ICML 2026 Papers

Over the years, the unsupervised and supervised learning research directions of tensor networks (TNs) have mainly developed in parallel. In this paper, we provide a view for their cooperative advancement through a novel mixed tensor network learning (MTNL) framework that unifies the two fields. Specifically, inspired by supervised TN learning tasks, multiple TNs are fused in a deep-network style in MTNL, enhancing the expressive power for the unsupervised TN learning tasks. We then develop a more flexible TN structure search prior with theoretical guarantees for learning multiple TN structures, aligning with trends in many supervised learning setups. More interestingly, by combining these components within a Bayesian framework, we show that MTNL induces a lightweight uncertainty quantification mechanism that is theoretically guaranteed by its connection to the dropout-based counterpart problem, making the mechanism a potential alternative for large-scale learning problems. Finally, we demonstrate the effectiveness of the MTNL framework on tensor recovery, parameter-efficient fine-tuning, and tensor regression experiments.

The paradigm of learning from automatic annotations—driven by pre-trained experts and Foundation Models—dominates data-hungry applications. However, it introduces a critical challenge: model-induced label noise. Unlike stochastic noise in classical robust learning, this noise stems from annotator inductive biases, manifesting as systematic errors tightly coupled with local feature manifolds. Existing methods relying on global transition matrices underfit these structural patterns, while learning instance-specific matrices remains mathematically intractable. We propose Model-Induced Noise Decoupling (MIND), a theoretically grounded framework addressing this dilemma. We demonstrate that the high-dimensional noise manifold can be decoupled into tractable, subspace-dependent components via Latent Manifold Disentanglement. Specifically, our Latent Decoupling Estimator (LDE) dynamically projects samples into latent structural clusters with consistent error modes, facilitating noise identifiability without ground-truth anchor points. To rigorously evaluate robustness, we adopt a hierarchical protocol: moving from controlled noise on CIFAR-100 to a structural stress test on large-scale real-world 3D datasets (S3DIS, ScanNet), where error patterns explicitly couple with geometric manifolds. Empirically, MIND significantly outperforms state-of-the-art methods on these complex benchmarks and effectively corrects zero-shot hallucinations from Vision-Language Models (e.g., OpenSeg), highlighting its potential as a robust distillation framework for Foundation Models.

This paper investigates the entropy dynamics of Chain-of-Thought (CoT) and uncovers a consistent two-phase structure: an ***Uncertainty Region*** of exploration transitioning sharply to a ***Confidence Region*** of convergence. We demonstrate that the Confidence Region possesses two critical properties: 1) ***High Reliability***—answers in confidence region become highly accurate and stable, and 2) ***High Redundancy***—models generate unnecessary tokens long after reaching the correct answer. These properties unlock more efficient and reliable inference strategies: 1) ***Early Exit*** leverages reliability and redundancy to terminate computation safely when returns diminish, and 2) ***Test-Time Scaling*** uses the Confidence Region signal to prioritize converged trajectories. To operationalize these insights, we formulate Confidence Region detection as a sequential change-point detection problem, being the first to apply classical change-point methods to monitor CoT reasoning. Using the Cumulative Sum (CUSUM) algorithm, a statistically optimal change-point detector, we develop a training-free framework for real-time inference control. Experiments show our approach establishes a superior Pareto-frontier for early exit. CUSUM achieves 63.06% accuracy with 11.1% token reduction, outperforming DEER and Dynasor by 3.28% and 4.36% in accuracy respectively. For test-time scaling, CUSUM-weighted voting consistently outperforms self-consistency.

Large language models (LLMs) with extended context windows enable powerful applications but impose significant memory overhead, as caching all key-value (KV) states scales linearly with sequence length and batch size. Existing cache eviction methods address this by exploiting attention sparsity, yet they typically rank tokens heuristically using accumulated attention weights without considering their true impact on attention outputs. We propose Optimal Brain Cache (OBCache), a principled framework that formulates cache eviction as a layer-wise structured pruning problem. Building upon the Optimal Brain Damage (OBD) theory, OBCache quantifies token saliency by measuring the perturbation in attention outputs induced by pruning tokens, with closed-form scores derived for isolated keys, isolated values, and joint key-value pairs. Our scores account not only for attention weights but also for information from value states and attention outputs, thereby enhancing existing eviction strategies with output-aware signals. Experiments on LLaMA and Qwen models demonstrate that replacing the heuristic scores in existing works, which estimate token saliency across different query positions, with OBCache's output-aware scores consistently improves long-context accuracy. Code is available at https://github.com/DreamSoul-AI/OBCache.

Variational autoencoders (VAEs) compress high resolution CT volumes into compact latents while preserving clinically relevant structure. However, training CT-specific VAEs from scratch or heavily fine-tuning them incurs substantial computational and engineering cost, and often degrades under heterogeneous scanners, protocols, and diseases. This paper makes a progressive stride toward training-free medical VAEs by leveraging a critical observation: a single Foundation VAE, pretrained at scale on natural images and videos, can serve as a unified interface for CT Reconstruction, Augmentation, and Generation. With both encoder and decoder frozen, the Foundation VAE reconstructs CT volumes with preserved anatomy while suppressing acquisition noise; training segmentation models on these reconstructions improves surface accuracy by 3.9\% NSD on average for pancreatic tumor and lung tumor. Within the same Foundation VAE latent space, a conditional latent diffusion model achieves 3.9\% lower average FVD with 36.2\% higher CT CLIP score, and improves multi-disease generation faithfulness across 18 types by 2.76\% AUC. These results demonstrate Foundation VAEs as a practical interface for scalable CT representation reuse and faithful CT generation. Our code and demo are available at https://github.com/qic999/Foundation-VAE.

Recent advances in image and video generation raise hopes that these models possess world modeling capabilities—the ability to generate realistic, physically plausible videos. This could revolutionize applications in robotics, autonomous driving, and scientific simulation. However, before treating these models as world models, we must ask: Do they adhere to physical laws? Current evaluation methods rely on subjective judgments or trajectory matching, limiting their usage for physical reasoning estimation, where many generations could be physically plausible. Thus, we introduce **Morpheus**, one of the first physics-informed evaluation frameworks for measuring the ability of video generation models to comprehend Newtonian dynamics. **Morpheus** features 130 real-world videos capturing physical phenomena, guided by conservation laws. Using those as conditioning for video generation, we assess physical plausibility leveraging interpretable metrics evaluated with respect to infallible conservation laws known per physical setting, leveraging advances in physics-informed neural networks and vision-language foundation models. Importantly, **Morpheus** targets controlled Newtonian rigid-body settings to enable quantitative checks. Our findings reveal that even with advanced prompting and video conditioning, contemporary models struggle to encode physical principles despite generating aesthetically pleasing videos. Code and data available [here](https://github.com/physics-from-video/Morpheus).

In recent advances, to enable a fully data-driven learning paradigm on relational databases (RDB), relational deep learning (RDL) is proposed to structure the RDB as a heterogeneous entity graph and adopt the graph neural network (GNN) as the predictive model. However, existing RDL methods neglect the imbalance problem of relational data in RDBs and risk under-representing the minority entities, leading to an unusable model in practice. In this work, we investigate, for the first time, class imbalance problem in RDB entity classification and design the relation-centric minority synthetic over-sampling GNN (**Rel-MOSS**), in order to fill a critical void in the current literature. Specifically, to mitigate the issue of minority-related information being submerged by majority counterparts, we design the relation-wise gating controller to modulate neighborhood messages from each individual relation type. Based on the relational-gated representations, we further propose the relation-guided minority synthesizer for over-sampling, which integrates the entity relational signatures to maintain relational consistency. Extensive experiments on 12 entity classification datasets provide compelling evidence for the superiority of Rel-MOSS, yielding an average improvement of up to 2.46% and 4.00% in terms of *Balanced Accuracy* and *G-Mean*, compared with SOTA RDL methods and classic methods for handling class imbalance.

Reinforcement learning (RL) has become a cornerstone for fine-tuning Large Language Models (LLMs), with Proximal Policy Optimization (PPO) serving as the de facto standard algorithm. Despite its ubiquity, we argue that the core ratio clipping mechanism in PPO is structurally ill-suited for the large vocabularies inherent to LLMs. PPO constrains policy updates based on the probability ratio of sampled tokens, which serves as a noisy single-sample Monte Carlo estimate of the true policy divergence. This creates a sub-optimal learning dynamic: updates to low-probability tokens are aggressively over-penalized, while potentially catastrophic shifts in high-probability tokens are under-constrained, leading to training inefficiency and instability. To address this, we propose Divergence Proximal Policy Optimization (DPPO), which substitutes heuristic clipping with a more principled constraint based on a direct estimate of policy divergence (e.g., Total Variation or KL). To avoid huge memory footprint, we introduce the efficient Binary and Top-K approximations to capture the essential divergence with negligible overhead. Extensive empirical evaluations demonstrate that DPPO achieves superior stability and efficiency compared to existing methods, offering a more robust foundation for RL-based LLM fine-tuning. Our code is available at \url{https://github.com/sail-sg/Stable-RL}.

Quantile estimation and inference play essential roles in diverse scientific and industrial applications, and their accuracy can often be enhanced by integrating auxiliary data from multiple sites. However, developing efficient aggregation methods for quantile inference under potential privacy constraints, particularly with heterogeneous datasets, remains challenging. To address these issues, we propose a systematic framework for quantile estimation and inference under potential local differential privacy (LDP). The key idea is to construct weighted estimators by adaptively aggregating quantile estimates from target and source sites. The adaptive weights are determined by minimizing the asymptotic variance, incorporating an additional $\ell_2$ penalty to account for parameter shift. A parallel stochastic gradient descent algorithm under LDP constraints is developed for weight estimation and valid inference. Additionally, we introduce a conservative weighted estimator to ensure robust inference across diverse heterogeneous scenarios. Rigorous theoretical analysis establishes the consistency, normality, and effectiveness of the proposed methods. Extensive numerical studies and real data application corroborate our theoretical findings.

We dream of a future where point clouds from all domains can come together to shape a single model that benefits them all. Toward this goal, we present Utonia, a first step toward training a single self-supervised point transformer encoder across heterogeneous domains, spanning remote sensing, outdoor LiDAR, indoor RGB-D sequences, object-centric CAD models, and point clouds lifted from RGB-only videos. Despite their distinct sensing geometries, densities, and priors, Utonia learns a consistent representation space that transfers across domains. This unification improves perception capability while revealing intriguing emergent behaviors that arise only when domains are trained jointly. Beyond perception, we observe that Utonia representations can also benefit embodied and multimodal reasoning: conditioning vision-language-action policies on Utonia features improves robotic manipulation, and integrating them into vision-language models yields gains on spatial reasoning. We hope Utonia can serve as a step toward foundation models for sparse 3D data, and support downstream applications in AR/VR, robotics, and autonomous driving.

Text-to-Image (T2I) models are capable of generating high-quality artistic creations and visual content. However, existing research and evaluation standards predominantly focus on image realism and shallow text-image alignment, lacking a comprehensive assessment of complex semantic understanding and world knowledge integration in text-to-image generation. To address this challenge, we propose WISE, the first benchmark specifically designed for World Knowledge-Informed Semantic Evaluation. WISE moves beyond simple word-pixel mapping by challenging models with 1000 meticulously crafted prompts across 25 subdomains in cultural common sense, spatio-temporal reasoning, and natural science. To overcome the limitations of traditional CLIP metric, we introduce WiScore, a novel quantitative metric for assessing knowledge-image alignment. Through comprehensive testing of 20 models (10 dedicated T2I models and 10 unified multimodal models) using 1,000 structured prompts spanning 25 subdomains, our findings reveal significant limitations in their ability to effectively integrate and apply world knowledge during image generation, highlighting critical pathways for enhancing knowledge incorporation and application in next-generation T2I models. Code and data will be available.

Dynamic graph anomaly detection is critical for many real-world applications but remains challenging due to the scarcity of labeled anomalies. Existing methods are either unsupervised or semi-supervised: unsupervised methods avoid the need for labeled anomalies but often produce ambiguous boundary, whereas semi-supervised methods can overfit to the limited labeled anomalies and generalize poorly to unseen anomalies. To address this gap, we consider a largely underexplored problem: learning a discriminative boundary from normal/unlabeled data, while leveraging limited labeled anomalies \textbf{when available} without sacrificing generalization to unseen anomalies. In this paper, we propose an effective, generalizable, and model-agnostic framework with three main components: (i) residual representation encoding that capture deviations between current interactions and their historical context, providing anomaly-relevant signals; (ii) a restriction loss that constrain the normal representations within an interval bounded by two co-centered hyperspheres, ensuring consistent scales while keeping anomalies separable; (iii) a bi-boundary optimization strategy that learns a discriminative and robust boundary using the log-likelihood distribution modeled by a normalizing flow. Extensive experiments demonstrate the superiority of our framework across diverse evaluation settings.

Achieving pixel-level accurate segmentation of structural cracks across diverse scenarios remains a formidable challenge. Existing methods face significant bottlenecks in balancing crack topology modeling with computational efficiency, often failing to reconcile high segmentation quality with low resource demands. To address these limitations, we propose the Ultra-Compact Structure-Calibrated Vision RWKV (SCRWKV), a network that achieves high-precision modeling via a novel Structure-Field Encoder (SFE) backbone while maintaining linear complexity. The SFE integrates the Adaptive Multi-scale Cascaded Modulator (AMCM) to enhance texture representation and utilizes the Structure-Calibrated Insight Unit (SCIU) as its core engine. Specifically, the SCIU employs the Geometry-guided Bidirectional Structure Transformation (GBST) to capture topological correlations and integrates the Dynamic Self-Calibrating Decay (DSCD) into Dy-WKV to suppress noise propagation. Furthermore, we introduce a lightweight Cross-Scale Harmonic Fusion (CSHF) decoder to achieve precise feature aggregation. Systematic evaluations on multiple benchmarks characterized by complex textures and severe interference demonstrate that SCRWKV, with only 1.22M parameters, significantly outperforms SOTA methods. Achieving an F1 score of 0.8428 and mIoU of 0.8512 on the TUT dataset, the model confirms its robust potential for efficient real-world deployment. The code is available at https://github.com/zhxhzy/SCRWKV.

LLM-based function calling enables intelligent agents to interact with external tools and environments, yet autoregressive decoding imposes a fundamental latency bottleneck that limits real-time applications such as embodied intelligence, game AI, and interactive avatars (e.g., 10 Hz control frequency). We observe that function calling differs fundamentally from free-form text generation: structured outputs exhibit substantial token redundancy (delimiters, parameter names) and weak causal dependencies among arguments---two properties that must be exploited jointly to achieve real-time performance. We present RealtimeTool, which introduces special tokens that serve a dual role: compressing low-entropy tokens (4--6× reduction) while acting as mode selectors that enable independent parallel generation of function name and arguments. This synergistic design achieves 3--6× end-to-end speedup (up to 9.6×) with only +8.2% parallelization overhead, while maintaining competitive or improved accuracy across five benchmarks on Qwen-series models (0.5B--14B). With quantization on a consumer-grade GPU, RealtimeTool reaches 61.2 ms P50 latency at 4B scale---enabling 16 Hz real-time control and bridging the gap between LLM function calling and latency-critical real-world deployment.

Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after training, but existing approaches are tailored to Euclidean geometry. Extending neural OT to high-dimensional Riemannian manifolds remains an open challenge. In this paper, we prove that any method for OT on manifolds that produces discrete approximations of transport maps necessarily suffers from the curse of dimensionality: achieving a fixed accuracy requires a number of parameters that grows exponentially with the manifold dimension. Motivated by this limitation, we introduce Riemannian Neural OT (RNOT) maps, which are continuous neural-network parameterizations of OT maps on manifolds that avoid discretization and incorporate geometric structure by construction. Under mild regularity assumptions, we prove that RNOT maps approximate Riemannian OT maps with sub-exponential complexity in the dimension. Experiments on synthetic and real datasets demonstrate improved scalability and competitive performance relative to discretization-based baselines.

Image clustering is a fundamental unsupervised task in computer vision. Recent studies have explored incorporating external linguistic information to facilitate visual feature learning and thereby enhance clustering performance. Nevertheless, these methods typically rely on fixed vocabularies (e.g., WordNet) to generate language counterparts, leading to inter-modal semantic misalignment due to granularity discrepancy between visual and textual semantics. Moreover, they often overlook the issue of intra-modal semantic redundancy caused by task-irrelevant knowledge. To address these challenges, we propose a new Multi-grAnularity lanGuage-informed Image Clustering method, dubbed MAGIC. To reduce semantic misalignment, we first prompt the vision-language models to generate multi-granularity language descriptions that capture rich image semantics, which are then integrated for effective multi-modal alignment. To alleviate semantic redundancy, we design modality-specific semantic adapters that adaptively refine and compress the semantically dense features into clustering-friendly representations under task guidance. A consensus representation is obtained by fusing the refined visual and textual features, which acts as a teacher to guide image clustering through a robust contrastive learning framework. Extensive experiments on benchmarks demonstrate that MAGIC outperforms state-of-the-art methods.

Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the relationship between model performance (validation loss) and three key factors: model size ($N$), dataset size ($D$), and compute budget ($C$). Across a range of models, we find that Aurora exhibits the strongest data-scaling behavior: increasing the training dataset by 10× reduces validation loss by up to 3.2×. GraphCast demonstrates the highest parameter efficiency, yet suffers from limited hardware utilization. Our compute-optimal analysis indicates that, under fixed compute budgets, allocating resources to more total training data yields greater performance gains than increasing model size. Furthermore, we analyze model shape and uncover scaling behaviors that differ fundamentally from those observed in language models: weather forecasting models consistently favor increased width over depth. These findings suggest that future weather models should prioritize wider architectures and larger effective training datasets to maximize predictive performance.

Analyzing attention weights has become a standard approach for interpreting the information flow of Large Language Models (LLMs). However, this approach has significant limitations as it neglects the geometric properties of the value vectors being aggregated. To address this gap, we introduce \emph{Contribution Weights}, a projection-based metric that quantifies a token's influence by accounting for it's attention weight, value magnitude, and directional alignment with the layer output. We demonstrate that contribution weights provide a more faithful measure of token importance, consistently outperforming attention-based metrics in identifying semantically critical tokens across different decoder-only models, tasks, and datasets. Further, our metric enables novel mechanistic analysis of \emph{attention sinks}. While previous work characterized sinks as passive repositories for excess attention, we reveal they serve an active functional role, suppressing information through a convex relationship between sink rate and output norm, stabilizing representations by opposing the semantic drift of low-confidence tokens.

Simulation-Based Inference (SBI) is critical for scientific discovery, with generative models offering a promising path toward efficient inference. However, existing methods struggle with effective multimodal modeling. They often rely on brute-force fusion strategies that ignore the structural disparities between parameters and observations, thus limiting estimation fidelity. In this work, we introduce FUSE (Feynman-Kac steered mUlti-modal flow matching for efficient Simulation-based posterior Estimation). Unlike prior work, FUSE employs a dual-track architecture that preserves the distinct features of multimodal inputs while facilitating dynamic interaction. Additionally, we propose an FK-steered sampling strategy that leverages intermediate observation likelihoods to guide the generative trajectories, effectively improving the sample quality during inference. Our approach outperforms state-of-the-art baselines on standard SBI benchmarks, producing posteriors that closely match ground-truth MCMC. Furthermore, in a real-world exoplanet orbital estimation task, FUSE successfully resolves complex parameter degeneracies that challenge existing methods, highlighting its potential to accelerate complex scientific discoveries in astrophysics and beyond.