ICML 2026 Papers

Causal representation learning (CRL) has garnered increasing interest from the causal inference and artificial intelligence communities due to its potential to disentangle complex data-generating mechanism into causally interpretable latent features by leveraging the heterogeneity of modern datasets. In this paper, we further contribute to the CRL literature, by focusing on the stylized linear structural causal model over latent features and assuming a linear mixing function that maps latent features to the observed data or measurements. Existing linear CRL methods often rely on stringent assumptions, such as access to single-node interventional data or restrictive distributional constraints on latent features and/or exogenous measurement noise. However, these prerequisites can be easy to violate in practice. In this work, we propose a novel linear CRL algorithm that, unlike existing methods, operates under weaker assumptions on environment heterogeneity and data-generating distributions while still recovering latent causal features up to an equivalence class. We further validate our new algorithm via synthetic experiments and an interpretability analysis of large language models, demonstrating both its superiority over competing methods in finite samples and its potential in integrating causality into understanding artificial intelligence. The source code is available at [the accompanying GitHub link](https://github.com/utulie/code_for_linear_crl_paper_creator).

Differentially private stochastic gradient descent (DP-SGD) achieves privacy by clipping per-sample gradients and injecting Gaussian noise, but its utility is highly sensitive to the choice of the clipping threshold $C$. A fixed $C$ often degrades performance and necessitates repeated empirical calibration. Existing adaptive clipping methods either modify the gradient update in vanilla DP-SGD, causing additional tuning or optimization overhead, or introduce separate private queries to monitor gradient statistics. In contrast, we leverage the *slack* information induced by the standard clipping operation, an overlooked signal in prior work, and show that it provides an effective indication for adapting $C$. In light of this, we propose *SlaClip*, a privacy-preserving adaptive clipping strategy using a post-hoc *Slack Indicator*. Under the same training configuration and privacy accountant, *SlaClip* preserves the sampling rule, noise multiplier, and global $\ell_2$ sensitivity bound of vanilla DP-SGD. Therefore, *SlaClip* is a plug-and-play module for vanilla DP-SGD and its variants. Moreover, *SlaClip* is accounted under the same per-step privacy bound, while requiring no additional private query. Across diverse datasets and tasks, experiments show that *SlaClip* consistently outperforms baseline adaptive clipping methods.

Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose *Constraint-Sensitive Policy Optimization (CSPO)*, a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods.

Trained attention layers exhibit striking and reproducible spectral structure of the weights, including low-rank collapse, bulk deformation, and isolated spectral outliers, yet the origin of these phenomena and their implications for generalization remain poorly understood. We study empirical risk minimization in a single-head tied-attention layer trained on synthetic high-dimensional sequence tasks generated from the attention-indexed model. Using tools from random matrix theory, spin-glass theory, and approximate message passing, we obtain an exact high-dimensional characterization of training and test error, interpolation and recovery thresholds, and the spectrum of the key and query matrices. Our theory predicts the full singular-value distribution of the trained query–key map—including low-rank structure and isolated spectral outliers—in qualitative agreement with observations in more realistic transformers. Finally, for targets with power-law spectra, we show that learning proceeds through sequential spectral recovery, leading to the emergence of power-law scaling laws.

Modeling the interplay between external stimuli and internal neural representations is a pivotal research area for Brain-Computer Interfaces (BCIs). A major limitation of prior work is the prevailing paradigm of specialized, single-task models, which curtails versatility and neglects inter-task synergies. To address this, we propose Mind-Omni, the first versatile framework that unifies seven distinct encoding and decoding tasks through a discrete diffusion paradigm. At its core is a novel Brain Tokenizer that transforms heterogeneous, continuous brain signals into standardized, discrete tokens. This enables direct, token-level interactions for mutual understanding and generation between any two or more modalities within a shared semantic space. To unlock advanced reasoning capabilities, we further curate a specialized Brain Question Answering (BQA) instruction-tuning dataset. Our model not only establishes a new state-of-the-art among multi-task unified frameworks but also provides strong evidence for multi-task synergy. By demonstrating performance competitive with, and at times superior to, larger specialized models, our work offers a powerful new paradigm for neural modeling and paves the way for foundation models of neural activity.

Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical decomposition and struggle with the computational demands of real-time execution, due to their iterative denoising process. In this work, we introduce $\textbf{Hierarchical Diffusion-Flow}$ ($\texttt{\textbf{HDFlow}}$), a novel hierarchical planning framework that optimally leverages the strengths of $\textit{diffusion}$ and $\textit{rectified flow}$ models to overcome the limitations of single-paradigm generative planners. $\texttt{\textbf{HDFlow}}$ employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's powerful exploratory capabilities. These subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories, exploiting the speed and efficiency of ordinary differential equation (ODE)-based trajectory generation. We evaluate $\texttt{\textbf{HDFlow}}$ on four challenging furniture assembly tasks in both simulation and real-world, where it significantly outperforms state-of-the-art methods. Furthermore, we also showcase our method's generalizability on two long-horizon benchmarks comprising diverse locomotion and manipulation tasks. Project website: https://hdflow-page.github.io/

Evaluating alignment in language models requires testing how they behave under realistic pressure, not just what they claim they would do. While alignment failures increasingly cause real-world harm, comprehensive evaluation frameworks with realistic multi-turn scenarios remain lacking. We introduce an alignment benchmark spanning 904 scenarios across six categories---Honesty, Safety, Non-Manipulation, Robustness, Corrigibility, and Scheming---validated as realistic by human raters. Our scenarios place models under conflicting instructions, simulated tool access, and multi-turn escalation to reveal behavioral tendencies that single-turn evaluations miss. Evaluating 24 frontier models using LLM judges validated against human annotations, we find that even top-performing models exhibit gaps in specific categories, while the majority of models show consistent weaknesses across the board. Factor analysis reveals that alignment behaves as a unified construct (analogous to the g-factor in cognitive research) with models scoring high on one category tending to score high on others. We publicly release the benchmark and an interactive leaderboard to support ongoing evaluation, with plans to expand scenarios in areas where we observe persistent weaknesses and to add new models as they are released.

Pruning is a practical approach to compress large language models (LLMs), but it can amplify text degeneration, especially repetition loops, even when perplexity and task accuracy remain largely unchanged. In this work, we present a token-level analysis of this failure mode by viewing decoding as a dynamical process that enters and persists in a small set of recurrent contexts. Our analysis decomposes degeneration into loop entry risk and loop persistence, and shows that persistence is controlled by the escape mass assigned to plausible alternatives within the token sampling set. Motivated by these findings, we propose two token-level guidance objectives for post-pruning fine-tuning. FOCUS reweights distillation toward high-confidence teacher regions to suppress leakage, while RePAIR uses onset-centered positive/negative continuation pairs with a margin loss to promote plausible alternatives and prevent early commitment to repetition loops. Experiments on open-ended continuation and instruction-based generation show that both methods consistently reduce repetition and improve generation quality.

Stochastic Variance Reduced Gradient (SVRG) and its variants aim to speed-up training by using gradient corrections. Originally proposed over a decade ago, these methods have never been connected to any Bayesian method at a fundamental level. Here, we fill this gap and derive surprising new connections of SVRG to a recently proposed Bayesian method called `posterior correction'. Our main contribution is to show that SVRG can be recovered as a special case of posterior-correction over isotropic-Gaussian posteriors. Novel extensions of SVRG are automatically obtained by using more flexible exponential-family posteriors. We derive two new such extensions by using Gaussian families: a Newton-like variant with novel Hessian corrections, and an Adam-like extension that scales to large problems. Our work is the first to connect SVRG to Bayes and use it to speed-up training.

Kleinberg and Mullainathan showed that language generation in the limit is always possible at the level of computability: given enough positive examples, a learner can eventually generate data indistinguishable from a target language. However, such existence results do not address feasibility. We study the sample complexity of language generation in the limit for several canonical classes of formal languages. Our results show that infeasibility already appears for context-free and regular languages, and persists even for strict subclasses such as locally threshold testable languages, as well as for incomparable classes such as non-erasing pattern languages, a well-studied class in the theory of language identification. Overall, our results establish a clear gap between the theoretical possibility of language generation in the limit and its computational feasibility.

Spiking Neural Networks (SNNs), with their event-driven and biologically inspired mechanisms, are well-suited for energy-efficient neuromorphic hardware. Neural coding, which is critical to SNNs, determines how information is represented via spikes. While Time-to-First-Spike (TTFS) coding uses a single spike per neuron to offer extreme sparsity and energy efficiency, it often suffers from unstable training and low accuracy due to its sparse firing. To address these challenges, we propose a training framework that incorporates parameter initialization, training normalization, a temporal output decoder, and a re-evaluation of the pooling layer. The proposed parameter initialization and training normalization mitigate signal diminishing and gradient vanishing, which helps stabilize training. Our output decoder aggregates temporal spikes to encourage earlier firing, thereby reducing latency. The re-evaluation of the pooling layer demonstrates that max-pooling violates single-spike constraints, which should be avoided, whereas average-pooling preserves them. Experiments show that our framework stabilizes and accelerates training, reduces latency, and achieves state-of-the-art accuracy for step-by-step TTFS SNNs on MNIST ($99.48\%$), Fashion-MNIST ($92.90\%$), CIFAR10 ($90.56\%$), CIFAR100 ($70.27\%$) and DVS Gesture ($95.83\%$).

Large language models excel at short-horizon reasoning tasks, but performance drops as reasoning horizon lengths increase. In this work, we introduce a scalable method to bootstrap long-horizon reasoning capabilities using only existing, abundant short-horizon data. Our approach synthetically composes simple problems into complex, multi-step dependency chains of arbitrary length. We train models on this data using outcome-only rewards under a curriculum that automatically increases in complexity, allowing RL training to be scaled much further without saturating. Empirically, our method generalizes remarkably well: curriculum training on composed 6th-grade level math problems improves accuracy on longer, competition-level benchmarks. It also transfers significantly to diverse out-of-distribution ReasoningGym domains and long-context benchmarks, indicating broader generalization. Importantly, our long-horizon improvements are significantly higher than baselines even at high pass@k, showing that models can learn new reasoning paths under RL. Theoretically, we show that curriculum RL with outcome rewards could achieve an exponential improvement in sample complexity over full-horizon training, providing training signal comparable to dense supervision. h1 therefore introduces an efficient path towards scaling RL for long-horizon problems using only existing data.

Modern decision-making increasingly relies on contextual features (covariates) to improve optimization under uncertainty. In practice, however, such covariates are often only partially observed due to, e.g., data source heterogeneity or costly data collection. Nonetheless, most existing methods assume fully observed historical data and can become unreliable when this assumption is violated. We address this gap by proposing a distributionally robust optimization approach that exploits incomplete covariates to produce robust decisions without imputing a complete dataset. Our method builds ambiguity sets from the observed partial data and incorporates the general structure of the missingness mechanism, ensuring candidate distributions remain consistent with what is observed. Across settings with discrete or continuous covariates and outcomes, we derive tractable reformulations and establish finite-sample out-of-sample performance guarantees. Empirical results across a range of contextual decision-making tasks demonstrate that the proposed integrated approach consistently outperforms state-of-the-art baselines, including various impute-then-optimize pipelines, in both out-of-sample performance and reliability.

Understanding why gradient-based training in deep networks exhibits strong implicit bias remains challenging, in part because tractable singular-value dynamics are typically available only for balanced deep linear models. We propose an alternative route based on two theoretically grounded and empirically testable signatures of deep Jacobians: depth-induced exponential scaling of ordered singular values and strong spectral separation. Adopting a fixed-gates view of piecewise-linear networks, where Jacobians reduce to products of masked linear maps within a single activation region, we prove the existence of Lyapunov exponents governing the top singular values at initialization, give closed-form expressions in a tractable masked model, and quantify finite-depth corrections. We further show that sufficiently strong separation forces singular-vector alignment in matrix products, yielding an approximately shared singular basis for intermediate Jacobians. Together, these results motivate an approximation regime in which singular-value dynamics become effectively decoupled, mirroring classical balanced deep-linear analyses without requiring balancing. Experiments in fixed-gates settings validate the predicted scaling, alignment, and resulting dynamics, supporting a mechanistic account of emergent low-rank Jacobian structure as a driver of implicit bias.

Although transformers are most commonly optimized as statistical sequence models, it is unclear to what extent they can implement and learn exact algorithmic computations. Here, we specify a transformer implementation from first principles that executes a fundamental and widely used method for $k$-means clustering: Lloyd's algorithm. We theoretically prove and empirically demonstrate that this implementation of a transformer architecture, which we term the _$k$-means transformer_, exactly implements Lloyd's algorithm for $k$-means clustering using the standard circuit mechanisms of modern transformers: attention block, residual connections, and feed-forward block. In learning experiments, we find that training this base architecture on $k$-means clustering yields a generalizable clustering algorithm that surpasses Lloyd's algorithm in terms of clustering quality. Finally, we demonstrate that interpretable alterations (e.g., inclusion of layer normalizations) to this architecture yields diverse and novel variants of clustering algorithms, including soft $k$-means, spherical $k$-means, trimmed $k$-means. Overall, our results show that transformer circuit mechanisms can instantiate exact algorithmic routines for clustering, while simultaneously providing an effective learnable model.

Supervised fine-tuning (SFT) is the standard approach for post-training large language models (LLMs), yet it often shows limited generalization. We trace this limitation to its default training objective: negative log likelihood (NLL). While NLL is classically optimal when training from scratch, post-training operates in a different paradigm and could violate its optimality assumptions, where models already encode task-relevant priors and supervision can be long and noisy. In this work, we systematically study various probability-based objectives and characterize when and why different objectives succeed or fail under varying conditions. Through comprehensive experiments and extensive ablation studies across 8 model backbones, 27 benchmarks, and 7 domains, we uncover a critical dimension that governs objective behavior: the model-capability continuum. Near the model-strong end, prior-leaning objectives that downweight low-probability tokens (e.g., $-p$, $-p^{10}$, thresholded variants) consistently outperform NLL; toward the model-weak end, NLL dominates; in between, no single objective prevails. Our theoretical analysis further elucidates how objectives trade places across the continuum, providing a principled foundation for adapting objectives to model capability. The code is available at https://github.com/GaotangLi/Beyond-Log-Likelihood.

The annealing phase is a pivotal convergence stage in LLM pre-training that ultimately determines final model quality. However, effectively selecting training data during this phase remains a key challenge. Current strategies rely on empirical heuristics, such as domain filtering or context extension, which lack a principled grounding in optimization theory. In this work, we characterize the annealing phase through the lens of the loss landscape's spectral geometry. We argue that optimal convergence requires gradient updates to satisfy heterogeneous constraints across different eigen-directions. Building on this insight, we formulate data selection as a problem of satisfying these directional constraints. To this end, we propose **DiReCT** (**Di**rectionally-**Re**strained **C**onstrained **T**raining), a novel framework that reformulates sample selection in the annealing stage as a constrained optimization problem. By imposing explicit directional constraints on per-sample gradients based on the spectral properties of the Hessian, **DiReCT** identifies samples that align with the optimal curvature-aware descent path. Extensive experiments across various model scales demonstrate that **DiReCT** consistently achieves state-of-the-art performance. For future research, code is available at https://github.com/xuyj233/Direct.

Being probabilistic models, during inference large language models (LLMs) display *rare events*: behaviour that is far from typical but highly significant. By definition all rare events are hard to see, but the enormous scale of LLM usage means that events completely unobserved during development are likely to become prominent in deployment. Here we present an end-to-end framework for the systematic analysis of rare events in LLMs. We provide a practical implementation spanning theory, efficient generation strategies, probability estimation and error analysis, which we illustrate with concrete examples. We outline extensions and applications to other models and contexts, highlighting the generality of the concepts and techniques presented here.

Vision-Language-Action (VLA) models often suffer from performance degradation under distribution shifts, as they struggle to learn generalized behavior representations across varying environments. While existing approaches attempt to construct behavior representations through action-centric latent variables, they are often limited by short-horizon temporal fragmentation and static execution-alignment, leading to inconsistent behaviors in complex scenarios. To address these limitations, we propose \textbf{BehaviorVLA}, a framework that facilitates robust manipulation through the learning of a temporally coherent behavioral representations. Our approach features two symmetric components: (1) the \textbf{Visuomotor Behavior Encoder (VBE)}, which utilizes a causal Mamba-based architecture to aggregate long-horizon trajectory information into a unified behavior representation; and (2) the \textbf{Phase-conditioned Behavior Decoder (PBD)}, which decodes this representation into precise actions by dynamically aligning task-level priors with real-time execution progress. Experiments on RoboTwin 2.0, LIBERO, and CALVIN demonstrate state-of-the-art success rates of 58\%, 98\%, and 4.36 (Avg.Len), respectively. Notably, in real-world sim-to-real transfer, BehaviorVLA matches the performance of OpenVLA-OFT using only 50\% of the demonstration data, showcasing its superior data efficiency and generalization.