directed graphs and characterize their in- and out-degree Laplacians. We then leverage our construction to propose Cooperative Sheaf Neural Network (CSNN). Additionally, we formally characterize its receptive field and prove that it allows nodes to selectively attend (listen) to arbitrarily far nodes while ignoring all others in their path, which is key to alleviating oversquashing. Our results on synthetic data empirically substantiate our claims, showing that CSNN can handle long-range interactions while avoiding oversquashing. We also show that CSNN performs strongly in heterophilic node classification and long-range graph classification benchmarks.

Heterogeneous Information Networks (HINs) provide a powerful framework for modeling multi-typed entities and relations, typically defined under a fixed schema. Yet, most research assumes this structure is given, overlooking the fact that alternative designs can emphasize different aspects of the data and substantially influence downstream performance. As a theoretical foundation for such designs, we introduce the principle of entity-attribute duality: attributes can be atomized as entities with their associated relations, while entities can, in turn, serve as attributes of others. This principle motivates atomic HIN, a canonical representation that makes all modeling choices explicit and achieves maximal expressiveness. Building on this foundation, we propose a systematic framework for task-specific schema refinement. Within this framework, we demonstrate that widely used benchmarks correspond to heuristic refinements of the atomic HIN---often far from optimal. Across eight datasets, refinement alone enables a simplified Relational GCN (sRGCN) to reach state-of-the-art performance on node- and link-level tasks, with further gains from advanced HGNNs. These results highlight schema design as a key dimension in heterogeneous graph modeling. By releasing the atomic HINs, searched schemas, and refinement framework, we enable principled benchmarking and open the way for future work on schema-aware learning, automated structure discovery, and next-generation HGNNs.

Graph clustering is a fundamental task in data analysis, aiming at grouping nodes with similar characteristics in the graph into clusters. This problem has been widely explored using graph neural networks (GNNs) due to their ability to leverage node attributes and graph topology for effective cluster assignments. However, representations learned through GNNs typically struggle to capture global relationships between nodes via local message-passing mechanisms. Moreover, the redundancy and noise inherently present in the graph data may easily result in node representations lacking compactness and robustness. To address the aforementioned issues, we propose a conjoint framework called CoCo, which captures compactness and consistency in the learned node representations for deep graph clustering. Technically, our CoCo leverages graph convolutional filters to learn robust node representations from both local and global views, and then encodes them into low-rank compact embeddings, thus effectively removing the redundancy and noise as well as uncovering the intrinsic underlying structure. To further enrich the node semantics, we develop a consistency learning strategy based on compact embeddings to facilitate knowledge transfer from the two perspectives. Our experimental findings indicate that our proposed CoCo outperforms state-of-the-art counterparts on various benchmark datasets.

Knowledge graphs provide structured context for multi‑hop question answering, but deployed systems must balance answer accuracy with strict latency and cost targets while preserving provenance. Static $k$‑hop expansions and ``think‑longer'' prompting often over‑retrieve, inflate context, and yield unpredictable runtime. Thus, we introduce CLAUSE, an agentic three-agent neuro‑symbolic framework that treats context construction as a sequential decision process over knowledge graphs, deciding what to expand, which paths to follow or backtrack, what evidence to keep and when to stop. Latency (interaction steps) and prompt cost (selected tokens) are exposed as user‑specified budgets or prices, allowing per‑query adaptation to trade‑offs among accuracy, latency, and cost without retraining. CLAUSE employs the proposed Lagrangian‑Constrained Multi‑Agent Proximal Policy Optimization (LC‑MAPPO) algorithm to coordinate three agents: Subgraph Architect, Path Navigator, and Context Curator, so that subgraph construction, reasoning paths discovery, and evidence selection are jointly optimized under per‑query's resource budgets on edge edits, interaction steps, and selected tokens. Across HotpotQA, MetaQA, and FactKG, CLAUSE yields higher EM@1 while reducing subgraph growth and end-to-end latency at equal or lower token budgets. On MetaQA-2-hop, relative to the strongest RAG baseline (GraphRAG), CLAUSE achieves $+39.3$ EM@1 with 18.6% lower latency, and 40.9% lower edge growth. The resulting contexts are compact, provenance‑preserving, and deliver predictable performance under deployment constraints.

Watermarking provides an effective means for data governance. However, conventional post-editing graph watermarking approaches degrade the graph quality and involve NP-hard subroutines. Alternatively, recent approaches advocate for embedding watermarking patterns in the noisy latent during data generation from diffusion models, but remain uncharted for graph models due to the hardness of inverting the graph diffusion process. In this work, we propose CheckWate: the first watermarking framework for graph diffusion models embedding checkerboard watermark and providing polynomial time verification. To address NP-completeness due to graph isomorphism, CheckWate embeds the watermark into the latent eigenvalues, which are isomorphism-invariant. To detect the watermark through reversing the graph diffusion process, CheckWate leverages the graph eigenvectors to approximately dequantizes the discrete graph back to the continuous latent, with theoretical guarantees on the detectability and dequantization error. We further introduce a latent sparsification mechanism to enhance the robustness of CheckWate against graph modifications. We evaluate CheckWate on four datasets and four graph modification attacks, against three generation time watermark schemes. CheckWate achieves remarkable generation quality while being detectable under strong attacks such as isomorphism, whereas the baselines are unable to detect the watermark. Code available at: https://anonymous.4open.science/r/checkwate.

Graph neural networks (GNNs) are the standard for learning on graphs, yet they have limited expressive power, often expressed in terms of the Weisfeiler-Leman (WL) hierarchy or within the framework of first-order logic. In this context, topological neural networks (TNNs) have recently emerged as a promising alternative for graph representation learning. By incorporating higher-order relational structures into message-passing schemes, TNNs offer higher representational power than traditional GNNs. However, a fundamental question remains open: _what is the logical expressiveness of TNNs?_ Answering this allows us to characterize precisely which binary classifiers TNNs can represent. In this paper, we address this question by analyzing isomorphism tests derived from the underlying mechanisms of general TNNs. We introduce and investigate the power of higher-order variants of WL-based tests for combinatorial complexes, called $k$-CCWL test. In addition, we introduce the topological counting logic $TC_{k}$, an extension of standard counting logic featuring a novel pairwise counting quantifier $\exists^{N}(x_i,x_j) \varphi(x_i,x_j),$ which explicitly quantifies pairs $(x_i, x_j)$ satisfying property $\varphi$. We rigorously prove the exact equivalence: $\text{k-CCWL} \equiv \text{TC}_{k{+}2} \equiv \text{Topological }(k{+}2)\text{-pebble game}.$ These results establish a logical expressiveness theory for TNNs.

Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) face well-documented theoretical and practical limitations. Graph positional encoding (PE) has emerged as a promising direction to address these limitations. The Euler Characteristic Transform (ECT) is an efficiently computable geometric–topological invariant that characterizes shapes and graphs. In this work, we combine the differentiable approximation of the ECT (DECT) and its local variant ($\ell$-ECT) to propose LEAP, a new end-to-end trainable local structural PE for graphs. We evaluate our approach on multiple real-world datasets as well as on a synthetic task designed to test its ability to extract topological features. Our results underline the potential of LEAP-based encodings as a powerful component for graph representation learning pipelines.

Graph Neural Networks (GNNs) have demonstrated remarkable success in various domains such as social networks, molecular chemistry, and more. A crucial component of GNNs is the pooling procedure, in which the node features calculated by the model are combined to form an informative final descriptor to be used for the downstream task. However, previous graph pooling schemes rely on the last GNN layer features as an input to the pooling or classifier layers, potentially under-utilizing important activations of previous layers produced during the forward pass of the model, which we regard as \emph{historical graph activations}. This gap is particularly pronounced in cases where a node’s representation can shift significantly over the course of many graph neural layers, and worsen by graph-specific challenges such as over-smoothing in deep architectures. To bridge this gap, we introduce HistoGraph, a novel two‑stage attention‑based final aggregation layer that first applies a unified layer-wise attention over intermediate activations, followed by node-wise attention. By modeling the evolution of node representations across layers, our HistoGraph leverages both the activation history of nodes and the graph structure to refine features used for final prediction. Empirical results on multiple graph classification benchmarks demonstrate that HistoGraph offers strong performance that consistently improves traditional techniques, with particularly strong robustness in deep GNNs.

Graphon models have emerged as powerful tools for modeling complex network structures by capturing connection probabilities among nodes. A key challenge in their application lies in accurately characterizing the graphon function, particularly with respect to parameters that govern its smoothness, which significantly impact the estimation accuracy. In this article, we propose a novel graphon cross-validation method for selecting tuning parameters and estimation approaches. Our method is both theoretically sound and computationally efficient. We show that our proposed cross-validation score is asymptotically parallel to the estimation error. Through extensive simulations and real-world applications, we demonstrate that our method consistently delivers superior computational efficiency and accuracy.

We study the application of graph random features (GRFs) – a recently-introduced stochastic estimator of graph node kernels – to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference with GRFs enjoys $\mathcal{O}(N^{3/2})$ time complexity with respect to the number of nodes $N$, with probabilistic accuracy guarantees. In contrast, exact kernels generally incur $\mathcal{O}(N^{3})$. Wall-clock speedups and memory savings unlock Bayesian optimisation with over 1M graph nodes on a single computer chip, whilst preserving competitive performance.

Knowledge distillation has emerged as a pivotal technique for transferring knowledge from stronger large language models (LLMs) to smaller, more efficient models. However, traditional distillation approaches face challenges related to knowledge conflicts and high resource demands, particularly when leveraging multiple teacher models. In this paper, we introduce the concept of **Knowledge Purification**, which consolidates the rationales from multiple teacher LLMs into a single rationale, thereby mitigating conflicts and enhancing efficiency. To investigate the effectiveness of knowledge purification, we further propose five purification methods from various perspectives. Our experiments demonstrate that these methods not only improve the performance of the distilled model but also effectively alleviate knowledge conflicts. Moreover, router-based methods exhibit robust generalization capabilities, underscoring the potential of innovative purification techniques in optimizing multi-teacher distillation and facilitating the practical deployment of powerful yet lightweight models.

Autoregressive large language models (LLMs) have achieved remarkable improvement across many tasks but incur high computational and memory costs. Knowledge distillation (KD) mitigates this issue by transferring knowledge from a large teacher to a smaller student through distributional alignment. Previous studies have proposed various discrepancy metrics, but the capacity gap and training instability caused by near-zero probabilities, stemming from the high-dimensional output of LLMs, remain fundamental limitations. To overcome these challenges, several approaches implicitly or explicitly incorporating assistant distribution have recently been proposed. However, the past proposals of assistant distributions have been a fragmented approach without a systematic investigation of the interpolation path and the divergence. This paper proposes $\alpha$-mixture assistant distribution, a novel generalized family of assistant distributions, and $\alpha$-mixture distillation, coined AMiD, a unified framework for KD using the assistant distribution. The $\alpha$-mixture assistant distribution provides a continuous extension of the assistant distribution by introducing a new distribution design variable $\alpha$, which has been fixed in all previous approaches. Furthermore, AMiD generalizes the family of divergences used with the assistant distributions based on optimality, which has also been restricted in previous works. Through extensive experiments, we demonstrate that AMiD offers superior performance and training stability by leveraging a broader and theoretically grounded assistant distribution space.

Retrieval-augmented generation (RAG) has shown some success in augmenting large language models (LLMs) with external knowledge. However, as a non-parametric knowledge integration paradigm for LLMs, RAG methods heavily rely on external retrieval modules and the retrieved textual context prior. Especially for very large scale knowledge augmentation, they would introduce substantial inference latency due to expensive searches and much longer relevant context. In this paper, we propose a parametric knowledge integration method, called $\textbf{AtlasKV}$, a scalable, effective, and general way to augment LLMs with billion-scale knowledge graphs (KGs) (e.g. 1B triples) using very little GPU memory cost (e.g. less than 20GB VRAM). In AtlasKV, we introduce KG2KV and HiKVP to integrate KG triples into LLMs at scale with sub-linear time and memory complexity. It maintains strong knowledge grounding and generalization performance using the LLMs' inherent attention mechanism, and requires no external retrievers, long context priors, or retraining when adapting to new knowledge.

The graph edit distance (GED) is a widely used graph dissimilarity measure that quantifies the minimum cost of the edit operations required to transform one graph into another. Computing it, however, involves solving the associated NP-hard graph matching problem. Indeed, exact solvers already struggle to handle graphs with more than 20 nodes and classical heuristics frequently produce suboptimal solutions. This motivates the development of machine-learning methods that exploit recurring patterns in problem instances to produce high-quality approximate solutions. In this work, we introduce Gelato, a graph neural network model that constructs GED solutions incrementally by predicting a pair of nodes to be matched at each step. By conditioning each prediction autoregressively on the previous choices, it is able to capture complex structural dependencies. Empirically, Gelato achieves state-of-the-art results, even when generalizing to graphs larger than the ones seen during training, and runs orders of magnitude faster than competing ML-based methods. Moreover, it remains effective even under limited or noisy supervision, alleviating the demand for costly ground-truth generation.

Node affinity prediction is a common task that is widely used in temporal graph learning with applications in social and financial networks, recommender systems, and more. Recent works have addressed this task by adapting state-of-the-art dynamic link property prediction models to node affinity prediction. However, simple heuristics, such as persistent forecast or moving average, outperform these models. In this work, we analyze the challenges in training current Temporal Graph Neural Networks for node affinity prediction and suggest appropriate solutions. Combining the solutions, we develop NAVIS - Node Affinity prediction model using VIrtual State, by exploiting the equivalence between heuristics and state space models. While promising, training NAVIS is non-trivial. Therefore, we further introduce a novel loss function for node affinity prediction. We evaluate NAVIS on TGB and show that it outperforms the state of the art, including heuristics.

Existing Graph Neural Networks usually learn long-distance knowledge via stacked layers or global attention, but struggle to balance cost-effectiveness and global receptive field. In this work, we break the dilemma by proposing a novel forest-based graph learning (FGL) paradigm that enables efficient long-range information propagation. Our key insight is to reinterpret message passing on a graph as transportation over spanning trees that naturally facilitates long-range knowledge aggregation, where several trees--a forest--can capture complementary topological pathways. Theoretically, we demonstrate that as edge-homophily estimates improve, the induced distribution biases towards higher-homophily trees, which enables generating a high-quality forest by refining a homophily estimator. Furthermore, we propose a linear-time tree aggregator that realizes quadratic node-pair interactions. Empirically, our framework achieves comparable results against state-of-the-art counterparts on semi-supervised node classification tasks while remaining efficient. Codes are available at \url{https://anonymous.4open.science/r/FGL/}.

Large language models (LLMs) are increasingly applied in scientific research, offering new capabilities for knowledge discovery and reasoning. In single-cell biology, however, evaluation practices for both general and specialized LLMs remain inadequate: existing benchmarks are fragmented across tasks, adopt formats such as multiple-choice classification that diverge from real-world usage, and rely on metrics lacking interpretability and biological grounding. We present **SC-ARENA**, a natural language evaluation framework tailored to single-cell foundation models. SC-ARENA formalizes a *virtual cell* abstraction that unifies evaluation targets by representing both intrinsic attributes and gene-level interactions. Within this paradigm, we define five natural language tasks — cell type annotation, captioning, generation, perturbation prediction, and scientific QA — that probe core reasoning capabilities in cellular biology. To overcome the limitations of brittle string-matching metrics, we introduce **knowledge-augmented evaluation**, which incorporates external ontologies, marker databases, and scientific literature to support biologically faithful and interpretable judgments. Experiments and analysis across both general-purpose and domain-specialized LLMs demonstrate that: (i) under the *Virtual Cell* unified evaluation paradigm, current models achieve uneven performance on biologically complex tasks, particularly those demanding mechanistic or causal understanding; and (ii) our knowledge-augmented evaluation framework ensures biological correctness, provides interpretable, evidence-grounded rationales, and achieves high discriminative capacity, overcoming the brittleness and opacity of conventional metrics. **SC-ARENA** thus provides a unified and interpretable framework for assessing LLMs in single-cell biology, pointing toward the development of biology-aligned, generalizable foundation models.

Predictive modeling over relational databases (RDBs) powers applications in various domains, yet remains challenging due to the need to capture both cross-table dependencies and complex feature interactions. Recent Relational Deep Learning (RDL) methods automate feature engineering via message passing, while classical approaches like Deep Feature Synthesis (DFS) rely on predefined non-parametric aggregators. Despite promising performance gains, the comparative advantages of RDL over DFS and the design principles for selecting effective architectures remain poorly understood. We present a comprehensive study that unifies RDL and DFS in a shared design space and conducts large-scale architecture-centric searches across diverse RDB tasks. Our analysis yields three key findings: (1) RDL does not consistently outperform DFS, with performance being highly task-dependent; (2) no single architecture dominates across tasks, underscoring the need for task-aware model selection; and (3) validation accuracy is an unreliable guide for architecture choice. This search yields a curated model performance bank that links model architecture configurations to their performance; leveraging this bank, we analyze the drivers of the RDL–DFS performance gap and introduce two task signals—RDB task homophily and an affinity embedding that captures path, feature, and temporal structure—whose correlation with the gap enables principled routing. Guided by these signals, we propose Relatron, a task embedding-based meta-selector that first chooses between RDL and DFS and then prunes the within-family search to deliver strong performance. Lightweight loss-landscape metrics further guard against brittle checkpoints by preferring flatter optima. In experiments, Relatron resolves the “**more tuning, worse performance**” effect and, in joint hyperparameter–architecture optimization, achieves up to 18.5\% improvement over strong baselines with $10\times$ lower computational cost than Fisher information–based alternatives.