ICML 2026 Papers

Latent actions serve as an intermediate representation that enables consistent modeling of vision-language-action (VLA) models across heterogeneous datasets. However, approaches to supervising VLAs with latent actions are fragmented and lack a systematic comparison. This work structures the study of latent action supervision from two perspectives: (i) regularizing the trajectory via image-based latent actions, and (ii) unifying the target space with action-based latent actions. Under a unified VLA baseline, we instantiate and compare four representative integration strategies. Our results reveal a formulation-task correspondence: image-based latent actions benefit long-horizon reasoning, whereas action-based latent actions excel at complex motor coordination. Furthermore, we find that directly supervising the VLM with discrete latent action tokens yields the most effective performance. Finally, our experiments offer initial insights into the benefits of latent action supervision in mixed-data, suggesting a promising direction for VLA training.

Concept erasure has emerged as a promising approach to mitigate undesired or unsafe content in diffusion models, yet existing methods still face significant limitations. While training-based methods are effective, their high computational cost limits scalability. Editing-based methods are more efficient and deployment-friendly, yet they struggle to simultaneously achieve precise concept erasure and preserve overall generative capacity. We identify this core limitation of the editing-based methods as reliance on additive parameter updates. Our empirical analysis reveals that concept semantics primarily depend on *neuron direction* rather than *neuron magnitude*, while overall generative capacity relies on the *angular geometry* of neurons. As additive updates inherently entangle direction, magnitude, and angular geometry, they inevitably introduce unintended interference between concept erasure and overall generation performance. To address this, we propose **Orthogonal Concept Erasure (OCE)**, which reformulates editing-based erasure as multiplicative parameter updates from a geometric perspective. Specifically, OCE applies layer-wise orthogonal transformations derived from a closed-form solution to the parameters, enabling precise concept erasure while preserving the neuron magnitude and angular geometry. Furthermore, to address conflicting constraints in multi-concept erasure, OCE introduces a subspace-level objective with structured subspace manipulation, yielding a more effective and scalable erasure. Extensive experiments on single- and multi-concept erasure demonstrate that OCE outperforms existing methods in concept erasure and non-target preservation, erasing up to 100 concepts in 4.3 s. Code: https://github.com/HansSunY/OCE.

Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework that seeks to minimize the expected loss (risk) against a worst-case distribution consistent with the prediction set's coverage guarantee. We first characterize the minimax optimal policy for a fixed prediction set, showing that it balances the worst-case loss inside the set with a penalty for potential losses outside the set. Building on this, we derive the optimal prediction set construction that minimizes the resulting robust risk subject to a coverage constraint. Finally, we introduce Risk-Optimal Conformal Prediction (ROCP), a practical algorithm that targets these risk-minimizing sets while maintaining finite-sample distribution-free marginal coverage. Empirical evaluations on medical diagnosis and a toy static hazard-decision benchmark demonstrate that ROCP reduces critical mistakes compared to baselines, particularly when out-of-set errors are costly. The source code to reproduce our experiments is available at https://github.com/TaoWangPenn/Risk-Optimal-Conformal-Prediction.

Policies learned via continuous actor-critic methods often exhibit erratic, high-frequency oscillations, making them unsuitable for physical deployment. Current approaches attempt to enforce smoothness by directly regularizing the policy's output. We argue that this approach treats the symptom rather than the cause. In this work, we theoretically establish that policy non-smoothness is fundamentally governed by the differential geometry of the critic. By applying implicit differentiation to the actor-critic objective, we prove that the sensitivity of the optimal policy is bounded by the ratio of the Q-function's mixed-partial derivative (noise sensitivity) to its action-space curvature (signal distinctness). To empirically validate this theoretical insight, we introduce PAVE (Policy-Aware Value-field Equalization), a critic-centric regularization framework that treats the critic as a scalar field and stabilizes its induced action-gradient field. PAVE rectifies the learning signal by minimizing the Q-gradient volatility while preserving local curvature. Experimental results demonstrate that PAVE achieves smoothness comparable to policy-side smoothness regularization methods, while maintaining competitive task performance, without modifying the actor.

Spiking Neural Networks (SNNs) have attracted growing attention due to their sparse spike-based communication and inherent temporal dynamics. However, their discrete information representation fundamentally limits expressiveness, resulting in a notable performance gap relative to Artificial Neural Networks (ANNs) on language modeling tasks. In this paper, we reveal that this gap is fundamentally rooted in a spike saturation-induced information homogenization problem: within a bounded time window, distinct high-amplitude inputs converge to identical spike counts, compressing neural representations and impairing fine-grained semantic discrimination across layers. To address this, we propose SmoothSpike, which applies a randomized Hadamard transformation to smooth pre-activation inputs and theoretically proves that it bounds the maximum input to $\mathcal{O}(\sqrt{\frac{\log n}{n}})$ with high probability. To further improve adaptability across varying input distributions, we extend the fixed transformation within SmoothSpike to a learnable orthogonal matrix updated via Newton-Schulz iterations, which can be fused into model weights at inference with no additional overhead. Experiments on the GLUE benchmark show that SmoothSpike effectively reduces information homogenization, yielding an 8.2\% average improvement over the Spikingformer baseline without compromising the efficiency inherent to spike-driven computation. These results advance the prospects for energy-efficient and high-performance language modeling on edge devices. Code is available at https://github.com/CayleyZ/SmoothSpike.

Machine learning methods that predict protein fitness from sequence remain sensitive to changes in data distributions, limiting generalization across common conditions encountered in protein engineering. Practically, protein engineers are thus left wondering about the effective utility of ML tools. The FLIP benchmark established protocols for testing generalization under some domain shifts, but it was limited to measurements of stability, binding, and viral capsid viability. We introduce FLIP2, a protein fitness benchmark spanning seven new datasets, including enzymes, protein-protein interactions, and light-sensitive proteins, as well as splits that measure generalization relevant to real-world protein engineering campaigns. Evaluating a suite of benchmark models across these datasets and suites reveals that simpler models often matched or outperformed fine-tuned protein language models on FLIP2, challenging the utility of existing transfer learning techniques. Provenance for all datasets has been recorded and we redistribute all data CC-BY 4.0 to facilitate continued progress.

Scientific data annotation, such as tracking animals in video or proofreading neural reconstructions, remains bottlenecked by the “last mile” problem: even with strong automation, verification and correction consume substantial human effort. Standard approaches train models to directly predict annotations, discarding the rich supervision in how experts navigate, click, verify, and correct. We introduce a framework for studying behavioral cloning on scientific annotation: 9 synthetic tasks paired with synthetic annotations that simulate realistic human strategies including exploration, mistake correction, and strategic decision-making. Our experiments reveal several findings. First, skills emerge hierarchically: models learn GUI mechanics before task-critical decisions, and commit fewer mistakes than the training data while retaining the ability to correct errors when they occur. Second, scaling models on multi-task behavioral cloning shows that larger models are more data efficient within our scale range. Third, multi-task pretraining enables efficient fine-tuning to new tasks, while training from scratch fails entirely. Fourth, linear probes reveal that models internally represent latent variables of the annotation process such as task phase and data position; interestingly, we find a shared mistake representation that generalizes across different annotation tasks. Overall, our framework establishes systematic benchmarks and identifies key bottlenecks, providing a foundation for scaling behavioral cloning to real-world scientific data annotation.

Image-to-3D generation faces inherent semantic ambiguity under occlusion, where partial observation alone is often insufficient to determine object category. In this work, we formalize *text-driven amodal 3D generation*, where text prompts steer the completion of unseen regions while strictly preserving input observation. Crucially, we identify that these objectives demand distinct control granularities: rigid control for the observation versus relaxed structural control for the prompt. To this end, we propose **RelaxFlow**, a training-free dual-branch framework that decouples control granularity via a Multi-Prior Consensus Module and a Relaxation Mechanism. Theoretically, we prove that our relaxation is equivalent to applying a low-pass filter on the generative vector field, which suppresses high-frequency instance details to isolate geometric structure that accommodates the observation. To facilitate evaluation, we introduce two diagnostic benchmarks, **ExtremeOcc-3D** and **AmbiSem-3D**. Extensive experiments demonstrate that RelaxFlow successfully steers the generation of unseen regions to match the prompt intent without compromising visual fidelity. Code and datasets will be released.

Many real-world decisions require prioritizing high-risk cases, such as clinicians prioritizing high-risk patients before lower-risk ones. Falling rule lists (FRLs), which are ordered if--then rules with monotonically decreasing risks, provide an interpretable framework for such tasks; however, their single-path structure yields a highly restricted model class. We introduce falling trees, a new family of interpretable models that enforces the same monotonic risk constraint while permitting tree-structured branching. We present GraviTree, a novel dynamic-programming-with-bounds algorithm for learning the Rashomon set of falling trees under depth and branching constraints. Our formulation can interpolate between rule lists and full decision trees, enabling user-desired model expressivity. In a new clinical dataset and in many public classification benchmarks, falling trees match or outperform FRLs and other interpretable baselines, often producing more sparse decisions for high-risk instances. Our results show that falling trees strike a practical balance between interpretability, expressiveness, and risk prioritization for high-stakes settings.

Source-Free Domain Adaptation (SFDA) enables model adaptation under distribution shifts without access to source data, providing a practical solution for privacy-sensitive applications and having shown substantial progress in classification. In contrast, regression involves ordered and continuous target variables, posing unique challenges for representation adaptation and pseudo-label refinement in the SFDA setting. To address this gap, we propose a novel algorithm for continuous label prediction in SFDA that leverages instance-dependent, discretized density–informed supervisory signals to refine pseudo-labels within an uncertainty-aware paradigm. By incorporating auxiliary discretized distribution learning, our method also promotes more compact and structured feature representations, mitigating the inherent difficulties of adapting regression models under distribution shift. We theoretically demonstrate that the resulting density structure is robust to potential perturbations, supporting reliable SFDA for regression. Extensive experiments across multiple benchmarks validate the effectiveness of the proposed approach.

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in scientific domains. In this work, we develop a computationally cheap, mathematically justified, and highly flexible distributional modification for combating known pitfalls in equality-constrained generative models. We propose perturbing the data distribution in a constraint-aware way such that the new distribution has support matching the ambient space dimension while still implicitly incorporating underlying manifold geometry. Through theoretical analyses and empirical evidence on several representative tasks, we illustrate that our approach consistently enables data distribution recovery and stable sampling with both diffusion models and normalizing flows.

The pursuit of spatial intelligence fundamentally relies on access to large-scale, fine-grained 3D data. However, existing approaches predominantly construct spatial understanding benchmarks by generating question–answer (QA) pairs from a limited number of manually annotated datasets, rather than systematically annotating new large-scale 3D scenes from raw web data. As a result, their scalability is severely constrained, and model performance is further hindered by domain gaps inherent in these narrowly curated datasets. In this work, we propose \textbf{Holi-Spatial}, the first fully automated, large-scale, spatially-aware multimodal dataset, constructed from raw video inputs without human intervention, using the proposed data curation pipeline. Holi-Spatial supports multi-level spatial supervision, ranging from geometrically accurate 3D Gaussian Splatting (3DGS) reconstructions with rendered depth maps to object-level and relational semantic annotations, together with corresponding spatial Question–Answer (QA) pairs. Following a principled and systematic pipeline, we further construct \textbf{Holi-Spatial-4M}, the first large-scale, high-quality 3D semantic dataset, containing 12K optimized 3DGS scenes, 1.3M 2D masks, 320K 3D bounding boxes, 320K instance captions, 1.2M 3D grounding instances, and 1.2M spatial QA pairs spanning diverse geometric, relational, and semantic reasoning tasks. Holi-Spatial demonstrates exceptional performance in data curation quality, significantly outperforming existing feed-forward and per-scene optimized methods on datasets such as ScanNet, ScanNet++, and DL3DV. Furthermore, fine-tuning Vision-Language Models (VLMs) on spatial reasoning tasks using this dataset has also led to substantial improvements in model performance.

While *Prover-Verifier Games* (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, expressive *concept encodings* effectively allow to translate such data into interpretable concepts but are often utilised in the context of low-capacity linear predictors. In this work, we push towards real-world verifiability by combining the strengths of both approaches. We introduce *Neural Concept Verifier (NCV)*, a unified framework combining PVGs for formal verifiability with concept encodings to handle complex, high-dimensional inputs in an interpretable way. NCV achieves this by utilizing recent minimally supervised concept discovery models to extract structured concept encodings from raw inputs. A *prover* then selects a subset of these encodings, which a *verifier*, implemented as a nonlinear predictor, uses exclusively for decision-making. Our evaluations show that NCV outperforms classic concept-based models and pixel-based PVG classifier baselines on high-dimensional, logically complex datasets and helps mitigate shortcut behavior. Overall, we demonstrate NCV as a promising step toward concept-level, verifiable AI.

Model robustness against natural image corruptions is essential for safety-critical applications. While existing methods primarily focus on implicit representation learning, we provide the first systematic exploration of computational pathways to explicitly characterize internal robustness. We identify a progressive decay of robust features across network layers and establish a functional dependency between the prevalence of these features and model performance. To exploit these insights, we propose Suppress and Diversify (S\&D), a non-intrusive refinement approach that enhances robustness by dynamically selecting robust pathways and diversifying them through symmetry-preserving transformations. S\&D is architecture-agnostic, parameter-free, and incurs zero test-time overhead. Extensive evaluations across eight benchmarks demonstrate that S\&D consistently improves performance across multiple vision tasks, diverse backbones, and complex real-world scenarios, highlighting its broad efficacy and scalability.

Most current paradigms in visual mechanistic interpretability (MI) remain confined to interpreting internal units of the vision model via heuristic methods (e.g., top-$K$ activation retrieval or optimization with regularization). In this work, we establish a theoretical distributional view for visual MI, which models the influence of a feature activation on the natural image distribution, thereby formulating a Kullback-Leibler (KL)-minimal optimization problem to model the MI task. Under this framework, statistical biases are identified within previous MI paradigms, which reveal that they may either be perceptually uninterpretable to humans (i.e., deviate from the natural image distribution), or mechanistically unfaithful to the vision models (i.e., unable to activate model features). To resolve the biases under the distributional view, we propose a model with a KL-minimal soft-constraint principle for visual MI that theoretically balances interpretability and faithfulness. We realize this principle via energy-guided diffusion posterior sampling. Extensive experiments validate the theoretical soundness of the proposed distributional view and demonstrate the practical effectiveness of our paradigm on the DINOv3 vision model. The code is available at https://github.com/SII-ZhouGC/EnergyDPS.

Dataset bias often leads deep learning models to exploit spurious correlations instead of task-relevant signals. We introduce the Standard Anti-Causal Model (SAM), a unifying causal framework that characterizes bias mechanisms and yields a conditional independence criterion for causal stability. Building on this theory, we propose DISCO$_m$ and sDISCO, efficient and scalable estimators of conditional distance correlation that enable independence regularization in gradient-based models. Across six diverse datasets, our methods consistently outperform or are competitive in existing observed bias mitigation approaches, while requiring fewer hyperparameters and scaling seamlessly to multi-bias scenarios. This work bridges causal theory and practical deep learning, providing both a principled foundation and effective tools for robust prediction. Source Code: https://github.com/yakamoz5/DISCO.

We introduce Flower, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold, Flowers use no Fourier multipliers, no dot-product attention, and no convolutional mixing. Each head predicts a displacement field and warps the mixed input features. Motivated by physics and computational efficiency, displacements are predicted pointwise, without any spatial aggregation, and nonlocality enters *only* through sparse sampling at source coordinates, *one* per head. Stacking warps in multiscale residual blocks yields Flowers, which implement adaptive, global interactions at linear cost. We theoretically motivate this design through three complementary lenses: flow maps for conservation laws, waves in inhomogeneous media, and a kinetic-theoretic continuum limit. Flowers achieve excellent performance on a broad suite of 2D and 3D time-dependent PDE benchmarks, particularly flows and waves. A compact 17M-parameter model consistently outperforms Fourier, convolution, and attention-based baselines of similar size, while a 150M-parameter variant improves over recent transformer-based foundation models with much more parameters, data, and training compute.

Expressivity has been a major focus in the design of Graph Neural Networks (GNNs), yet a significant gap persists between theoretical universal expressivity and practical performance. While many expressive GNNs are efficient and achieve strong results, they often focus on specific graph properties and lack theoretical expressivity for general graph tasks. Conversely, theoretically universal-expressive models often suffer from high computational costs or poor generalization, limiting their real-world applicability. To bridge this gap, we introduce Equivariant Noise GNNs (ENGNNs), a framework that utilizes random noise features to enhance the expressivity of GNNs. Crucially, unlike prior methods that naively use noise, we enforce equivariance to nodewise noise transformations, such as orthogonal transformations. We prove that this property reduces the model's theoretical sample complexity, thereby improving generalization. Our framework simultaneously reaches theoretical universal expressivity, maintains the linear scalability of standard Message-Passing Neural Networks in practice, and achieves performance comparable to computationally expensive, high-expressivity models. Extensive experiments confirm strong performance across node, link, subgraph, and graph-level prediction tasks, demonstrating that the equivariant use of noise provides a powerful and practical pathway for building expressive GNNs. Our code is available at \url{https://github.com/MuLabPKU/EquivNoiseGNN}.

Recent reinforcement learning (RL) techniques have yielded impressive reasoning improvements in language models, yet it remains unclear whether RL truly extends a model's reasoning ability beyond pre-training. A central challenge is the lack of control in modern training pipelines, where opaque pre-training data, underexplored mid-training, and complex RL interactions obscure causal effects. To resolve this ambiguity, we develop a controlled experimental framework that isolates the causal contributions of pre-training, mid-training, and RL-based post-training. Our approach employs synthetic reasoning tasks with explicit atomic operations, parseable step-by-step reasoning traces, and systematic manipulation of training distributions. We evaluate along: *extrapolative generalization* to more complex compositions and *contextual generalization* across surface contexts. Using this framework, we reconcile competing views on RL’s effectiveness: 1) RL produces true capability gains (pass@128) only when pre-training leaves sufficient headroom and RL data target the model’s *edge of competence*, tasks that are difficult but not yet out of reach. 2) Contextual generalization requires minimal yet sufficient pre-training exposure, after which RL reliably transfers. 3) Mid-training significantly enhances performance under fixed compute compared with RL alone, demonstrating its central but underexplored role. 4) Process-level rewards reduce reward hacking and improve reasoning fidelity. Together, these results clarify the interplay between pre-training, mid-training, and RL, offering a foundation for improving reasoning language models training strategies. Codes and data are avaialble at [Github](https://github.com/Interplay-LM-Reasoning/Interplay-LM-Reasoning) and [HuggingFace](https://huggingface.co/Interplay-LM-Reasoning)