ICML 2026 Papers

Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on Normalizing Flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG), a novel autoregressive modelling framework that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132M parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, $\mathcal{E}$-$\mathcal{W}_2$, on 8-residue systems by $\sim 60$\%.

Causal discovery from observational count data poses unique challenges, particularly when the data exhibit inherent branching structures, such as an upstream ad impression event triggering a downstream purchase event with certain probability. Such branching dynamics are naturally modeled by thinning operators (for branching) and an independent Poisson distribution (for exogenous noise), constituting a Poisson Branching Structural Causal Model (PB-SCM). However, existing approaches based on PB-SCM rely on the restrictive assumption of causal sufficiency, failing to account for ubiquitous latent confounders. In this work, we propose a Latent Confounding Poisson Branching Structural Causal Model (LC-PB-SCM) to bridge this gap. We leverage Probability Generating Function (PGF) to characterize the complex dependencies introduced by latent confounding. Then, we establish a Trie representation theorem that maps the branching structure to algebraic properties of PGF monomials. Based on local PGF, we establish a complete identifiability condition for local 3-variables covering all causal patterns distinguishable up to monomial equivalence. Finally, we propose a practical algorithm to learn causal structures under latent confounding and demonstrate its effectiveness through experiments on both synthetic and real-world datasets.

Aligning Large Language Models (LLMs) with the diverse spectrum of human values remains a central challenge: preference-based methods often fail to capture deeper motivational principles. Value-based approaches offer a more principled path, yet three gaps persist: extraction often ignores hierarchical structure, evaluation detects presence but not calibrated intensity, and steerability of LLMs at controlled intensities remains insufficiently understood. To address these limitations, we introduce VALUEFLOW, a unified framework that spans extraction, evaluation, and steering with calibrated intensity control. The framework integrates three components: (i) HiVES, a hierarchical value embedding space that captures intra- and cross-theory value structure; (ii) the Value Intensity DataBase (VIDB), a large-scale resource of value-labeled texts with intensity estimates derived from ranking-based aggregation; and (iii) an anchor-based evaluator that produces consistent intensity scores for model outputs by ranking them against VIDB panels. Using VALUEFLOW, we conduct a comprehensive large-scale study across ten models and four value theories, identifying asymmetries in steerability and composition laws for multi-value control. This paper establishes a scalable infrastructure for evaluating and controlling value intensity, advancing pluralistic alignment of LLMs.

Foundational models pretrained on huge amounts of data learn representations that evolve across depth, forming a hierarchy of embeddings with distinct semantic content and geometric structure. Contrary to the widespread practice of using only the final layer or shallow mixtures, we show that task-relevant information is distributed non-monotonically across layers and cannot be recovered by na\"ive aggregation. Through a geometric and empirical study across multiple modalities, we show that effective transfer depends on identifying which layers encode task-discriminative structure and how their embeddings are geometrically organized. We introduce Layer-wise Optimal Embedding Selection (LOES), a constructive spectral method that identifies task-discriminative subspaces by minimizing residual error under orthogonality and isotropy constraints. To align fine-tuning with this selection principle, we further propose Geometric Regularization (GeoReg), which enforces a simplicial structure on class manifolds and stabilizes representation geometry during fine-tuning. Across a wide range of architectures, depths, modalities, and data regimes, LOES consistently outperforms standard baselines, with gains that grow as model depth increases. Beyond accuracy, our method reveals how semantic factors are distributed across layers, thereby enabling cross-lingual and cross-modal interpretability analyses. Together, our results provide strong evidence that layerwise embedding geometry is not incidental but central to how deep models represent and transfer knowledge.

Genomic foundation models have the potential to decode DNA syntax, yet face a fundamental tradeoff. Standard subword tokenizers fragment biologically meaningful motifs such as codons and regulatory elements, while nucleotide-level models preserve biological coherence but incur prohibitive computational costs for long contexts. We introduce dnaHNet, a state-of-the-art tokenizer-free autoregressive model that segments and models genomic sequences end to end. Using a differentiable dynamic chunking mechanism, dnaHNet compresses raw nucleotides into latent tokens adaptively, balancing compression with predictive accuracy. Pretrained on prokaryotic genomes, dnaHNet outperforms leading architectures including StripedHyena2 in scaling and efficiency. This recursive chunking yields quadratic FLOP reductions, enabling $>3 \times$ inference speedup over Transformers. On zero-shot tasks, dnaHNet achieves superior performance in predicting protein variant fitness and gene essentiality, while automatically discovering hierarchical biological structures without supervision. These results establish dnaHNet as a scalable, interpretable framework for next-generation genomic modeling.

Harmful fine-tuning can invalidate safety alignment of large language models, exposing significant safety risks. In this paper, we utilize the attention sink mechanism to mitigate harmful fine-tuning. Specifically, we first measure a statistic named sink divergence for each attention head and observe that different attention heads exhibit two different signs of sink divergence. To understand its safety implications, we conduct experiments and find that the number of attention heads of positive sink divergence increases along with the increase of the model's harmfulness when undergoing harmful fine-tuning. Based on this finding, we propose a separable sink divergence hypothesis -- attention heads associating with learning harmful patterns during fine-tuning are separable by their sign of sink divergence. Based on the hypothesis, we propose a fine-tuning-stage defense, dubbed Surgery. Surgery utilizes a regularizer for sink divergence suppression, which steers attention heads toward the negative sink divergence group, thereby reducing the model’s tendency to learn and amplify harmful patterns. Extensive experiments demonstrate that Surgery improves defense performance by 5.90\%, 11.25\%, and 9.55\% on the BeaverTails, HarmBench, and SorryBench benchmarks, respectively. Source code is available on https://github.com/Lslland/Surgery.

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets $\Sigma$ that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto $\Sigma$, ensuring feasibility without iterative Newton solves or projection failures. By leveraging underdamped dynamics, we accelerate mixing toward the prior distribution, effectively alleviating the high simulation costs typically associated with constrained diffusion. Empirically, this approach reduces function evaluations and memory usage during both training and inference while preserving sample quality. On benchmarks featuring equality and mixed constraints, our method achieves comparable sample quality to state-of-the-art baselines while significantly reducing computational cost, providing a practical and scalable solution for diffusion on nonconvex feasible sets.

Agents powered by advanced large language models (LLMs) have demonstrated impressive capabilities across diverse complex applications. Recently, Multi-Agent Systems (MAS), wherein multiple agents collaborate and communicate with each other, have exhibited enhanced capabilities in complex tasks, such as high-quality code generation and arithmetic reasoning. However, the development of such systems often relies on handcrafted methods, and the literature on systematic design and optimization of LLM-based MAS remains limited. In this work, we introduce OMAC, a general framework designed for holistic optimization of LLM-based MAS. Specifically, we identify five key optimization dimensions for MAS, encompassing both agent functionality and collaboration structure. Building upon these dimensions, we first propose a general algorithm, utilizing two actors termed the Semantic Initializer and the Contrastive Comparator, to optimize any single dimension. Then, we present an algorithm for joint optimization across multiple dimensions. Extensive experiments demonstrate the superior performance of OMAC on diverse tasks against recent approaches. Codes are available at: https://github.com/xiwenchao/OMAC.

Large Language Models (LLMs) have demonstrated sophisticated comprehension of sequential code, yet their capacity for reasoning about concurrent programs remains largely unquantified. We introduce DRPBench, a benchmark designed to evaluate the concurrent code comprehension of LLMs by measuring their data race prediction performance. To address the challenge of runtime non-determinism for evaluation on concurrent programs, we frame the evaluation as a fine-grained static prediction task using 1,003 programs from the SV-COMP suite, featuring 557 manually annotated data races with precise variable- and line-level granularity. Our evaluation of 15 state-of-the-art LLMs—spanning standard, reasoning, and agentic variants—reveals that DRPBench effectively differentiates concurrent code comprehension capabilities of LLMs. While the top-performing model (Gemini 3 with test-time reasoning) achieves an F1 score of 74.89%, most models struggle significantly (scoring less than 60%), with Llama 3 70B achieving only 8.80%. Beyond benchmarking, we characterize two primary failure modes: (1) shared-variable distraction, where multiple variable appearances degrade comprehension accuracy, and (2) synchronization-logic myopia, the inability to interpret non-standard synchronization implementations. Our findings provide a diagnostic roadmap for enhancing concurrent code comprehension of LLMs in future development.

Expert-annotated time series datasets often suffer from low agreement, especially in medical applications where decisions rely on subjective criteria and inconsistent thresholds. Such variability degrades annotation quality and thus limits the reliability of supervised classification models. To address this, we propose to rely on a pairwise comparison-based approach, which provides a more robust alternative to individual annotation, since relative judgments are typically easier and yield higher consistency. The problem is thus transformed into a ranking problem and we introduce an ideal point model adapted to time series data using elastic similarity measures such as Dynamic Time Warping (DTW) and Time Warp Edit Distance (TWED). We prove Lipschitz continuity of these distances and demonstrate several convergence guarantees for this model. To facilitate gradient-based optimization, we also introduce a differentiable version of the TWED. Finally, we show through multiple experiments that our approach produces accurate and robust rankings under noisy annotation conditions.

We study *grokking* — the onset of generalization long after overfitting — in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight decay. Specifically, we prove that the following stages occur: (i) the model overfits the training data early during training; (ii) poor generalization persists long after overfitting has manifested; and (iii) the generalization error eventually becomes arbitrarily small. Moreover, we show, both theoretically and empirically, that grokking can be amplified or eliminated in a principled manner through proper hyperparameter tuning. To the best of our knowledge, these are the first rigorous quantitative bounds on the generalization delay (which we refer to as the "grokking time") in terms of training hyperparameters. Lastly, going beyond the linear setting, we empirically demonstrate that our quantitative bounds also capture the behavior of grokking on non-linear neural networks. Our results suggest that grokking is not an inherent failure mode of deep learning, but rather a consequence of specific training conditions, and thus does not require fundamental changes to the model architecture or learning algorithm to avoid.

Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization ($\boldsymbol{\mu}$P) provides a theoretical safeguard for width-invariant $\Theta(1)$ activation control, whereas emerging optimizers like Muon are only "half-aligned" with these constraints: they control updates but allow weights to drift. To address this limitation, we introduce the **Spectral Sphere Optimizer (SSO)**, which enforces strict module-wise spectral constraints on both weights and their updates. By deriving the steepest descent direction on the spectral sphere, SSO realizes a fully $\boldsymbol{\mu}$P-aligned optimization process. To enable large‑scale training, we implement SSO as an efficient parallel algorithm within Megatron. Through extensive pretraining on diverse architectures, including Dense 1.7B, MoE 8B-A1B, and 200-layer DeepNet models, SSO consistently outperforms AdamW and Muon. Furthermore, we observe significant practical stability benefits, including improved MoE router load balancing, suppressed outliers, and strictly bounded activations.

We examine the interplay between ordinal, preference-based solution concepts in games and the outcomes of payoff-driven learning dynamics, asking to what extent the combinatorial data of a game—its *preference graph*—can predict the long-run behavior of no-regret dynamics such as *follow-the-regularized-leader* (FTRL). In one direction, we show that the skeleton of every *dynamically stable* set (i.e., the set of pure profiles it contains) must also be *preferentially stable*, that is, it must be closed under profitable deviations. We then ask the converse question: when are preferences sufficient to describe the long-run behavior of the players' learning dynamics? We begin by showing that preferences are indeed enough to fully characterize asymptotic stability in the case of *subgames*—i.e., subsets of pure profiles obtained by restricting players' action sets. Beyond this case however, the equivalence between dynamic and preferential stability breaks down: in particular, we construct a three-player game with a preferentially stable set whose span is dynamically *unstable*, showing that preferences are *not sufficient* to describe dynamically stable behavior in general. To restore stability, we introduce the notion of *leaklessness*, a measure of aggregate payoff drift away from a set of pure profiles, and we use it to identify a payoff-based condition guaranteeing that the span of a set of pure profiles is stable and attracting.

Modern LLMs show mastery over an ever-growing range of skills, as well as the ability to compose them flexibly. However, extending model capabilities to new skills in a scalable manner is an open problem: fine-tuning and parameter-efficient variants risk catastrophic forgetting, while context-based approaches have limited expressiveness and are constrained by the model's effective context. We explore *skill neologisms*--soft tokens integrated in the model's vocabulary and optimized to improve capabilities over a specific skill--as a way to selectively acquire new skills without weight updates. We first observe that pre-trained LLMs already exhibit tokens associated with procedural knowledge. We then show on a controlled synthetic task that skill neologisms can be learned to improve model capabilities on specific skills while being composable with out-of-distribution skills, and that independently trained skill neologisms can be composed zero-shot. Finally, we validate zero-shot composition of independently learned skill neologisms on the more realistic natural language setting of the Skill-Mix benchmark. These results suggest that skill neologisms may provide a scalable path towards skill-based continual learning.

Midtraining, the practice of mixing specialized data with more general pretraining data in an intermediate training phase, has become widespread in language model development, yet there is little understanding of what makes it effective. We propose that midtraining functions as distributional bridging by providing better initialization for posttraining. We conduct controlled pretraining experiments, and find that midtraining benefits are largest for domains distant from general pretraining data, such as code and math, and scale with the proximity advantage the midtraining data provides toward the target distribution. In these domains, midtraining consistently outperforms continued pretraining on specialized data alone both in-domain and in terms of mitigating forgetting. We further conduct an investigation on the starting time and mixture weight of midtraining data, using code as a case study, and find that time of introduction and mixture weight interact strongly such that early introduction of specialized data is amenable to high mixture weights, while late introduction requires lower ones. This suggests that late introduction of specialized data outside a plasticity window cannot be compensated for by increasing data mixtures later in training. Beyond midtraining itself, this suggests that distributional transitions between any training phases may benefit from similar bridging strategies.

Fine-tuning APIs offered by major AI providers create new attack surfaces where adversaries can bypass safety measures through targeted fine-tuning. We introduce **Trojan-Speak**, an adversarial fine-tuning method that bypasses Anthropic's Constitutional Classifiers. Our approach uses curriculum learning combined with GRPO-based hybrid reinforcement learning to teach models a communication protocol that evades LLM-based content classification. Crucially, while prior adversarial fine-tuning approaches report more than 25\% capability degradation on reasoning benchmarks, Trojan-Speak incurs less than 5\% degradation while achieving 99+\% classifier evasion for models with 14B+ parameters. We demonstrate that fine-tuned models can provide detailed responses to expert-level CBRN (Chemical, Biological, Radiological, and Nuclear) queries from Anthropic's Constitutional Classifiers bug-bounty program. Our findings reveal that LLM-based content classifiers alone are insufficient for preventing dangerous information disclosure when adversaries have fine-tuning access, and we show that activation-level probes can substantially improve robustness to such attacks.

Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We introduce the Iterative Refinement Neural Operator (IRNO), which augments pre-trained operators with a learned refinement module iteratively applied via fixed-point iteration. IRNO decomposes the prediction into a coarse initialization followed by successive residual corrections, paralleling classical numerical solvers. Under mild assumptions, we establish contraction of the induced operator, ensuring convergence to a unique fixed point. To explicitly target high-frequency errors, we propose a progressive spectral loss that adaptively increases penalty on high-frequency components over refinement steps during training. Across physical systems, IRNO consistently lowers error, with up to 56.05\% improvement on turbulent flow. On Active Matter, spectral analysis reveals that, relative to base operator, the normalized error ratios decrease to 27.72–36.10\% in low-, 5.07–6.68\% in mid-, and 1.48–2.04\% in high-frequencies, remaining stable beyond the trained iteration count.

Multi-compartment Hodgkin–Huxley (HH) models provide a principled framework for predicting neural dynamics and responses to electrical stimulation. However, fitting HH biophysical parameters typically requires intracellular recordings, which are invasive and low-throughput, limiting the ability to capture the geometry and cell-specific properties of many neurons in a given neural circuit. Multi-electrode arrays (MEAs) offer a scalable alternative—high-density extracellular measurements from full neural populations—but HH model complexity has so far precluded reliable biophysical inference from extracellular data alone. Here, we introduce a framework to rapidly infer HH parameters from designed features of extracellular MEA measurements by leveraging differentiable biophysical simulation and simulation-based inference, unlocking a wide range of downstream applications. In this work, we focus on a central goal of translational neuroengineering: predicting neural spiking responses to candidate neurostimulation patterns that would take hours to measure clinically. To validate our approach, we collected hundreds of hours of stimulation and recording data from isolated macaque retina with a 30 µm-pitch 512-electrode array. Our framework predicted previously unseen multi-electrode stimulation responses with 90.4\% accuracy using HH models fit from only a few minutes of recording, replacing hours of stimulus testing.

Diffusion models have transformed image synthesis by establishing unprecedented quality and creativity benchmarks. Nevertheless, their large-scale deployment faces challenges due to computationally intensive iterative denoising processes. Although post-training quantization (PTQ) provides an effective pathway for accelerating sampling, the iterative nature of diffusion models causes stepwise quantization errors to accumulate progressively during generation, inevitably compromising output fidelity. To address this challenge, we develop a theoretical framework that mathematically formulates error propagation in Diffusion Models (DMs), deriving per-step quantization error propagation equations and establishing the first closed-form solution for cumulative error. Building on this theoretical foundation, we propose a timestep-aware cumulative error compensation scheme. Extensive experiments on multiple image datasets demonstrate that our compensation strategy effectively mitigates error propagation, significantly enhancing existing PTQ methods. Specifically, it achieves a 1.2 PSNR improvement over SVDQuant on SDXL W4A4, while incurring only an additional $<$ 0.5\% time overhead.