ICML 2026 论文列表

Token attribution methods provide intuitive explanations for language model outputs by identifying causally important input tokens. However, as modern LLMs increasingly rely on extended reasoning chains, existing schemes face two critical challenges: (1) efficiency bottleneck, where attributing a target span of $M$ tokens within a context of length $N$ requires $\mathcal{O}(M \cdot N)$ operations, making long-context attribution prohibitively slow; and (2) faithfulness drop, where intermediate reasoning tokens absorb attribution mass, preventing importance from propagating back to the original input. To address these, we introduce FlashTrace, an efficient multi-token attribution method that employs span-wise aggregation to compute attribution over multi-token targets in a single pass, while maintaining faithfulness. Moreover, we design a recursive attribution mechanism that traces importance through intermediate reasoning chains back to source inputs. Extensive experiments on long-context retrieval (RULER) and multi-step reasoning (MATH, MorehopQA) tasks demonstrate that FlashTrace achieves over $130\times$ speedup over existing baselines while maintaining superior faithfulness. We further analyze the dynamics of recursive attribution, showing that even a single recursive hop improves faithfulness by tracing importance through the reasoning chain.

High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension. We propose **Riemannian metric matching**: a denoising probabilistic framework for learning the Riemannian geometry of data using neural networks. Specifically, we learn the *carré du champ* operator, which, using diffusion geometry, gives us access to the Riemannian geometry toolkit for downstream machine learning and statistical tasks. Our key observation is that the carré du champ operator can be formulated as a conditional expectation over random perturbations of the data, which can be exploited for sample-wise training and constant cost, amortized inference without explicit kernel construction. Empirically, metric matching rivals or improves the accuracy of $k$-NN-based diffusion geometry estimators, while enabling amortized inference that is up to $400\times$ faster, and supports graph-free geometric analysis on high-dimensional images where nearest neighbors break down.

MoE-PEFT methods combine Mixture of Experts with parameter-efficient fine-tuning for multi-task adaptation, but require separate adapters per expert—causing trainable parameters to scale linearly with expert count and limiting applicability to adapter-based architectures. We propose LiME (Lightweight Mixture of Experts), which achieves expert specialization through lightweight modulation rather than adapter replication. Instead of separate adapters, LiME uses a single shared PEFT module and modulates its output with lightweight expert vectors, reducing expert parameters while generalizing to any PEFT method. Notably, LiME introduces zero-parameter routing by leveraging existing frozen and adapted representations—eliminating learned router parameters typically required per layer. Theoretically, we prove that (i) more experts preserve more task-relevant information and (ii) modulation approximates full expert-specific PEFT with bounded error. LiME further incorporates n-gram windowed routing and adaptive expert selection (Auto Top-K) based on routing confidence. Experiments on MMT-47, a multimodal multi-task benchmark with 47 tasks spanning text, image, and video, demonstrate that LiME achieves competitive or superior performance while using up to 4× fewer trainable parameters and up to 29% faster training compared to corresponding MoE-PEFT baselines.

Understanding when learning is statistically possible yet computationally hard is a central challenge in high-dimensional statistics. In this work, we investigate this question in the context of single- and multi-index models, classes of functions widely studied as benchmarks to probe the ability of machine learning methods to discover features in high-dimensional data. Our main contribution is to show that a Noise Sensitivity Exponent (NSE)—a simple quantity determined by the activation function—governs the existence and magnitude of statistical-to-computational gaps within a broad regime of these models. We first establish that, in single-index models with large additive noise, the onset of a computational bottleneck is fully characterized by the NSE. We then demonstrate that the same exponent controls a statistical-computational gap in the specialization transition of large separable multi-index models, where individual components become learnable. Taken together, our results identify the NSE as a unifying property linking noise robustness, computational hardness, and feature specialization in high-dimensional learning.

For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems ($4 \leq d \lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems ($d\gg 10$), spectral methods suffer frome the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. Recently proposed spectral-informed neural networks (SINNs) combine spectral methods with PINNs, operating directly in the spectral domain to avoid spatial derivative computations and to reduce memory consumption. In this work, we introduce Modified SINNs, which integrate coefficient decay scaling and basis embeddings motivated by harmonic analysis to enhance accuracy in high-dimensional problems and enable accurate approximation of unknown spectral coefficients. Numerical experiments on steady and time-dependent partial differential equations demonstrate that Modified SINNs outperform sparse grid spectral methods on middle-dimensional problems with incomplete spectral information and achieve superior accuracy compared to PINNs on high-dimensional problems.

Training 3D Gaussian Splatting (3DGS) at billion-primitive scale is fundamentally memory-bound: each Gaussian primitive carries a large attribute vector, and the aggregate parameter table quickly exceeds GPU capacity, limiting prior systems to tens of millions of Gaussians on commodity single-GPU hardware. We observe that 3DGS training is inherently sparse and trajectory-conditioned: each iteration activates only the Gaussians visible from the current camera batch, so GPU memory can serve as a working-set cache rather than a persistent parameter store. Building on this insight, we introduce TideGS, an out-of-core training framework that manages parameters across an SSD-CPU-GPU hierarchy via three synergistic techniques: block-virtualized geometry for SSD-aligned spatial locality, a hierarchical asynchronous pipeline to overlap I/O with computation, and trajectory-adaptive differential streaming that transfers only incremental working-set deltas between iterations. Experiments show that TideGS enables training with over one billion Gaussians on a single 24-GB GPU while achieving the best reconstruction quality among evaluated single-GPU baselines on large-scale scenes, scaling beyond prior out-of-core baselines (e.g., ~100M Gaussians) and standard in-memory training (e.g., ~11M Gaussians). Project page: https://sponge-lab.github.io/TideGS/

Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data toward a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn serves as a stepping stone to efficiently learn rare long-tailed skills. Our results offer an alternative perspective on what constitutes an effective data distribution for training models.

Optimal-transport distributionally robust optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline consists of a two-step procedure, where the ambiguity set is first designed and subsequently embedded into the downstream OT-DRO problem. However, this separation between uncertainty quantification and optimization may lead to excessive conservatism. We introduce an end-to-end pipeline to automatically learn decision-focused ambiguity sets for OT-DRO problems, where the loss function informs the shape of the ambiguity set, leading to less conservative decisions whose distributional robustness is enforced via data-driven bootstrapping. We formulate the learning problem as a bilevel optimization program and solve it via a hypergradient-based method. By leveraging the recently introduced nonsmooth conservative implicit function theorem, we establish convergence to a critical point of the bilevel problem. We present experiments validating our method on standard portfolio optimization and linear regression tasks.

Multi-fidelity (MF) regression often operates in regimes of extreme data imbalance, where the commonly-used Gaussian-process surrogates struggle with cubic scaling costs and overfit to sparse high-fidelity observations, limiting efficiency and generalization in real-world applications. We introduce FIRE, a training-free MF framework that couples tabular foundation models (TFMs) to perform zero-shot in-context Bayesian inference via a high-fidelity correction model conditioned on the low-fidelity model's posterior predictive distributions. This cross-fidelity information transfer via distributional summaries captures heteroscedastic errors, enabling robust residual learning without model retraining. Across 31 benchmark problems spanning synthetic functions and real-world tasks (e.g., DrivAerNet, LCBench), FIRE delivers a stronger performance–time trade-off than seven state-of-the-art GP-based or deep learning MF regression methods, ranking highest in accuracy and uncertainty quantification with runtime advantages. Limitations include context window constraints and dependence on the quality of the pre-trained TFMs. Code & data can be found here: https://github.com/rosenyu304/FIRE.

Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the likelihood of harmful model outputs. However, when models are queried billions of times in a day, even rare worst-case behaviors will occur. Current safety evaluations focus on capturing the distribution of inputs that yield harmful outputs. These evaluations disregard the probabilistic nature of models and their tail output behavior. To measure this tail risk, we propose a method to efficiently estimate the probability of harmful outputs for any input query. Instead of naive brute-force sampling from the target model, where harmful outputs could be rare, we operationalize importance sampling by creating unsafe versions of the target model. These unsafe versions enable sample-efficient estimation by making harmful outputs more probable. On benchmarks measuring misuse and misalignment, these estimates match brute-force Monte Carlo estimates using 10–20× fewer samples. For example, we can estimate probability of harmful outputs on the order of $10^{−4}$ with just 500 samples. Additionally, we find that these harmfulness estimates can reveal the sensitivity of models to perturbations in model input and predict deployment risks. Our work demonstrates that rare-event estimation is both critical and feasible for safety evaluations.

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically constrain their task predictor to a single expression whose functional form is set a priori, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of expressions, referred to as experts, employed by the task predictor to map concepts to the task, and the functional form each expression takes, thus exposing an underexplored region of this design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data subject to user-specified operator vocabularies. Empirical evaluation demonstrates that varying the number of expressions and their functional form provides a robust framework for navigating the accuracy-interpretability trade-off.

We study the computational cost of differential privacy in terms of memory efficiency. Specifically, we establish for the first time an unconditional space lower bound for user-level differential privacy by introducing a novel proof technique based on a multi-player communication game. We apply our framework, as an example, to the fundamental problem of estimating the number of distinct elements in a stream: we prove that any private algorithm requires almost $\widetilde{\Omega}(T^{1/3})$ space (where $T$ denotes the length of the stream) to achieve certain error rates in a promise variant of the problem, resolving an open problem in the literature (by Jain et al. 2023 and Cummings et al. 2025) and establishes the first exponential separation between the space complexity of private algorithms and their non-private $\widetilde{O}(1)$ counterparts for a natural statistical estimation task. Furthermore, we show that this communication-theoretic technique generalizes to broad classes of problems, yielding lower bounds for private medians, quantiles, and max-select.

Monte Carlo Tree Search (MCTS) scales poorly in cooperative multi-agent domains because expansion must consider an exponentially large set of joint actions, severely limiting exploration under realistic search budgets. We propose \textsc{NonZero}, which keeps multi-agent MCTS tractable by running surrogate-guided selection over a low-dimensional nonlinear representation using an interaction-guided proposal rule, instead of directly exploring the full joint-action space. Our exploration uses an interaction score: single-agent deviations are ranked by predicted gain, while two-agent deviations are scored by a mixed-difference measure that reveals coordination benefits even when no single agent can improve alone. We formalize candidate proposal as a bandit problem over local deviations and derive a proposal rule, \textsc{NonUCT}, with a sublinear local-regret guarantee for reaching approximate graph-local optima without enumerating the joint-action space. Empirically, \textsc{NonZero} improves sample efficiency and final performance on MatGame, SMAC, and SMACv2 relative to strong model-based and model-free baselines under matched search budgets.

While on-policy distillation offers dense supervision for training small reasoning models, its optimization dynamics in the multimodal domain remain under-explored. In this work, we challenge the standard monolithic view of Vision-Language Model (VLM) distillation by mathematically decomposing the loss into two distinct components: the language prior and visual grounding. Our analysis uncovers that gradient vectors for these components are nearly orthogonal, indicating that the objective of aligning with the teacher's language distribution is geometrically independent from the objective of matching its visual perception. Consequently, standard optimization passively follows a suboptimal compromise trajectory that implicitly balances the two objectives. Hypothesizing that visual grounding constitutes the primary bottleneck for vision-language reasoning, we introduce Visual Gradient Steering (VGS), a method that dynamically reorients the update vector to prioritize the visual subspace. Experimental results on multiple distillation settings and complex multimodal benchmarks demonstrate that VGS significantly outperforms the standard monolithic formulation of on-policy distillation, achieving superior grounding with minimal training overhead.

Solving complex geometric problems inherently requires interleaved reasoning: a tight alternation between constructing diagrams and performing logical deductions. Although recent Multimodal Large Language Models (MLLMs) have demonstrated strong capabilities in visual generation and plotting, we identify a counter-intuitive and underexplored phenomenon. Naively applying Supervised Fine-Tuning (SFT) on interleaved plot–solution data leads to a substantial degradation in reasoning performance compared to text-only baselines. We argue that this failure stems from a fundamental limitation of SFT, which primarily induces distributional alignment: the model learns to reproduce the surface format of interleaved plotting but fails to internalize the causal dependency between the generated plot and reasoning steps. To overcome this limitation, we propose Faire (**F**unctional **a**lignment for **i**nterleaved **re**asoning), a reinforcement learning framework that enforces three casual constraints to move beyond superficial imitation toward functional alignment. Extensive experiments show that Faire induces a qualitative shift in model behavior in which the plotting is effectively internalized, yielding competitive performance on challenging geometric reasoning benchmarks.

Recent progress in large-scale robotic datasets and vision-language models (VLMs) has advanced research on vision-language-action (VLA) models. However, existing VLA models still face two fundamental challenges: (\textit{i}) producing precise low-level actions from high-dimensional observations, (\textit{ii}) bridging domain gaps across heterogeneous data sources, including diverse robot embodiments and human demonstrations. Existing methods often encode latent variables from either visual dynamics or robotic actions to guide policy learning, but they fail to fully exploit the complementary multi-modal knowledge present in large-scale, heterogeneous datasets. In this work, we present \textbf{XR-1}, a novel framework for versatile and scalable VLA learning across diverse robots, tasks, and environments. At its core, XR-1 introduces the \emph{Unified Vision-Motion Codes (UVMC)}, a discrete latent representation learned via a dual-branch VQ-VAE that jointly encodes visual dynamics and robotic motion. UVMC addresses these challenges by (\textit{i}) serving as an intermediate representation between the observations and actions, and (\textit{ii}) aligning multimodal dynamic information from heterogeneous data sources to capture complementary knowledge. To effectively exploit UVMC, we propose a \emph{three-stage training paradigm}: (\textit{i}) self-supervised UVMC learning, (\textit{ii}) UVMC-guided pretraining on large-scale cross-embodiment robotic datasets, and (\textit{iii}) task-specific post-training. We validate XR-1 through extensive real-world experiments with more than 12,000 rollouts on six different robot embodiments, spanning over 120 diverse manipulation tasks. XR-1 consistently outperforms state-of-the-art baselines such as $\pi_0$ and GR00T-N1.5 while demonstrating strong generalization to novel objects, background variations, distractors, and illumination changes. Our project is at \href{https://xr-1-vla.github.io/}{https://xr-1-vla.github.io/}.

The rapid evolution of generative models has unlocked new potentials in protein binder design, a pivotal task in structural biology, by facilitating end-to-end generation via joint sequence-structure modeling or hallucination. However, existing approaches are predominantly implemented under a single-target, single-state assumption, limiting their ability to model multi-target or multi-state interactions required for advanced function-oriented protein design. Here, we introduce Chamaileon, which unifies multi-target and multi-state binder design by formulating the problem as cross-context binding landscape modeling. The framework is underpinned by a training paradigm termed \textit{In-Context Complex Co-Design (I3CD)} for context-aware sequence-structure co-modeling. During inference, we employ \textit{Mixture-of-Paths Sampling (MoPS)}, a scalable strategy that optimizes a single sequence across contexts while alleviating the scarcity of high-quality multi-conformational paired data. Extensive evaluation on our newly constructed benchmark, \textit{CROSS}, demonstrates that Chamaileon effectively generates sequences adaptable to diverse conformational landscapes and multi-target requirements.

When a learner faces a new task with few samples, it must leverage any available side information. In practice, this often comes in the form of model evaluations on related tasks in public benchmarks. A key question then is how to model task relatedness such that it is both realistic and the benchmark evaluations lead to provable gains. Empirically, we observe that *weak monotonicity* is often approximately satisfied: if a model dominates another on many benchmarks, it also tends to outperform on the new task. We explore the statistical complexity of learning under (approximate) weak monotonicity, leveraging it within two learning paradigms: transfer learning and model selection aggregation. We show that not only can we prune the model class based on monotonicity, but we can also further adapt to the geometry of the available trade-offs by *hedging on the frontier*.

We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS (Sheffet, 2017), they are typically viewed as less competitive than the Adaptive Sufficient Statistics Perturbation (AdaSSP) method (Wang, 2018), which directly perturbs the sufficient statistics $(X^{\top}X, X^{\top}Y)$. This method was shown to be close to information-theoretically optimal, while also exhibiting strong empirical performance. In this work, we propose \emph{Iterative Hessian Mixing} (IHM), an algorithm that builds on Gaussian-sketching approaches to DP-OLS and is inspired by the Iterative Hessian Sketch (Pilanci & Wainwright, 2016). We prove that IHM is differentially private and provide utility guarantees in the form of excess empirical risk bounds. These bounds improve upon those of AdaSSP by removing a multiplicative factor that can be as large as the square root of the data dimension. The design of the IHM is based on new accuracy guarantees that we present for prior Gaussian sketching approaches for DP-OLS, which clarify when these methods are expected to perform well and how IHM circumvents their inherent limitations. We also conduct a rigorous empirical evaluation on a large suite of datasets, demonstrating that IHM consistently outperforms prior baselines, including AdaSSP.