ICML 2026 Papers

International Conference on Machine Learning

Decision breakdown

6,341papers

Counted from the official paper list; may differ slightly from the number the conference announced.

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  • Poster
    5,80591.5%

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SEMIR: Semantic Minor-Induced Representation Learning on Graphs for Visual Segmentation

Luke James Miller, Yugyung Lee

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Segmenting small and sparse structures in large-scale images is fundamentally constrained by voxel-level, lattice-bound computation and extreme class imbalance--dense, full-resolution inference scales poorly and forces most pipelines to rely on fixed regionization or downsampling, coupling computational cost to image resolution and attenuating boundary evidence precisely where minority structures are most informative. We introduce \textbf{SEMIR} (\emph{Semantic Minor-Induced Representation Learning}), a representation framework that decouples inference from the native grid by learning a task-adapted, topology-preserving latent graph representation with exact decoding. \textbf{SEMIR} transforms the underlying grid graph into a compact, boundary-aligned graph minor through parameterized edge contraction, node deletion, and edge deletion, while preserving an exact lifting map from minor predictions to lattice labels. Minor construction is formalized as a few-shot structure learning problem that replaces hand-tuned preprocessing with a \emph{boundary-alignment objective}: minor parameters are learned by maximizing agreement between predicted boundary elements and target-specific semantic edges under a \emph{boundary Dice criterion}, and the induced minor is annotated with scale- and rotation-robust geometric and intensity descriptors and supports efficient region-level inference via message passing on a graph neural network (GNN) with relational edge features. We benchmark \textbf{SEMIR} on three tumor segmentation datasets—\textbf{BraTS 2021}, \textbf{KiTS23}, and \textbf{LiTS}—where targets exhibit high structural variability and distributional uncertainty. \textbf{SEMIR} yields consistent improvements in \emph{minority-structure Dice} at practical runtime. More broadly, SEMIR establishes a framework for learning task-adapted, topology-preserving latent representations with exact decoding for high-resolution structured visual data.

Poster
Synergistic Space-Vision Processing for Predicate Inference

Zhenhua Lei, Zefang Han, yu qiu

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Scene graph generation (SGG) aims to parse an image into a structured graph of objects and their predicates, enabling explicit relational reasoning for visual understanding. However, prevailing methods often over-predict geometric predicates, resulting in scene graphs that are factually correct yet semantically shallow. While recent works effectively attribute this phenomenon to the long-tailed data distribution, we identify another critical factor driving such biased prediction: co-occurrence-induced representation entanglement, where geometric and non-geometric predicates that frequently co-occur are encoded into overly similar representations. To this end, we introduce Dual-stream Synergistic Network (DS-Net) that models geometric and non-geometric predicates with two specialized streams, coupled with a bidirectional cross-stream fusion mechanism. The space stream focuses on spatial and structural cues, while the vision stream captures fine-grained visual evidence and semantic priors. Extensive experiments show that DS-Net consistently improves predicate inference, achieving 1.3\% $\sim$ 6.1\% absolute gains in mR@100 on the SGGen task when integrated into existing SGG methods. These results highlight the importance of synergistic modeling of geometric and non-geometric predicates for generating semantically richer scene graphs.

Poster
Causal Forcing: Autoregressive Diffusion Distillation Done Right for High-Quality Real-Time Interactive Video Generation

Hongzhou Zhu, Min Zhao, Guande He, Hang Su, Chongxuan Li, Jun Zhu

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To achieve real-time interactive video generation, current methods distill pretrained bidirectional video diffusion models into few-step autoregressive (AR) models, facing an *architectural gap* when full attention is replaced by causal attention. However, existing approaches do not bridge this gap theoretically. They initialize the AR student via ODE distillation, which requires *frame-level injectivity*, where each noisy frame must map to a unique clean frame under the PF-ODE of an *AR teacher*. Distilling an AR student from a bidirectional teacher violates this condition, preventing recovery of the teacher's flow map and instead inducing a conditional-expectation solution, which degrades performance. To address this issue, we propose *Causal Forcing*, which uses an autoregressive teacher for ODE initialization to bridge the architectural gap, and then applies the same DMD procedure as in Self Forcing. Empirical results show that our method outperforms all baselines across all metrics, surpassing the SOTA Self Forcing by 19.3\% in Dynamic Degree, 8.7\% in VisionReward, and 16.7\% in Instruction Following. Project page: https://thu-ml.github.io/CausalForcing.github.io/; the code: https://github.com/thu-ml/Causal-Forcing.

Poster
Token Sparse Attention: Efficient Long-Context Inference with Interleaved Token Selection

Dongwon Jo, Beomseok Kang, Jiwon Song, Jae-Joon Kim

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The quadratic complexity of attention remains the central bottleneck in long-context inference for large language models. Prior acceleration methods either sparsify the attention map with structured patterns or permanently evict tokens at specific layers, which can retain irrelevant tokens or rely on irreversible early decisions despite the layer-/head-wise dynamics of token importance. In this paper, we propose Token Sparse Attention, a lightweight and dynamic token-level sparsification mechanism that compresses per-head $Q, K, V$ to a reduced token set during attention and then decompresses the output back to the original sequence, enabling token information to be reconsidered in subsequent layers. Furthermore, Token Sparse Attention exposes a new design point at the intersection of token selection and sparse attention. Our approach is fully compatible with dense attention implementations, including Flash Attention, and can be seamlessly composed with existing sparse attention kernels. Experimental results show that Token Sparse Attention consistently improves accuracy–latency trade-off, achieving up to $\times$3.23 attention speedup at 128K context with less than 1\% accuracy degradation. These results demonstrate that dynamic and interleaved token-level sparsification is a complementary and effective strategy for scalable long-context inference.

Poster
MotionMAR: Multi-scale Auto-Regressive Human Motion Reconstruction from Sparse Observations

Yuhua Luo, Junsheng Zhang, Mengyin Liu, Xincheng Lin, Ming Yan, Zhudi Chen, Chenglu Wen, Lan Xu, Siqi Shen, Cheng Wang

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Human motion follows a temporal hierarchical structure, transitioning from low-frequency global trajectories to high-frequency details. Inspired by the success of multi-level autoregressive models in computer vision, we propose MotionMAR, a coarse-to-fine framework for motion reconstruction from sparse observations. It first estimates the global trajectory of human motion and then gradually refines the temporal details. This architecture consists of four integrated components. The Temporal Multi-scale Tokenization (TMT) VQ-VAE encodes the data at multiple temporal resolutions, separating semantic motion from minor jitters. The Motion Autoregressive Network (MAN) operates in this latent space, predicting motion across scales. It first establishes the global structure through coarse indices and then generates finer indices to recover specific details. Meanwhile, the Scale-Aware Control (SAC) module integrates sparse tracking data to ensure the generated output aligns with actual observations. The Motion Refinement Network (MRN) subsequently smooths consecutive poses and eliminates quantization artifacts. Experiments show that MotionMAR achieves state-of-the-art accuracy on the AMASS dataset, providing a reliable and structure-aware approach for motion reconstruction. The source code is publicly available at \url{http://www.lidarhumanmotion.net/motionmar/}.

Poster
Learnability-Driven Knowledge Assimilation for Class-Incremental Semantic Segmentation

Xinyue Zhang, Xu Zou, Wanjia Luo, Yanjie Wang, Jiahuan Zhou, Sheng Zhong, Luxin Yan

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Class-incremental semantic segmentation learns new classes while retaining old ones without access to past data. Although existing methods alleviate catastrophic forgetting on old classes, new-class performance remains limited. We identify that the key bottleneck arises from low-margin regions, where the logit of the ground-truth class is close to that of the most competitive non-ground-truth class. Our theoretical analysis suggests that optimization in these regions is characterized by high second-order margin sensitivity and a small stability radius, making learning prone to class confusion. Based on the above analysis, we propose Learnability-Driven Knowledge Assimilation (LDKA), which targets low-margin learning via three complementary optimization strategies: (i) Progressive Margin Learning continuously reallocates pixel-wise optimization budget in a threshold-free manner, shifting emphasis from high-margin to low-margin regions; (ii) Smooth Knowledge Distillation applies second-order sensitivity damping along the margin direction and perturbation stabilization to suppress high-frequency updates and increase the stability radius; (iii) Misclassification-Aware Decoupling measures inter-class confusion with a competition matrix and decouples highly competitive class representations. Experiments show that LDKA improves mIoU on new classes while preserving performance on old classes across 9 incremental protocols.

Poster
DynaTok: Token-Based 4D Reconstruction from Partial Point Clouds

Weirong Chen, Keisuke Tateno, Hidenobu Matsuki, Michael Niemeyer, Daniel Cremers, Federico Tombari

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We address 4D reconstruction from partial point cloud sequences, where depth-sensor observations are incomplete, unordered, and lack explicit temporal correspondences. This geometry-only setting is challenging due to missing observations and ambiguous dynamics. While recent progress has largely relied on image-based methods, existing point-based approaches typically focus on single objects, assume relatively complete inputs, or require explicit correspondences. To address these limitations, we propose DynaTok, a point-based framework for correspondence-free 4D reconstruction from partial point cloud sequences without images. DynaTok encodes frames into compact latent tokens, aggregates incomplete observations over time with a Transformer-based spatiotemporal encoder, and decouples geometry and motion through residual tokens in a unified model. A flow-matching decoder then reconstructs complete, temporally consistent 4D point-cloud sequences conditioned on the latent tokens. Experiments on object- and scene-level benchmarks demonstrate improved reconstruction quality and temporal coherence from partial point cloud observations.

Poster
VFMF: Dense Forecasting by Generating Foundation Model Features

Gabrijel Boduljak, Yushi Lan, Christian Rupprecht, Andrea Vedaldi

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Forecasting by generating RGB videos is computationally expensive, often physically implausible, and not directly actionable, since it requires translation into decision-making signals. Direct modality forecasting (e.g., predicting future segmentation) produces directly actionable outputs but fails to scale due to the need for labels. Vision Foundation Model (VFM) features offer the best of both worlds: they contain actionable semantic and geometric information that can be easily decoded from the predicted features, while requiring no labels on the downstream task for training. However, almost all existing VFM feature forecasting methods regress future features from fixed number of input frames, with evaluation predominantly on short horizons matching the training setup. We firstly show that existing regression methods struggle with forecasting from partial observations because they average over multiple plausible futures, failing to capture uncertainty in the future given the past. Interestingly, naively replacing deterministic forecasting with generative flow matching does not match the sample quality of the regression model, despite being a mathematically appropriate formulation of the forecasting task. In this work, we explain why this is the case, and we show how to optimally generate foundation model features. Our key insight is that generative modeling of VFM features requires (auto)encoding into a compact latent space suitable for diffusion. We show that this latent space preserves information more effectively than previously used alternatives, such as uncompressed feature diffusion or PCA-based compression, both for forecasting and other applications, such as image generation. Our results suggest that conditional generation of (compressed) VFM features offers a promising and scalable foundation for future scene forecasters.

Poster
Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning

Dan Qiao, Binbin Chen, Fengyu Cai, Jianlong Chen, Wenhao Li, Fuxin Jiang, Zuzhi Chen, Hongyuan Zha, Tieying Zhang, Baoxiang Wang

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Multi-Agent Debate (MAD) has shown promise in improving reasoning and reducing hallucinations, yet it remains unclear how information exchange shapes individual reasoning behavior. Empirically, MAD exhibits paradoxical phenomena, including rising accuracy with increasing token entropy and marked differences between homogeneous and heterogeneous agent combinations. In this paper, we introduce a Bayesian uncertainty analysis framework for MAD, which decomposes answer-level predictive uncertainty into epistemic uncertainty and aleatoric uncertainty, corresponding to the potential gain and cost of debate. Across multiple agent configurations, we find that effective debate depends on achieving high epistemic gain under controlled aleatoric cost. Building on this insight, we design an uncertainty-guided multi-agent reinforcement learning algorithm that encourages lower aleatoric cost and more effective epistemic information utilization. Experiments show that our approach simultaneously enhances each agent's accuracy and promotes a more productive debate process, providing an operational Bayesian perspective for understanding and improving MAD.

Poster
On Revisiting Entropy for Identifying Mislabeled Images

Chunlei Li, Zixuan Zheng, Yilei Shi, Guanglu Dong, Pengfei Li, Jingliang Hu, Xiao Xiang Zhu, Lichao Mou

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Mislabeled samples in training datasets severely degrade the performance of deep networks, as overparameterized models tend to memorize erroneous labels. We address this challenge by proposing a novel approach for mislabeled data detection that leverages training dynamics. Our method is grounded in the key observation that correctly labeled samples exhibit consistent entropy decrease during training, while mislabeled samples maintain relatively high entropy throughout the training process. Building on this insight, we introduce a signed entropy integral (SEI) statistic that captures both the magnitude and temporal trend of prediction entropy across training epochs. SEI is broadly applicable to classification networks and demonstrates particular effectiveness when integrated with contrastive language-image pretraining (CLIP) architectures. Through extensive experiments on four medical imaging datasets---a domain particularly susceptible to labeling errors due to diagnostic complexity---spanning diverse modalities and pathologies, we demonstrate that SEI achieves state-of-the-art performance in mislabeled data identification, outperforming existing methods while maintaining computational efficiency and implementation simplicity. Our code is available at https://github.com/MedAITech/SEI.

Poster
In-Context Learning Is Provably Bayesian Inference: A Generalization Theory for Meta-Learning

Tomoya Wakayama, Taiji Suzuki

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This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We leverage a Bayes risk identity that separates the total ICL risk into two orthogonal components: Bayes Gap and Posterior Variance. The Bayes Gap quantifies how well the trained model approximates the Bayes-optimal in-context predictor. For a uniform-attention Transformer, we derive a non-asymptotic upper bound on this gap, which explicitly clarifies the dependence on the number of pretraining prompts and their context length. The Posterior Variance is a model-independent risk representing the intrinsic task uncertainty. Our key finding is that this term is determined solely by the difficulty of the true underlying task, while the uncertainty arising from the task mixture vanishes exponentially fast with only a few in-context examples. Together, these results provide a unified view of ICL: the uniform-attention Transformer selects the optimal meta-algorithm during pretraining and rapidly converges to the optimal algorithm for the true task at test time.

Poster
Membership Inference Attacks for Unseen Classes

Pratiksha Thaker, Neil Kale, Steven Wu, Virginia Smith

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A key tool in developing safe AI models is *data auditing*, i.e., using statistical tools to determine whether harmful content may have been used in the training data of a black-box model. Unfortunately, most *membership inference attacks* (MIAs) used to perform this type of auditing themselves assume *access* to examples of harmful content from the same distribution as the query data. In real-world auditing scenarios, auditors often face legal and ethical restrictions preventing them from accessing a representative set of samples of harmful content to train MIA models effectively. We abstract and formalize this setting into a new data access model, the “unseen class” setting, and show that the state-of-the-art MIAs fail due to the lack of access to the full target distribution. We show that in this setting, *quantile regression attacks* outperform approaches typically considered to be state of the art. We demonstrate this both empirically and theoretically, showing that quantile regression attacks achieve up to **11× the TPR** of shadow model-based approaches in practice, and providing a theoretical model that outlines the generalization properties required for this approach to succeed. Our work identifies an important failure mode in existing MIAs and provides a cautionary tale for practitioners who aim to directly use existing tools for real-world applications of AI safety.

Poster
Induction Heads Interpolate N-Grams

Francesco D'Angelo, Oğuz Kaan Yüksel, Swathi Shree Narashiman, Nicolas Flammarion

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Induction heads are attention circuits believed to underlie in-context learning in transformers, yet a precise characterization of the estimators they implement remains elusive. We study transformers trained on order-$k$ Markov chains and identify two complementary smoothing mechanisms. First, at finite attention-weight scale, the circuit implements a soft context-matching estimator: it aggregates contributions from exact and partial context matches, weighted exponentially by their overlap, and induces a data-dependent interpolation across context orders analogous to Jelinek--Mercer smoothing. Second, a beginning-of-sequence (BOS) token induces additive pseudo-counts, recovering Dirichlet-style smoothing. We construct a disentangled transformer implementing both mechanisms and show that trained transformers recover the predicted attention patterns. Across settings where pseudo-count smoothing is optimal or lower-order contexts provide structured evidence, trained transformers match or outperform classical count-based baselines. Our results bridge mechanistic interpretability of induction heads with classical statistical smoothing, revealing that transformers learn to regularize in-context estimation rather than simply count.

Poster
PACER: Acyclic Causal Discovery from Large-scale Interventional Data

Ramon Viñas Torné, Sílvia Fábregas Salazar, Soyon Park, Ivo Ban, Artyom Gadetsky, Nikita Doikov, Maria Brbic

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Inferring the structure of directed acyclic graphs (DAGs) from data is a central challenge in causal discovery, particularly in modern high-dimensional settings where large-scale interventional data are increasingly available. While interventional data can improve identifiability, existing methods remain limited by soft acyclicity constraints, leading to optimization over invalid cyclic graphs, numerical instability, and reduced scalability. We introduce PACER (Perturbation-driven Acyclic Causal Edge Recovery), a scalable framework for causal discovery that guarantees acyclicity by construction. PACER parameterizes a distribution over DAGs through a joint model of variable permutations and edge probabilities, enabling direct optimization over valid causal structures without surrogate penalties. The framework supports a unified likelihood-based treatment of observational and interventional data, flexible conditional density models, and the incorporation of structural prior knowledge. For linear-Gaussian mechanisms, we derive closed-form expressions for the expected interventional log-likelihood and its gradients, yielding substantial computational gains. Empirically, PACER matches or exceeds state-of-the-art methods on protein signaling and large-scale genetic perturbation benchmarks, while scaling efficiently to networks with thousands of variables and achieving up to two orders of magnitude speedups over penalty-based differentiable approaches. These results demonstrate that exact and scalable causal discovery from high-dimensional perturbation data is achievable through principled search space design.

Poster
Enhancing LLMs for Graph Tasks via Graph-aware LoRA Generation

Junshu Sun, Wanxing Chang, Qingming Huang, Shuhui Wang

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Graph neural networks (GNNs) tightly couple their input-output parameters to dataset-specific feature spaces and target sets, exhibiting limited transferability across different datasets. In contrast, language models (LMs) generalize flexibly via a unified input-output interface, motivating recent attempts to adapt LMs to graph tasks. However, existing methods struggle to encode whole-graph information, leading to potential information loss and suboptimal graph understanding. In this work, we propose a novel weight-level information injection paradigm for adapting LMs to graph tasks. This paradigm injects whole-graph information by generating task-specific weight updates that interact directly with hidden representations. Instantiating this paradigm following low-rank adaptation (LoRA), we introduce GaRA, a Graph-aware LoRA generation model. GaRA constructs low-rank weight updates conditioned on the original graph structures and constrains the norm of the generated updates, thus injecting whole-graph information and avoiding the optimization bias in the weight generation. Empirical studies demonstrate that GaRA consistently outperforms baselines on zero-shot graph learning tasks.

Poster
DiLA: Disentangled Latent Action World Models

Tianqiu Zhang, Muyang Lyu, Yufan Zhang, Fang Fang, Si Wu

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Latent Action Models (LAMs) enable the learning of world models from unlabeled video by inferring abstract actions between consecutive frames. However, LAMs face a fundamental trade-off between action abstraction and generation fidelity. Existing methods typically circumvent this issue by using two-stage training with pre-trained world models or by limiting predictions to optical flow. In this paper, we introduce *DiLA*, a novel **Di**sentangled **L**atent **A**ction world model that aims to resolve this trade-off via content-structure disentanglement. Our key insight is that disentanglement and latent action learning are co-evolving: the predictive bottleneck inherent in latent action learning serves as a driving force for disentanglement, compelling the model to distill spatial layouts into the structure pathway while offloading visual details to a separate content pathway for generation. This synergy yields a continuous, semantically structured latent action space without compromising generative quality. *DiLA* achieves superior results in video generation quality, action transfer, visual planning, and manifold interpretability. These findings establish *DiLA* as a unified framework that simultaneously achieves high-level action abstraction and high-fidelity generation, advancing the frontier of self-supervised world model learning.

Poster
From Similarity to Vulnerability: Key Collision Attack on LLM Semantic Caching

Zhixiang Zhang, Zesen Liu, Yuchong Xie, Quanfeng Huang, Dongdong She

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Semantic caching has emerged as a pivotal technique for scaling LLM applications, widely adopted by providers including AWS and Microsoft. By utilizing embedding vectors as cache keys, this mechanism effectively minimizes latency and redundant computation for semantically similar queries. In this work, we conceptualize semantic cache keys as a form of fuzzy hashes. We demonstrate that the locality required to maximize cache hit rates fundamentally conflicts with the cryptographic avalanche effect necessary for collision resistance. Our conceptual analysis formalizes this inherent trade-off between performance (locality) and security (collision resilience), revealing that semantic caching is inherently vulnerable to key collision attacks. While prior research has focused on side-channel and privacy risks, we present the first systematic study of integrity risks arising from cache collisions. We introduce CacheAttack, an automated framework for launching black-box collision attacks. We evaluate CacheAttack in security-critical tasks and agentic workflows. It achieves a hit rate of 86\% in LLM response hijacking and can induce malicious behaviors in LLM agent, while preserving strong transferability across different embedding models. A case study on a financial agent further illustrates the real-world impact. Finally, we discuss mitigation strategies, highlighting a persistent trade-off between cache efficiency and robustness.

Poster
MINT: Minimal Information Neuro-Symbolic Tree for Objective-Driven Knowledge-Gap Reasoning and Active Elicitation

Zeyu Fang, Mahdi Imani, Tian Lan

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Joint planning through language-based interactions is a key area of human-AI teaming. Planning problems in the open world often involve various aspects of incomplete information and unknowns, e.g., objects involved, human goals/intents -- thus leading to knowledge gaps in joint planning. We consider the problem of discovering optimal interaction strategies for AI agents to actively elicit human inputs in object-driven planning. To this end, we propose Minimal Information Neuro-Symbolic Tree (MINT) to reason about the impact of knowledge gaps and leverage self-play with MINT to optimize the AI agent’s elicitation strategies and queries. More precisely, MINT builds a symbolic tree by making propositions of possible human-AI interactions and by consulting a neural planning policy to estimate the uncertainty in planning outcomes caused by remaining knowledge gaps. Finally, we leverage LLM to search and summarize MINT’s reasoning process and curate a set of queries to optimally elicit human inputs for best planning performance. By considering a family of extended Markov decision processes with knowledge gaps, we analyze the return guarantee for a given MINT with active human elicitation. Our evaluation on three benchmarks involving unseen/unknown objects of increasing realism shows that MINT-based planning attains near-expert returns by issuing a limited number of questions per task while achieving significantly improved rewards and success rates.

Poster
Bridging Structure and Semantics: Uncertainty-Modulated Dual-Path Diffusion for Robust Text-Attributed Graph Learning

Zhizhi Yu, Jiachen Liu, Qingyu Li, Dongxiao He, Di Jin

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Representation learning on text-attributed graphs (TAGs) is crucial for real-world applications, as it enables effective modeling of both rich node semantics and complex graph structure. Nevertheless, this task is intrinsically challenging due to structural–semantic mismatch stemming from divergent modality distributions, as well as dual-source noise inherent in node textual content and graph structure. Existing approaches often enforce a rigid fusion of distinct modalities while overlooking their inherent noise, which inevitably results in persistent distribution gaps and amplifies mixed interference during information propagation. To address these issues, we propose UDPD, an Uncertainty-modulated Dual-Path Diffusion model for robust text-attributed graph learning. Specifically, we first employ a dual-perspective node encoding strategy to separately learn semantic and structural embeddings. We then introduce a cooperative diffusion paradigm with parallel semantic and structural branches, where mutual guidance enables progressive alignment of different distributions while effectively suppressing modality inherent noise. Crucially, the reverse process is guided by node uncertainty, which is used to adaptively modulate cross-branch interaction strength, ensuring robust coupling and maximizing denoising effectiveness. Extensive experiments on five public benchmarks demonstrate the effectiveness and superiority of our UDPD over state-of-the-art baselines.

Poster
Local Minima in Quadratic-Penalty Relaxations of Binary Linear Programs

Cheng-Han Huang, Yongliang Sun, Chaoyan Huang, Ismail Alkhouri, Rongrong Wang

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Many combinatorial optimization problems admit quadratic unconstrained binary formulations (QUBO) which can often be relaxed to the box $[0,1]^n$ and optimized using scalable gradient-based methods. However, the resulting non-convex landscape can often contain local optima that are spurious or infeasible. In this paper, we establish sufficient structural conditions on quadratic penalties that rule out these failures, guaranteeing that every local minimizer of the relax problem is both binary and feasible. For each problem we study, we examine existing QUBO formulations when available, identify why they fail when they do, and propose alternative relaxed QUBOs that satisfy our conditions. We show for several common combinatorial problems, including open-pit mining, knapsack, and traveling salesman formulations, that these constructions allow gradient-based methods such as projected gradient descent and Adam to be safely applied to obtain valid binary solutions. Our results clarify when differentiable optimization is a reliable local solver for quadratic combinatorial objectives.

Poster