ICML 2026 Papers

Computational approaches have become central to Protein–Protein Interaction (PPI) research, complementing experimental techniques that remain costly and incomplete. While modern deep learning methods capture diverse biological signals and hold promise in expanding the known interactome, empirical validation remains a critical bottleneck due to its long and expensive procedures. To address this challenge, we introduce the problem of PPI candidate ranking, aiming to prioritize interactions for experimental testing. We propose a novel framework that leverages domain knowledge through interpretability-guided ranking and further refines prioritization by integrating complementary sources of evidence, including interaction scores, structural plausibility, and biomedical language features. Evaluations on a large-scale dataset constructed from successive STRING releases demonstrate that our approach yields significant improvements over two state-of-the-art PPI prediction models, providing more accurate and biologically coherent rankings.

Pre-trained foundation models have demonstrated remarkable success in many domains, enabling a unified backbone to generalize across diverse downstream tasks. However, extending this paradigm to graph learning remains challenging due to the intrinsic mismatch between graph data and fixed architectural designs. In this work, we show that this limitation can be overcome via recurrent graph models. To achieve this, we conduct a systematic theoretical analysis, rigorously deriving step dependence as a necessary and sufficient condition for an adaptively convergent recurrent process. Building on this foundation, we propose AdaR, an Adaptive Recurrent graph model, empowering flexible test-time computing on various downstream tasks without changing model parameters. To enable adaptive inference, AdaR explicitly encodes normalized step information and representation–target relations into the recurrent updates. To ensure convergence of the recurrent process, AdaR employs gradient-based supervision signals that guide representation updates throughout the recurrence. Empirical results demonstrate that AdaR consistently outperforms strong baselines in both inductive and transductive settings.

AI model hubs provide access to a rapidly growing collection of powerful pre-trained models, enabling off-the-shelf mixture-of-experts systems with different routing strategies. However, this rapid growth poses two fundamental challenges: scaling model selection across thousands of experts and continually updating routing mechanisms as new models and tasks are introduced. In this paper, we formalise this setting as Continual Model Routing (CMR) and propose *CMRBench*, a new large-scale benchmark simulating realistic hub expansion and including over 2,000 candidate models. Finally, we introduce *CARvE*, a contrastive embedding approach for efficient continual model routing via domain-stratified coreset replay and checkpoint-based anchoring. Extensive empirical results and ablations show that CARvE significantly outperforms zero-shot retrieval, fine-tuning, and adapter-merging baselines in model, family, and domain-level accuracy.

Link prediction is a core challenge in graph machine learning, demanding models that capture rich and complex topological dependencies. While Graph Neural Networks (GNNs) are the standard solution, state-of-the-art pipelines often rely on explicit structural heuristics or memory-intensive node embeddings—approaches that struggle to generalize or scale to massive graphs. Emerging Graph Transformers (GTs) offer a potential alternative but often incur significant overhead due to complex structural encodings, hindering their applications to large-scale link prediction. We challenge these sophisticated paradigms with PENCIL, an encoder-only plain Transformer that replaces hand-crafted priors with attention over sampled local subgraphs, retaining the scalability and hardware efficiency of standard Transformers. Through experimental and theoretical analysis, we show that PENCIL extracts richer structural signals than GNNs, implicitly generalizing a broad class of heuristics and subgraph-based expressivity. Empirically, PENCIL outperforms heuristic-informed GNNs and is far more parameter-efficient than ID-embedding–based alternatives, while remaining competitive across diverse benchmarks—even without node features. Our results challenge the prevailing reliance on complex engineering techniques, demonstrating that simple design choices are potentially sufficient to achieve the same capabilities. Our code is publicly available at https://github.com/quang-truong/pencil.

Personalization has become a pivotal field of study in contemporary intelligent systems. Federated learning enables privacy-preserving collaborative training, but highly heterogeneous client data remain challenging, especially in graph federated learning where clients possess structurally diverse graphs. Existing personalized federated learning (PFL) methods ignore the intrinsic geometric properties of diverse graph structures. We propose FlatLand, a novel personalized Federated learning method that embeds different clients' data in tailored Lorentz space of hyperbolic geometry. Our key insight is that hyperbolic geometry naturally accommodates the intrinsic negative curvature prevalent in real-world graphs, while the time-like dimension in Lorentz space provides a principled way to encode client-specific heterogeneity. We develop a parameter decoupling strategy that separates heterogeneous information (captured in time-like parameters) from common knowledge (preserved in space-like parameters), enabling direct aggregation without requiring client similarity estimation and extra calculation modules. Empirical results on diverse federated graph learning tasks demonstrate that FlatLand achieves superior performance, particularly in low-dimensional settings. Code is available in our GitHub repository.

This paper focuses on a key challenge in Neural Architecture Search (NAS): integrating established architectural knowledge while exploring new designs under expensive evaluations. Large language models (LLMs) are a promising assistant for NAS because they can translate rich architectural and coding priors into executable code edits. However, in practice, seemingly local revisions often propagate into non-local behavioral and performance shifts because a single edit can inadvertently couple multiple interacting functional factors, a phenomenon we refer to as functional entanglement. To make LLM knowledge usable under such entanglement, we propose Structured Progressive Knowledge Activation (SPARK), which activates relevant priors by explicitly selecting the functional factor to modify and conditioning the edit on that factor. This factor-conditioned editing reduces entangled side effects and yields more targeted, reliable architecture modifications. On CLRS-DFS, SPARK achieves a 28.1x sample-efficient architecture evolution speedup and yields a 22.9% relative improvement in OOD accuracy. Our code is available at https://github.com/AIM-ResearchLab/SPARK.

Relational deep learning (RDL) converts relational databases (RDBs) into heterogeneous graphs, but graphs derived directly from database schemas are often not well suited for how graph neural networks (GNNs) perform relational reasoning. We study what makes a relational graph suitable for deep learning and show that schema-derived graphs suffer from two systematic failures: information overload and semantic fragmentation. Through an empirical analysis on real-world databases, we find that effective graphs arise from a task-dependent balance between removing task-irrelevant structure and injecting task-aligned relational connectivity. Filtering exhibits a non-monotonic effect on performance, while structural injection is beneficial only when it reflects the logic of the downstream task. Based on these findings, we develop an end-to-end structural optimizer that applies both operations to adapt relational graphs automatically. Across 23 tasks spanning classification, regression, and recommendation, the optimized graphs consistently improve accuracy while often reducing inference cost.

This work proposes a framework LGKDE that learns kernel density estimation for graphs. The key challenge in graph density estimation lies in effectively capturing both structural patterns and semantic variations while maintaining theoretical guarantees. Combining graph kernels and kernel density estimation (KDE) is a standard approach to graph density estimation, but has unsatisfactory performance due to the handcrafted and fixed features of kernels. Our method LGKDE leverages graph neural networks to represent each graph as a discrete distribution and utilizes maximum mean discrepancy to learn the graph metric for multi-scale KDE, where all parameters are learned by maximizing the density of graphs relative to the density of their well-designed perturbed counterparts. The perturbations are conducted on both node features and graph spectra, which helps better characterize the boundary of normal density regions. Theoretically, we establish consistency and convergence guarantees for LGKDE, including bounds on the mean integrated squared error, robustness, and generalization. We validate LGKDE by demonstrating its effectiveness in recovering the underlying density of synthetic graph distributions and applying it to graph anomaly detection across diverse benchmark datasets. Extensive empirical evaluation shows that LGKDE demonstrates superior performance compared to state-of-the-art baselines on most benchmark datasets.

Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have been developed, but the most popular is Gaussian Belief Propagation (GBP), a variant that assumes all distributions are locally Gaussian. GBP is widely used due to its efficiency and empirically strong performance in applications like computer vision or sensor networks – even when modelling non-Gaussian problems. In this paper, we seek to provide a theoretical guarantee for when Gaussian approximations are valid in highly non-Gaussian, sparsely-connected factor graphs performing BP (common in Spatial AI). We leverage the Central Limit Theorem to prove mathematically that variables’ beliefs under BP converge to a Gaussian distribution in complex, loopy factor graphs obeying our 4 key assumptions. We then confirm experimentally that variable beliefs become increasingly Gaussian after just a few BP iterations in a stereo depth estimation task.

Probabilistic forecasting with exogenous variables is vital for decision-making but remains underexplored compared to deterministic methods. We propose KITE, a knowledge-guided probabilistic modeling framework designed to bridge this gap by addressing two key bottlenecks: (1) topological disparity in sampling initialization and (2) spurious covariate correlations during the iterative conditional generation process. KITE introduces a *History-Conditional Manifold* to construct an informative source distribution from historical dynamics, effectively anchoring the starting point closer to the target space. Additionally, a *Knowledge-Guided Conditioning* module is developed to regularize variable interactions using statistical priors, suppressing spurious correlations and enhancing the robustness of covariate conditioning. Extensive experiments demonstrate that KITE outperforms state-of-the-art methods in both deterministic and probabilistic forecasting.

Causal language models factorize sequence probabilities using only preceding context, leaving future information unexploited during training despite its availability in the training data. This paper introduces Regret Pre-training, a self-supervised framework grounded in the Learning Using Privileged Information (LUPI) paradigm. The framework employs a dual-view architecture in which a single model generates both a causal Student distribution and a future-conditioned Teacher distribution. The training objective augments standard language modeling with a regret loss that minimizes the KL divergence from teacher to student, transferring future-aware signals to the causal representations. We investigate two teacher configurations on the OLMoE-1B-7B architecture:LocalRegret, which extends attention by one future token, andGlobalRegret, which conditions on bidirectional context with the target position masked. Experiments on nine downstream tasks following 4 billion tokens of training demonstrate that both configurations consistently outperform the baseline. On average,GlobalRegret andLocalRegret achieve 33.9% and 32.2% accuracy respectively, surpassing the baseline's 30.2%. Most notably,GlobalRegret improves BoolQ performance by 18.1 percentage points (61.0% vs 42.9%). The framework introduces no additional parameters and requires only one extra inference-mode forward pass per training step.

Mitigating sensitive and harmful outputs is fundamental to ensuring safe deployment of LLMs. Existing approaches typically follow two paradigms: Knowledge Deletion (KD), which erases undesirable information during training, and Distinguishable Refusal (DR), which steers models away from using sensitive knowledge during inference. Despite rapid progress, KD-based unlearning struggles with biased deletion due to suppressing specific token sequences as a substitute for complete knowledge removal, whereas DR-based unlearning risks the re-emergence of harmful knowledge because the underlying knowledge remains intact. To address these issues, we propose Distinguishable Deletion ($\mathrm{D^2}$), a paradigm that restricts the response distribution in the latent representation rather than specific tokens to erase undesirable knowledge, while distinguishing it from retained knowledge, enabling a refusal mechanism to handle unlearned inputs safely and coherently. To implement $\mathrm{D^2}$, we introduce an energy index that quantifies the presence of knowledge and the separation between unlearned and retained content. Mathematical and empirical analyses show that energy is both accurate and efficient, enabling Energy-based Unlearning Alignment (EUA) to enforce energy-boundary unlearning during training and apply an energy-based refusal mechanism at inference. Extensive experiments demonstrate that EUA significantly outperforms previous methods, indicating the superiority of $\mathrm{D^2}$. Our code is available at https://github.com/Puning97/EUA-for-LLM-Unlearning.

Retrieval augmented generation (RAG) has enhanced large language models by enabling access to external knowledge, with graph-based RAG emerging as a powerful paradigm for structured retrieval and reasoning. However, existing graph-based methods often over-rely on entity-centric node matching and lack explicit causal modeling, leading to unfaithful or spurious answers. Prior attempts to incorporate causality are typically limited to local or single-document contexts and also suffer from information isolation that arises from modular graph structures, which hinders scalability and cross-module causal reasoning. To address these challenges, we propose CausalRAG2, a framework that rethinks knowledge organization for graph-based RAG through causal gating across hierarchical modules. CausalRAG2 explicitly models causal relationships to suppress spurious correlations while enabling scalable reasoning over large-scale knowledge graphs. We also introduce HolisQA, a benchmark for holistic comprehension beyond entity-centric matching. Extensive experiments demonstrate that CausalRAG2 consistently outperforms competitive graph-based RAG baselines across multiple datasets and evaluation metrics. Our work establishes a principled foundation for structured, scalable, and causally grounded RAG systems.

Large-scale web-harvested datasets have fueled the progress of cross-modal retrieval but inevitably suffer from noisy correspondence, which severely degrades model generalization. Existing methods primarily address this by filtering out noise or seeking a substitute label, yet they predominantly remain bound by a “Discrete Selection” paradigm. We argue that relying on a single discrete proxy induces SinglePoint Fragility and Discretization Error. To overcome these limitations, we propose a novel framework, Intra-modal Neighbor-aware Noise Rectification (IN2R), which shifts the paradigm from searching for a substitute to synthesizing a reliable supervision target. Leveraging the intrinsic geometric stability of intra-modal data, IN2R employs a Graph Refiner to perform relational reasoning over neighbors retrieved from a dynamic Cross-Model Memory. Instead of propagating discrete labels, our method synthesizes a continuous, soft prototype that reflects the consensus of the local semantic neighborhood, effectively rectifying inter-modal misalignment. Extensive experiments on Flickr30K, MS-COCO, and CC152K demonstrate that IN2R significantly outperforms state-of-the-art methods.

By synergizing graph topology with the global expressive power of attention, Graph Transformers (GTs) have emerged as a powerful architecture for node classification. Existing GTs mainly focus on diverse topology injection paradigms, which fundamentally construct different propagation operators. However, a unified theoretical understanding of what constitutes a desirable propagation operator remains largely unexplored. To bridge this gap, this paper rethinks GTs from a graph signal denoising perspective, revealing that a block-diagonal structure is a desirable structural prior for graph denoising. To efficiently instantiate this prior, this paper introduces BDFormer, which imposes spectral block regularization on the affinity of a compact set of latent anchors. Furthermore, by introducing hard assignments between nodes and anchors, BDFormer establishes sparse, structured propagation that suppresses noisy cross-class propagation in linear time. Meanwhile, the learned global affinity guides the pruning of inter-class edges in the graph topology, enabling both global and local propagation to jointly adhere to the target block-diagonal structure. Extensive experiments on benchmark datasets demonstrate the superiority and scalability of BDFormer.

Knowledge augmentation has significantly enhanced the performance of Large Language Models (LLMs) in knowledge-intensive tasks. However, existing methods typically operate on the simplistic premise that model performance equates with internal knowledge, overlooking the knowledge-confidence gaps that lead to overconfident errors or uncertain truths. To bridge this gap, we propose a novel meta-cognitive framework for reliable knowledge augmentation via differentiated intervention and alignment. Our approach leverages internal cognitive signals to partition the knowledge space into mastered, confused, and missing regions, guiding targeted knowledge expansion. Furthermore, we introduce a cognitive consistency mechanism to synchronize subjective certainty with objective accuracy, ensuring calibrated knowledge boundaries. Extensive experiments demonstrate the our framework consistently outperforms strong baselines, validating its rationality in not only enhancing knowledge capabilities but also fostering cognitive behaviors that better distinguish knowns from unknowns. All codes are available at https://github.com/AI9Stars/Know-More-Know-Clearer.

Incremental object detection (IOD) aims to extend detectors to new categories while retaining previously acquired knowledge. Existing methods often adopt a class incremental learning perspective, separating feature spaces to sharpen decision boundaries. However, this separation-oriented paradigm may overlook object symbiosis in detection, where co-occurrence and occlusion introduce spatial and semantic dependencies that benefit from shared representations. Ignoring these dependencies distorts the shared representations, exacerbates confusion between old and new classes, and accelerates catastrophic forgetting. To address this, we propose Symbiosis-Inspired Knowledge Distillation (SIKD), which explicitly leverages object symbiosis at two complementary levels. Spatial Symbiosis Distillation (SpSD) focuses on symbiotic regions where the old model responds with high overlap to objects in the new task. It preserves generalizable old class cues, suppresses class-specific bias and redundancy, and distills the refined evidence to the new model at matched spatial locations with slot-aligned supervision. Semantic Symbiosis Distillation (SeSD) maintains class level structure by forming confidence weighted prototypes for old classes and aligning their inter class soft ranks over the old class logits, which stabilizes the semantic topology during adaptation. Extensive experiments demonstrate the effectiveness and superiority of the proposed method.

The growing scale of deep neural networks, encompassing large language models (LLMs) and vision transformers (ViTs), has made training from scratch prohibitively expensive and deployment increasingly costly. These models are often used as computational monoliths with fixed cost, hindering adaptive deployment across different cost budgets. We argue that nested components, ordered by importance, can be extracted from pretrained models and selectively activated within the available computational budget. To this end, our proposed FlexRank method leverages low-rank weight decomposition with nested, importance-based consolidation to extract submodels of increasing capabilities. Our approach enables a _``train-once, deploy-everywhere''_ paradigm offering a graceful trade-off between cost and performance without training from scratch for each budget - advancing practical deployment of large models.

We study linear seriation from noisy point clouds: given samples from an unknown one-dimensional curve embedded in $\mathbb{R}^d$, recover their latent order along the curve, up to reversal. Unlike much of the seriation literature, which starts from a precomputed similarity matrix, this setting retains ambient coordinates and therefore local geometric information. We propose STAGE, a geometric ordering method that estimates local tangent directions by neighborhood PCA, resolves their sign ambiguity through a graph-wide $\mathbb{Z}_2$ synchronization step, and constructs signed local displacement estimates by projecting ambient differences onto the oriented tangents. These increments are then integrated into a global scalar embedding through an inhomogeneous least-squares problem, equivalently a Laplacian linear system with a nonzero right-hand side, and the final order is obtained by sorting the embedding. We prove a finite-sample Kendall's $\tau$ recovery bound that makes explicit the roles of curvature, noise, neighborhood scale, sampling density, and graph connectivity. Empirically, STAGE gives accurate and fast order recovery on high-dimensional synthetic curves, compares favorably with spectral seriation, 1D UMAP, 1D t-SNE, Recanati's method, LTSA, and SABRE, and produces meaningful pseudotime orderings on single-cell RNA-seq datasets.