ICLR 2026 论文列表

Incremental Object Detection (IOD) enables AI systems to continuously learn new object classes over time while retaining knowledge of previously learned categories. This capability is essential for adapting to dynamic environments without forgetting prior information. Although existing IOD methods have made progress in mitigating catastrophic forgetting, they usually lack explicit and quantitative modeling of information conflicts during knowledge preservation, making task boundaries ambiguous. Such conflicts often stem from the fact that a single image can contain objects belonging to previous, present, and future tasks, where unlabeled past and future objects are often mistakenly treated as background. In this paper, we propose a novel approach grounded in Elastic Weight Consolidation (EWC) to alleviate conflict knowledge preservation caused by task interference. Specifically, we introduce the Interference Knowledge Isolated Elastic Weight Consolidation (IKI-EWC) framework for IOD, which leverages the mispredictions of the old detector on new task data to estimate task conflicts and suppresses them at the parameter level. By reformulating the Bayesian posterior of model parameters, we derive a mathematical relationship between previously learned knowledge and interference knowledge, enabling targeted elimination of conflicts during model weight updates. In addition, we also propose a prototype-based knowledge calibration (PKC) mechanism to further preserve old knowledge during the training of the objector's classification head. This method employs a learnable projection layer to compensate semantic drift in old class prototypes, and then jointly trains the classification head using both calibrated prototypes and current task features, thereby mitigating forgetting caused by classifier updates. Extensive experiments on PASCAL VOC and MS-COCO benchmarks demonstrate the effectiveness of the proposed method, outperforming state-of-the-art approaches across various settings.

Document-level knowledge graph (KG) construction faces a fundamental scaling challenge: existing methods either rely on expensive large language models (LLMs), making them economically unviable for large-scale corpora, or employ smaller models that produce incomplete and inconsistent graphs. We identify that this limitation stems not from model capabilities but from the absence of high-quality training data for document-level KG construction. To address this gap, we introduce SynthKG, a multi-step data synthesis pipeline that generates high-quality document-KG pairs through systematic chunking, decontextualization, and structured extraction using LLMs. By further fine-tuning a smaller LLM on synthesized document-KG pairs, we streamline the multi-step process into a single-step KG generation approach called Distill-SynthKG. Furthermore, we re-purpose existing question-answering datasets to establish KG evaluation datasets and introduce new evaluation metrics. Using KGs produced by Distill-SynthKG, we also design a novel graph-based retrieval framework for RAG. Experimental results demonstrate that Distill-SynthKG not only surpasses all baseline models in KG quality (including models up to eight times larger) but also consistently excels in retrieval and question-answering tasks. Additionally, our proposed graph retrieval framework outperforms all KG-retrieval methods across multiple benchmark datasets. We make SynthKG and Distill-SynthKG publicly available.

In this work, we introduce a new perspective on comparative image assessment by representing an image pair as a structured composition of its regions. In contrast, existing methods focus on whole image analysis, while implicitly relying on region-level understanding. We extend the intra-image notion of a scene graph to inter-image, and propose a novel task of Distortion Graph (DG). DG treats paired images as a structured topology grounded in regions, and represents dense degradation information such as distortion type, severity, comparison and quality score in a compact interpretable graph structure. To realize the task of learning a distortion graph, we contribute (i) a region-level dataset, PandaSet, (ii) a benchmark suite, PandaBench, with varying region-level difficulty, and (iii) an efficient architecture, Panda, to generate distortion graphs. We demonstrate that PandaBench poses a significant challenge for state-of-the-art multimodal large language models (MLLMs) as they fail to understand region-level degradations even when fed with explicit region cues. We show that training on PandaSet or prompting with DG elicits region-wise distortion understanding, opening a new direction for fine-grained, structured pairwise image assessment.

We investigate theoretical guarantees for the \emph{false-negative rate} (FNR)—the fraction of true causal edges whose orientation is not recovered, under single-variable random interventions and an $\epsilon$-interventional faithfulness assumption that accommodates latent confounding. For sparse Erdős--Rényi directed acyclic graphs, where the edge probability scales as $p_e = \Theta(1/d)$, we show that the FNR concentrates around its mean at rate $O\bigl(\tfrac{\log d}{\sqrt d}\bigr)$, implying that large deviations above the expected error become exponentially unlikely as dimensionality increases. This concentration ensures that derived upper bounds hold with high probability in large-scale settings. Extending the analysis to generalized Barabási--Albert graphs reveals an even stronger phenomenon: when the degree exponent satisfies $\gamma > 3$, the deviation width scales as $O\bigl(d^{\beta - \frac{1}{2}}\bigr)$ with $\beta = 1/(\gamma - 1) < \frac{1}{2}$, and hence vanishes in the limit. This demonstrates that heterogeneous, heavy-tailed degree structures commonly observed in empirical networks can intrinsically regularize causal discovery by reducing variability in orientation error. These finite-dimension results provide the first dimension-adaptive, faithfulness-robust guarantees for causal structure recovery, and challenge the intuition that high dimensionality and network heterogeneity necessarily hinder accurate discovery. Our simulation results corroborate these theoretical predictions, showing that the FNR indeed concentrates and often vanishes in practice as dimensionality grows.

Predicting molecule-protein interactions (MPIs) is a fundamental task in computational biology, with crucial applications in drug discovery and molecular function annotation. However, existing MPI models face two major challenges. First, the scarcity of labeled molecule-protein pairs significantly limits model performance, as available datasets capture only a small fraction of biological relevant interactions. Second, most methods rely solely on molecular and protein features, ignoring broader biological context—such as genes, metabolic pathways, and functional annotations—that could provide essential complementary information. To address these limitations, our framework first aggregates diverse biological datasets, including molecular, protein, genes and pathway-level interactions, and then develop an optimal transport-based approach to generate high-quality pseudo-labels for unlabeled molecule-protein pairs, leveraging the underlying distribution of known interactions to guide label assignment. By treating pseudo-labeling as a mechanism for bridging disparate biological modalities, our approach enables the effective use of heterogeneous data to enhance MPI prediction. We evaluate our framework on multiple MPI datasets including virtual screening tasks and protein retrieval tasks, demonstrating substantial improvements over state-of-the-art methods in prediction accuracies and zero shot ability across unseen interactions. Beyond MPI prediction, our approach provides a new paradigm for leveraging diverse biological data sources to tackle problems traditionally constrained by single or bi-modal learning, paving the way for future advances in computational biology and drug discovery.

Hyperbolic Neural Networks (HNNs) have shown remarkable success in representing hierarchical and tree-like structures, yet most existing work relies on the Poincaré ball and hyperboloid models. While these models admit closed-form Riemannian operators, their constrained nature potentially leads to numerical instabilities, especially near model boundaries. In this work, we explore the Proper Velocity (PV) space, an unconstrained representation of hyperbolic space rooted in Einstein’s special relativity, as a stable alternative. We first establish the complete Riemannian toolkit of the PV space. Building on this foundation, we introduce Proper Velocity Neural Networks (PVNNs) with core layers including Multinomial Logistic Regression (MLR), Fully Connected (FC), convolutional, activation, and batch normalization layers. Extensive experiments across four tasks, namely numerical stability, image classification, graph node classification, and genomic sequence learning, demonstrate the stability and effectiveness of PVNNs. The code is available at https://github.com/NickyoyoSu/PVNN.

Despite significant advances in Graph Neural Networks (GNNs), their limited expressivity remains a fundamental challenge. Research on GNN expressivity has produced many expressive architectures, leading to architecture hierarchies with models of increasing expressive power. Separately, derivatives of GNNs with respect to node features have been widely studied in the context of the oversquashing and over-smoothing phenomena, GNN explainability, and more. To date, these derivatives remain unexplored as a means to enhance GNN expressivity. In this paper, we show that these derivatives provide a natural way to enhance the expressivity of GNNs. We introduce High-Order Derivative GNN (HOD-GNN), a novel method that enhances the expressivity of Message Passing Neural Networks (MPNNs) by leveraging high-order node derivatives of the base model. These derivatives generate expressive structure-aware node embeddings processed by a second GNN in an end-to-end trainable architecture. Theoretically, we show that the resulting architecture family's expressive power aligns with the WL hierarchy. We also draw deep connections between HOD-GNN, Subgraph GNNs, and popular structural encoding schemes. For computational efficiency, we develop a message-passing algorithm for computing high-order derivatives of MPNNs that exploits graph sparsity and parallelism. Evaluations on popular graph learning benchmarks demonstrate HOD-GNN’s strong performance on popular graph learning tasks.

We show that language models’ activations linearly encode when information was learned during training. Our setup involves creating a model with a known training order by sequentially fine-tuning Llama-3.2-1B on six disjoint but otherwise similar datasets about named entities. We find that the average activations of test samples corresponding to the six training datasets encode the training order: when projected into a 2D subspace, these centroids are arranged exactly in the order of training and lie on a straight line. Further, we show that linear probes can accurately (∼90%) distinguish “early” vs. “late” entities, generalizing to entities unseen during the probes’ own training. The model can also be fine-tuned to explicitly report an unseen entity’s training stage (∼80% accuracy). Notably, the training-order encoding does not seem attributable to simple differences in activation magnitudes, losses, or model confidence. Our paper demonstrates that models are capable of differentiating information by its acquisition time, and carries significant implications for how they might manage conflicting data and respond to knowledge modifications.

Large language models (LLMs) struggle with inaccurate and outdated information, driving the emergence of knowledge editing as a lightweight alternative. Despite their effectiveness in modifying structured knowledge, existing editing methods often fail to generalize to unstructured cases, particularly those involving inherently hard-to-edit knowledge, where the original facts tend to be more resistant to change. To address this, we propose a metric, TangleScore, that quantifies the intrinsic difficulty of editing a given knowledge instance. This difficulty, in turn, strongly correlates with the model’s ability to generalize the edit to paraphrased and related prompts. Building on this insight, we introduce a TangleScore-driven method termed Purge-Imprint Patch Editing (PIPE), an editing framework that adaptively modulates the purge and imprint of knowledge based on TangleScore of the target knowledge to be edited, thus adjusting the editing strength to match the instance's difficulty, thereby enabling more precise and effective model updates. Experiments applying PIPE to four LLMs of varying sizes on two unstructured knowledge editing datasets show that PIPE significantly outperforms previous editing methods by 6.49% in terms of generalization performance. Extensive evaluation show that PIPE also exhibits effectiveness in structured knowledge editing and strong robustness under batch and sequential editing.

We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned input is a forest that must be given additional edges to form a full spanning tree. Veldt et al. (2025) showed that optimally completing the forest takes $\Omega(n^2)$ time, but designed a 2.62-approximation for MFC with subquadratic complexity. The same method is a $(2\gamma + 1)$-approximation for the original MST problem, where $\gamma \geq 1$ is a quality parameter for the initial forest. We introduce a generalized method that interpolates between this prior algorithm and an optimal $\Omega(n^2)$-time MFC algorithm. Our approach considers only edges incident to a growing number of strategically chosen "representative" points. One corollary of our analysis is to improve the approximation factor of the previous algorithm from 2.62 for MFC and $(2\gamma+1)$ for metric MST to 2 and $2\gamma$ respectively. We prove this is tight for worst-case instances, but we still obtain better instance-specific approximations using our generalized method. We complement our theoretical results with a thorough experimental evaluation.

This paper analyzes Cross-Entropy (CE) loss in knowledge distillation (KD) for recommender systems. KD for recommender systems targets at distilling rankings, especially among items most likely to be preferred, and can only be computed on a small subset of items. Considering these features, we reveal the connection between CE loss and NDCG in the field of KD. We prove that when performing KD on an item subset, minimizing CE loss maximizes the lower bound of NDCG, only if an assumption of closure is satisfied. It requires that the item subset consists of the student's top items. However, this contradicts our goal of distilling rankings on the teacher's top items. We empirically demonstrate the vast gap between these two kinds of top items. To bridge the gap between our goal and theoretical support, we propose Rejuvenated Cross-Entropy for Knowledge Distillation (RCE-KD). It splits the top items given by the teacher into two subsets based on whether or not it is ranked high by the student. For the subset that defies the condition, a sampling strategy is devised to use teacher-student collaboration to approximate our assumption of closure. We also combine the losses on the two subsets adaptively. Extensive experiments demonstrate the effectiveness of our method. Our code is available at https://anonymous.4open.science/r/RCE-KD.

Developing a mobile system capable of generating responses based on stored user data is a crucial challenge. Since user data is stored in the form of Knowledge Graphs, the field of knowledge graph question answering (KGQA) presents a promising avenue towards addressing this problem. However, existing KGQA systems face two critical limitations that preclude their on-device deployment: resource constraints and the inability to handle data accumulation. Therefore, we propose MobileKGQA, the first on-device KGQA system capable of adapting to evolving databases with minimal resource demands. MobileKGQA significantly reduces computational overhead through embedding hashing. Moreover, it successfully adapts to evolving databases under resource constraints through a novel annotation generation method. Its mobile applicability is validated on the NVIDIA Jetson Orin Nano edge-device platform, achieving 20.3% higher performance while using only 30.4% of the energy consumed by the SOTA (state of the art). On standard KGQA benchmarks, using just 7.2% of the computation and 9% of the parameters, MobileKGQA demonstrates performance that is empirically indistinguishable from the SOTA and outperforms baselines under distribution shift scenarios.

When language models are trained on textual data, they acquire both knowledge about the structure of language as well as knowledge of facts about the world. At inference time, their knowledge of facts can be leveraged to solve interesting problems and perform useful knowledge work for users. It is well known that language models can verbatim memorize long sequences from their training data. However, it is much less well understood how language models memorize facts seen during training. In this work, we propose a new dataset to specifically empower researchers to study the dual processes of fact memorization and verbatim sequence memorization. The dataset consists of synthetically-generated, webtext-like documents about fictional events, as well as question-answer pairs about the events. We conduct training experiments showing how synthetic data about fictional events can be effective in teasing apart different forms of memorization. We also document the challenges in effectively building realistic, fictional synthetic data.

Federated Recommender Systems (FRS) preserve privacy by training decentralized models on client-specific user-item subgraphs without sharing raw data. However, FRS faces a unique challenge: subgraph structural imbalance, where drastic variations in subgraph scale (user/item counts) and connectivity (item degree) misalign client representations, making it challenging to train a robust model that respects each client’s unique structural characteristics. To address this, we propose a Low-pass Personalized Subgraph Federated recommender system (LPSFed). LPSFed leverages graph Fourier transforms and low-pass spectral filtering to extract low-frequency structural signals that remain stable across subgraphs of varying size and degree, allowing robust personalized parameter updates guided by similarity to a neutral structural anchor. Additionally, we leverage a localized popularity bias-aware margin that captures item-degree imbalance within each subgraph and incorporates it into a personalized bias correction term to mitigate recommendation bias. Supported by theoretical analysis and validated on five real-world datasets, LPSFed achieves superior recommendation accuracy and enhances model robustness.

Large Language Models (LLMs) are increasingly applied to chemistry, tackling tasks such as molecular name conversion, captioning, text-guided generation, and property or reaction prediction. A molecule’s properties are fundamentally determined by its composition and structure, encoded in its molecular graph; thus, reasoning about molecular properties requires understanding and reasoning over the molecular structure. Yet, most existing benchmarks emphasize general chemical knowledge, rely on literature or surrogate labels that risk leakage or bias, or reduce evaluation to multiple-choice questions. We introduce MolecularIQ, a molecular structure reasoning benchmark focused exclusively on symbolically verifiable tasks. MolecularIQ spans three orthogonal axes — molecular complexity, multi-task load, and reasoning complexity — covering feature counting, index-based feature attributions, and constrained generation. MolecularIQ enables fine-grained evaluation of reasoning over molecular graphs and produces capability fingerprints that localize model failures to specific tasks and molecular regimes. This provides actionable insights into the strengths and limitations of current chemistry LLMs and guides the development of models that reason faithfully over molecular structure. On MolecularIQ, large MoE models with higher reasoning budgets lead across categories, while chemistry-tuned LLMs underperform their generalist bases, indicating limited transfer from narrow task fine-tuning.

Existing Temporal Knowledge Graph (TKG) representation learning approaches focus on modeling entity correlations. However, since TKG datasets are constructed from events, which inherently contain heterogeneous causalities, focusing solely on entity or relation level correlations is inadequate for event prediction in TKGs. Although a TKG structural causal model can be established as a theoretical framework for event level causality disentangling, practical disentanglement is non-trivial due to the lack of explicit supervision signals. To this end, we propose a Heterogeneous Event causality Disentangling Representation learning Approach (HEDRA) for TKG reasoning, which is the first work that focuses on disentangling heterogeneous causalities at the event level in TKGs. Specifically, a counterfactual detector module is proposed to disentangle non-causality by leveraging event importance and distributional discrepancies of event representations. Moreover, an Instrumental Variable (IV)-guided disentangling module is proposed to disentangle spurious causality by constructing IVs, which can produce robust event representations against spurious causality through multi-view causality subgraphs. Finally, an evolutionary orthogonal module is proposed to separate dynamic causality from static causality for event prediction. Comprehensive experiments on five real-world datasets demonstrate that HEDRA achieves the state-of-the-art performance. The source code of HEDRA is available at https://anonymous.4open.science/r/HEDRA-8A2F.

In this paper, we establish a dimension- and precision-independent impossibility result for a simplified transformer model. Due to their size, a comprehensive understanding of the internal operations of frontier large language models (LLMs) is beyond the reach of current methods, but research into small and interpretable models has proven successful. We study the representational limits of attention, the core of transformer models, through the lens of the Endpoint Selection Problem (ESP), a simple yet expressive learning task defined over arcs of a directed graph. Our main theoretical results are twofold: (i) 1-head, 1-layer, attention-only transformers cannot solve ESP on any graph containing a cycle, even with unbounded dimension and precision; but, all DAGs (Directed Acyclic Graph) are solvable with zero error (ii) in contrast, a 2-head, 1-layer, attention-only transformer can solve ESP on arbitrary directed graphs with constant embedding dimension and logarithmic precision. Prior lower bounds were conditional on bounds on dimension and precision. Through a transformation, we extend our impossibility result from ESP to the much studied 2-hop induction head problem. Further, we uncover a surprising connection to NP-completeness by showing that the optimal error of the 1-head transformer is em exactly related to the size of MAS (Maximum Acyclic Subgraph) and hence inapproximable. Finally, we validate our theory with experiments and observe that gradient-based optimization can reliably find 1-head solutions for DAGs and 2-head solutions for arbitrary graphs with cycles, whereas 1-head models struggle to reach the optimal solution in graphs with cycles. We believe that our techniques are of independent interest and have the potential to establish a new fine-grained hierarchy of transformer architectures, each with greater problem-solving power than the last.

As a topological invariant for discrete structures, discrete curvature has been widely adopted in the study of complex networks and graph neural networks. A prevailing viewpoint posits that edges with highly negative curvature will induce graph bottlenecks and the over-squashing phenomenon. In this paper, we critically re-examine this view and put forward our central claim: **high negative curvature is a sufficient but not a necessary condition for over-squashing**. We first construct a family of counterexamples demonstrating the failure of discrete curvature, where some edges are severely squashed, but the curvature still appears positive. Furthermore, extensive experiments demonstrate that the most commonly used discrete curvature measure --- Ollivier–Ricci curvature --- fails to detect as many as 30%~40% of over-squashed edges. To alleviate this limitation, we propose Weighted Augmented Forman-3 Curvature ($\mathsf{WAF3}$), which significantly improves the detection of over-squashed edges. Additionally, we develop a highly efficient approximation algorithm for $\mathsf{WAF3}$, enabling curvature computation on graphs with five million edges in only 23.6 seconds, which is 133.7 times faster than the existing algorithm with the lowest complexity for curvatures.

After a renaissance phase in which researchers revisited the message-passing paradigm through the lens of deep learning, the graph machine learning community shifted its attention towards a deeper and practical understanding of message-passing's benefits and limitations. In this paper, we notice how the fast pace of progress around the topics of oversmoothing and oversquashing, the homophily-heterophily dichotomy, and long-range tasks, came with the consolidation of commonly accepted beliefs and assumptions -- under the form of universal statements -- that are not always true nor easy to distinguish from each other. We argue that this has led to ambiguities around the investigated problems, preventing researchers from focusing on and addressing precise research questions while causing a good amount of misunderstandings. Our contribution is to make such common beliefs explicit and encourage critical thinking around these topics, refuting universal statements via simple yet formally sufficient counterexamples. The end goal is to clarify conceptual differences, helping researchers address more clearly defined and targeted problems. The hope is to clarify the distinction between the different issues and promote separate but intertwined research directions to address them.