ICML 2026 Papers

We investigate the capabilities and scalability of Large Language Models (LLMs) in optimization modeling, a domain requiring structured reasoning and precise formulation. To this end, we introduce OPT-ENGINE, an extensible benchmark framework with quantifiable and controllable complexity. OPT-ENGINE spans ten canonical Operations Research problems, systematically scaling from Linear Programming to Mixed-Integer Programming, providing a structured environment to probe the limits of automated problem formulation and solving. Utilizing OPT-Engine, we address three pivotal research questions. First, we examine whether Pure-Text Reasoning (PTR) via classical Chain-of-Thought can efficiently tackle optimization tasks, finding that PTR suffers from a critical robustness gap as task complexity increases. Second, we examine whether integrating external computational tools can mitigate PTR's arithmetic weaknesses and improve performance. Our results show that while such tools aid local calculations, they still fail to adhere to global optimization constraints. Finally, we pinpoint that for the current SOTA paradigm, Solver-integrated Reasoning (SIR), the automated formulation of constraints represents the primary bottleneck. These findings clarify current paradigms' limitations and provide a structured roadmap for developing next-generation LLMs for optimization modeling. We release our code and data to facilitate future research (https://github.com/Cardinal-Operations/OPTEngine).

Conformal Prediction (CP) provides a statistical framework for uncertainty quantification that constructs prediction sets with coverage guarantees. While CP yields uncontrolled prediction set sizes, Backward Conformal Prediction (BCP) inverts this paradigm by enforcing a predefined upper bound on set size and estimating the resulting coverage guarantee. However, the looseness induced by Markov's inequality within the BCP framework causes a significant gap between the estimated coverage bound and the empirical coverage. In this work, we introduce ST-BCP, a novel method that introduces a data-dependent transformation of nonconformity scores to narrow the coverage gap. In particular, we develop a computable transformation and prove that it outperforms the baseline identity transformation. Extensive experiments demonstrate the effectiveness of our method, reducing the average coverage gap from 4.20\% to 1.12\% on common benchmarks.

Dense associative memories (DAMs) store and retrieve patterns via energy-function based fixed points, but existing models are limited to vector representations. We extend DAMs to Gaussian densities equipped with the 2-Wasserstein distance. Our framework defines a log-sum-exp energy over stored distributions and a retrieval dynamics aggregating optimal transport maps in a Gibbs-weighted manner. Stationary points correspond to self-consistent Wasserstein barycenters, generalizing classical DAM fixed points. We prove exponential storage capacity and provide quantitative retrieval guarantees under Wasserstein perturbations. We validate the method on synthetic and real-world image (CelebA and CIFAR-10 datasets) and text (text8 and NLI corpus) datasets. By generalizing from vectors to distributions, our work bridges classical DAMs with modern generative modeling and paves way for distributional storage and retrieval in memory-augmented learning.

Despite its importance to applications in protein design, predicting protein properties like binding affinity and thermostability from sparse experimental data remains a significant challenge. Accordingly, we introduce a class of sequence kernels that exploit evolutionary substitution matrices as well as local linearity and demonstrate that the resulting Gaussian processes provide data-efficient models of protein property landscapes, frequently outperforming alternatives that rely on foundation model embeddings. Furthermore--by learning what are in effect structure-aware substitution matrices--we show that our kernels can readily incorporate structural information from foundation models. We demonstrate that these structure-conditioned kernels are well suited to multi-task learning across multiple protein property landscapes and can decisively outperform local supervised learning methods.

In this work, we study **Human-Object Interaction Video Generation (HOIVG)**, which aims to synthesize high-quality human-object interaction videos conditioned on text, reference images, audio, and pose. We present **OmniShow**, the first all-in-one model tailored for this practical yet challenging task, capable of harmonizing multimodal conditions and delivering industry-grade performance. To overcome the trade-off between controllability and quality, we introduce **Unified Channel-wise Conditioning** for efficient image and pose injection, and **Gated Local-Context Attention** to ensure precise audio-visual synchronization. To effectively address data scarcity, we develop a **Decoupled-Then-Joint Training** strategy that leverages a multi-stage training process with model merging to efficiently harness heterogeneous sub-task datasets. Furthermore, to fill the evaluation gap in this field, we establish HOIVG-Bench, a dedicated and comprehensive benchmark for HOIVG. Extensive experiments demonstrate that OmniShow achieves overall state-of-the-art performance across various multimodal conditioning settings, setting a solid standard for the emerging HOIVG task.

Full fine-tuning of large language models (LLMs) incurs prohibitive computational and storage costs. Parameter-efficient fine-tuning (PEFT) addresses this limitation, with Low-Rank Adaptation (LoRA) gaining widespread adoption due to its simplicity and zero inference overhead. However, LoRA and its variants typically rely on uniform rank allocation or a single importance metric such as gradient magnitude or output sensitivity to guide rank distribution. This approach fails to recognize that gradient magnitude and output contribution are decoupled properties, leading to suboptimal allocation where critical layers are under-provisioned while less important ones waste capacity. To address this challenge, we propose COBRA, a principled framework integrating dual importance factors for adaptive rank allocation. COBRA operates in three stages: (1) layer conductance attribution quantifies each layer's contribution via path-integral attribution; (2) dual-factor aggregation combines contribution with adaptation demand, producing the Task-Adaptive Layer Conductance (TA-LC) distribution; and (3) Bayesian rank allocation translates this distribution into optimal heterogeneous ranks via variational optimization. Layer conductance provides layer-level interpretability by explicitly quantifying how much each layer contributes to predictions without redundancy, directly aligning with the granularity of rank allocation decisions and enabling principled cross-layer comparison for rank distribution. Experiments across diverse architectures and tasks demonstrate that COBRA consistently outperforms existing methods, achieving up to 1.6 points improvement on GLUE and a 6.6\% average MSE reduction in high-rank regression regimes under comparable parameter budgets.

Differentially private (DP) training protects individual examples by adding noise to gradients, but the injected noise interacts nontrivially with adaptive optimizers. Recent DP methods temporally filter privatized gradients to reduce variance; however, filtering also changes the DP noise statistics seen by AdamW’s second-moment accumulator. As a result, bias corrections derived for unfiltered DP noise (e.g., subtracting $\sigma_w^2$) can become miscalibrated when filtering is present. We propose FIBER, a DP optimizer designed for temporally filtered privatized gradients. FIBER (i) performs denoising in innovation space by filtering the residual stream and integrating it to form the filtered gradient estimate, (ii) decouples the two-point observation geometry from the innovation gain to enable independent tuning, and (iii) introduces a filter-aware second-moment calibration that subtracts the attenuated DP noise contribution $A(\omega)\sigma_w^2$, where $A(\omega)$ is derived in closed form for the innovation filter and can be computed for general stable linear filters. Across vision and language benchmarks, FIBER consistently demonstrates substantial improvements in the performance of DP optimizers, surpassing state-of-the-art results under equivalent privacy constraints on multiple tasks.

Weightless Neural Networks (WNNs) based on interconnected Lookup Tables (LUTs) have attracted attention for inference in extremely compact models, but achieving competitive accuracy under such tight resource budgets remains challenging. To address these issues, we introduce the Convolutional Learnable-Group Weightless Neural Network (CLGN). CLGN constructs convolutional layers using LUTs and incorporates a learnable GroupSum connection, thereby enhancing the accuracy of WNNs while maintaining low implementation resource consumption. Moreover, we propose a hierarchical training strategy to improve the training efficiency. We evaluate CLGN in two edge computing scenarios: (1) FPGA, where we evaluate accuracy, latency, throughput, power consumption, LUTs usage, and parameter size; and (2) Microprocessor, where we evaluate latency and memory usage. Compared with the state-of-the-art solutions, the proposed CLGN achieves superior accuracy while maintaining lower implementation resource consumption.

Latent diffusion models have become the dominant paradigm for video generation, making the video tokenizer a critical role. While most existing tokenizers are trained primarily for reconstruction, diffusion models are optimized to denoise heavily corrupted latents, which creates a mismatch between tokenizer training objectives and downstream generative learning. As a result, reconstruction metrics (e.g., rFVD) can be a poor proxy for generation quality (gFVD), and overly prioritizing reconstruction may even hinder diffusion training. We propose VideoMAETok, a simple family of ViT-based video tokenizers trained explicitly as corruption-inversion models for latent video diffusion. VideoMAETok builds on masked autoencoders: we (i) apply high-ratio token masking and encode only visible spatiotemporal tokens for efficiency, and (ii) corrupt latent tokens with interpolative Gaussian noise to better match the denoising nature of diffusion generators. Training under such corruption encourages latents that remain informative and well-conditioned for downstream denoising. Extensive experiments show that VideoMAETok consistently improves generation quality when paired with off-the-shelf diffusion models (SiT and LightningDiT), achieving state-of-the-art gFVD on Kinetics-600 and UCF-101 while remaining compute-efficient. Code is available at https://github.com/yztongzhan/VideoMAETok.

Safety-critical scenarios are essential for evaluating autonomous driving (AD) systems, yet they are rare in practice. Existing generators produce trajectories, simulations, or single-view videos—but they don’t meet what modern AD systems actually consume: realistic multi-view video. We present SMD, the first framework for generating multi-view safety-critical driving videos in the real-world domain. SMD couples a safety-critical trajectory engine with a diffusion-based multi-view video generator through three design choices. First, we pick the right adversary: a GRPO-fine-tuned vision-language model (VLM) that understands multi-camera context and selects vehicles most likely to induce hazards. Second, we generate the right motion: a two-stage trajectory process that (i) produces collisions, then (ii) transforms them into natural evasion trajectories—preserving risk while staying within what current video generators can faithfully render. Third, we synthesize the right data: a diffusion model that turns these trajectories into multi-view videos suitable for end-to-end planners. Videos generated by SMD substantially increase collision rates when stress testing multiple end-to-end planners, and reduce collision rates when incorporated into training, improving planner robustness and safety. Our code and video examples are available at: \href{https://icml-2.github.io/SMD/}{https://icml-2.github.io/SMD/}.

The ability to adapt to physical actions and constraints in an environment is crucial for embodied agents (e.g., robots) to effectively collaborate with humans. Such physically grounded human-AI collaboration must account for the increased complexity of the continuous state-action space and constrained dynamics caused by physical constraints. However, most existing collaboration benchmarks are discrete or do not consider physical attributes and constraints. To address this, we introduce Moving Out, a human-AI collaboration benchmark that resembles a wide range of collaboration modes affected by physical attributes and constraints, such as moving heavy items together and coordinating actions to move an item around a corner. Moving Out consists of two challenges and human-human interaction data to comprehensively evaluate models' abilities to adapt to diverse human behaviors and unseen physical attributes. To give embodied agents the capability to collaborate with humans under physical attributes and constraints, we propose a novel method, BASS (Behavior Augmentation, Simulation, and Selection), to enhance the diversity of agents and their understanding of the outcome of actions. We systematically compare BASS and state-of-the-art models in AI-AI and human-AI experiments, showing that BASS can effectively collaborate with both unseen AI and humans.

LLM parameter editing methods commonly rely on computing an ideal target hidden-state at a target layer (referred as anchor point) and distributing the target vector to multiple preceding layers (commonly known as backward spreading) for cooperative editing. Although widely used for a long time, its underlying basis have not been systematically investigated. In this paper, we first conduct a systematic study of its foundations, which helps clarify its capability boundaries, practical considerations, and potential failure modes. Then, we propose a simple and elegant alternative that replaces backward spreading with forward-propagation. Instead of optimizing the target at the last editing layer, we optimize the anchor point at the first editing layer, and then propagate it forward to obtain accurate and mutually compatible target hidden-states for all subsequent editing layers. This approach achieves the same computational complexity as existing methods while producing more accurate layer-wise targets. Our method is simple, without interfering with either the computation of the initial target hidden state or any other components of the subsequent editing pipeline, and thus constituting a benefit for a wide range of LLM parameter editing methods.

To handle ambiguous and open-ended requests, Large Language Models (LLMs) are increasingly trained to interact with users to surface intents they have not yet expressed (e.g., ask clarification questions). However, users are often ambiguous because they have not yet formed their intents: they must observe and explore outcomes to discover what they want. Simply asking "what kind of tone do you want?" fails when users themselves do not know. We introduce DiscoverLLM, a novel and generalizable framework that trains LLMs to help users form and discover their intents. Central to our approach is a novel user simulator that models cognitive state with a hierarchy of intents that progressively concretize as the model surfaces relevant options---where the degree of concretization serves as a reward signal that models can be trained to optimize. Resulting models learn to collaborate with users by adaptively diverging (i.e., explore options) when intents are unclear, and converging (i.e., refine and implement) when intents concretize. Across proposed interactive benchmarks in creative writing, technical writing, and SVG drawing, DiscoverLLM achieves over 10% higher task performance while reducing conversation length by up to 40%. In a user study with 75 human participants, DiscoverLLM improved conversation satisfaction and efficiency compared to baselines.

Predicting molecular properties from three-dimensional structures is fundamentally hindered by limited labeled data. While researchers have adapted self-supervised pre-training techniques from computer vision and natural language processing to address this scarcity, these approaches frequently neglect the intrinsic physical principles unique to molecular systems. From a physical perspective, denoising pre-training can be formally proven equivalent to learning molecular force fields. However, existing methods indiscriminately apply uniform noise across all molecules, thereby introducing systematic bias into the modeling of molecular distributions. To mitigate this issue, we introduce MOES-Pred, a denoising pre-training framework featuring an energy sentinel mechanism that dynamically tailors noise perturbations to individual molecules. Leveraging chemical prior knowledge, our molecule-specific noising strategies enhance conformational sampling coverage and improve distribution modeling fidelity. Extensive experiments show that MOES-Pred surpasses mainstream approaches in both force prediction and downstream quantum chemical property prediction, demonstrating substantial improvements.

Shapley values are widely used for model-agnostic data valuation and feature attribution, yet they implicitly assume contributors are interchangeable. This can be problematic when contributors are dependent (e.g., reused/augmented data or causal feature orderings) or when contributions should be adjusted by factors such as trust or risk. We propose Priority-Aware Shapley Value (PASV), which incorporates both hard precedence constraints and soft, contributor-specific priority weights. PASV is applicable to general precedence structures, recovers precedence-only and weight-only Shapley variants as special cases, and is uniquely characterized by natural axioms. We develop an efficient adjacent-swap Metropolis–Hastings sampler for scalable Monte Carlo estimation and analyze limiting regimes induced by extreme priority weights. Experiments on data valuation (MNIST/CIFAR10) and feature attribution (Census Income) demonstrate more structure-faithful allocations and a practical sensitivity analysis via our proposed ``priority sweeping".

From generating headlines to fabricating news, the Large Language Models (LLMs) are typically assessed by their final outputs, under the safety assumption that a refusal response signifies safe reasoning throughout the entire process. Challenging this assumption, our study reveals that during fake news generation, even when a model rejects a harmful request, its Chain-of-Thought (CoT) reasoning may still internally contain and propagate unsafe narratives. To analyze this phenomenon, we introduce a unified safety-analysis framework that systematically deconstructs CoT generation across model layers and evaluates the role of individual attention heads through Jacobian-based spectral metrics. Within this framework, we introduce three interpretable measures: stability, geometry, and energy to quantify how specific attention heads respond or embed deceptive reasoning patterns. Extensive experiments on multiple reasoning-oriented LLMs show that the generation risk rise significantly when the thinking mode is activated, where the critical routing decisions concentrated in only a few contiguous mid-depth layers. By precisely identifying the attention heads responsible for this divergence, our work challenges the assumption that refusal implies safety and provides a new understanding perspective for mitigating latent reasoning risks.

Modern neural classifiers can achieve remarkable predictive performance, yet often suffer from *miscalibration*. In this paper, we introduce a unified calibration framework applicable to arbitrary distribution-based classifiers. The proposed calibration objective guarantees a *monotone Probably Approximately Individually Calibrated (mPAIC)* predictor, which theoretically implies the properties of a *Probably Approximately Calibrated Classifier (PACC)* with explicit error bounds. To enable stable and effective optimization, we further devise a *Decoupled Dual-Stream Optimization (DDSO)* strategy with gradient detachment to reconcile discriminative representation learning and continuous calibration. Notably, our framework bridges calibration paradigms, supporting flexible deployment either as an end-to-end *pre-calibration* objective or as a lightweight *post-calibration* adapter. Extensive experiments across nine real-world datasets demonstrate that our approach consistently outperforms strong baselines, achieving superior performance on both *accuracy* and multi-level *calibration*.

Model merging combines knowledge from separately fine-tuned models, yet the factors driving its success remain poorly understood. While recent work treats mergeability as an intrinsic property of the models, we show with an architecture-agnostic framework that it fundamentally depends on both the merging method and the partner tasks. Using L1-regularized linear optimization over a set of interpretable pairwise metrics (e.g., gradient L2 distance), we uncover properties correlating with post-merge normalized accuracy across five merging methods. We find that the drivers of merge success vary across architectures and merging methods, overall with only a moderate agreement (64.0% average top-5 metric overlap; 79.3% sign agreement). Crucially, however, gradient alignment metrics consistently emerge as the most fundamental signals of mergeability. These findings provide a diagnostic foundation for understanding mergeability and motivate future merge-aware fine-tuning strategies.

Large language models (LLMs) have revolutionized research in software engineering, and among various tasks, LLM-based code synthesis is promising. A recent line of benchmarks aims to evaluate LLM-generated codes in time efficiency, beyond their correctness. However, *space*, another vital aspect of code efficiency, is rarely evaluated in prior benchmarks. To fill in the gap, this paper introduces *BEST*, the first benchmark for evaluating the efficiency of LLM-generated codes in *both time and space*. It comprises $440$ coding tasks that are rigorously constructed by experts. In addition, we propose a fine-grained *subtask-based* evaluation scheme by dividing each task into multiple subtasks, with different input scales and difficulties. Each subtask is then accompanied by an expert-crafted standard implementation as the efficiency baseline, which achieves the *Pareto optimum*. Building on BEST, we introduce a unified and novel dual-indicator (time and space) metric, named dual@${k}$, generalizing the notion of the standard pass@${k}$ metric and building on a careful and novel construction of a *weight matrix* of subtasks. Through extensive experiments with dual@${k}$ across $50$ LLMs on BEST, our evaluation demonstrates that while LLMs exhibit weak capabilities in generating time-efficient code, their capabilities in space-efficient code generation are even worse. The benchmark is provided at https://github.com/kmsgk0/BEST.