ICML 2026 Papers

Tokenization is used almost universally by modern language models, enabling efficient text representation using multi-byte or multi-character tokens. However, prior work has shown that tokenization can introduce distortion into the model's generations, an issue known as the Prompt Boundary Problem (PBP). For example, users are often advised not to end their prompts with a space because it prevents the model from including the space as part of the next token. While this heuristic is effective in English, the underlying PBP continues to affect code generation and languages such as Chinese, where tokens often do not line up with word and syntactic boundaries. In this work, we present an inference-time method to convert any autoregressive LM with a BPE tokenizer into a character-level or byte-level LM. Our method efficiently solves the PBP and is also able to unify the vocabularies of language models with different tokenizers, allowing one to ensemble LMs with different tokenizers at inference time or transfer the post-training from one model to another using proxy-tuning.

Existing time series foundation models (TSFMs), often based on transformer variants, lack adaptability to different sampling rates, struggle with generalization across varying context and target lengths and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that achieves sampling-rate–equivariant forecasting through a unified design that pairs a state space model (SSM) encoder with a functional basis decoder (FBD). This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons without retraining. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being one of the smallest TSFMs, FlowState achieves state-of-the-art results on the widely used GIFT-Eval benchmark, while demonstrating superior adaptability to unseen sampling rates. Our detailed analyses confirm the effectiveness of its components, and we demonstrate its unique ability to adapt to varying input sampling rates.

Messages embedded in diffusion generation noise suffer from severe attenuation due to denoising and VAE decoding, creating a persistent capacity–robustness trade-off. Identifying that extraction accuracy strictly correlates with the distance between candidate hypothesis images, we propose ASIR, a training-free and provably secure steganography framework for both pixel and latent diffusion models. ASIR introduces two key innovations: (i) Antipodal Sampling, which maximizes signal separation in probability space to enhance distinguishability, and (ii) Iterative Recovery, a paradigm shift that treats extraction as a gradient-based optimization problem to reverse non-linear distortions. Extensive experiments demonstrate that ASIR achieves state-of-the-art performance, embedding up to 65,536 bits (pixel-space) and 16,384 bits (latent-space) with 99\% accuracy, while remaining statistically undetectable to deep steganalyzers.

Designing sampling algorithms for multimodal targets that remain stable under refinement of the finite-dimensional approximation of an underlying function-space problem is a central challenge. Annealed Langevin dynamics (ALD) is a natural alternative to classical Langevin in this context, since it is often observed to improve exploration across modes. Yet a gap remains between its empirical success and existing theory: under which conditions can ALD be guaranteed to remain stable across dimensions? In this paper, we bridge this gap by providing a uniform-in-dimension analysis of continuous-time ALD for Gaussian-mixture targets. Along an explicit annealing path obtained by gradually removing Gaussian smoothing from the target, we identify spectral conditions linking the smoothing covariance to the component covariances under which ALD achieves a prescribed accuracy in Kullback-Leibler divergence within a dimension-uniform time horizon. We then establish stability in a perturbative regime with imperfect initialization and approximate scores. Under a misspecified-mixture score model, we show that preconditioning ALD with an operator whose spectrum decays sufficiently fast prevents error terms from accumulating across coordinates and thereby preserves dimension-uniform control.

We study the problems of approximate sampling from and distribution testing of \emph{mixture models}, where the modes satisfy a functional inequality called \emph{approximate tensorization of entropy} (ATE). While it is known that ATE makes these tasks more efficient in the unimodal setting, mixtures of few distributions satisfying ATE do not necessarily satisfy ATE overall, leading to a lack of theoretical guarantees for multimodal distributions, which are a key challenging case of modern generative models. We show this gap can be overcome by establishing the following pair of results for mixtures of ATE distributions: 1) We show fast mixing of Glauber dynamics from a \emph{data-based initialization}, with \emph{optimal} sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities, building on similar results in (Koehler et al., 2024, Huang et al., 2024) for mixtures satisfying the weaker Poincaré inequality. 2) Answering an open question from (Blanca et al., 2023), we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.

How can we generate samples from a conditional distribution that we never fully observe? This question arises across a broad range of applications in both modern machine learning and classical statistics, including image post-processing in computer vision, approximate posterior sampling in simulation-based inference, and conditional distribution modeling in complex data settings. In such settings, compared with unconditional sampling, additional feature information can be leveraged to enable more adaptive and efficient sampling. Building on this, we introduce Conditional Generator using MMD (CGMMD), a novel framework for conditional sampling. Unlike many contemporary approaches, our method frames the training objective as a simple, adversary-free direct minimization problem. A key feature of CGMMD is its ability to produce conditional samples in a single forward pass of the generator, enabling practical one-shot sampling with low test-time complexity. We establish rigorous theoretical bounds on the loss incurred when sampling from the CGMMD sampler, and prove convergence of the estimated distribution to the true conditional distribution. In the process, we also develop a uniform concentration result for nearest-neighbor based functionals, which may be of independent interest. Finally, we show that CGMMD performs competitively on synthetic tasks involving complex conditional densities, as well as on practical applications such as image denoising and image super-resolution.

We study a sampling problem whose target distribution is $\pi \propto \exp(-f-r)$ where the data fidelity term $f$ is Lipschitz smooth while the regularizer term $r=r_1-r_2$ is a non-smooth difference-of-convex (DC) function, i.e., $r_1,r_2$ are convex. By leveraging the DC structure of $r$, we can smooth out $r$ by applying Moreau envelopes to $r_1$ and $r_2$ separately. In line with DC programming, we then redistribute the concave part of the regularizer to the data fidelity and study its corresponding proximal Langevin algorithm (termed DC-LA). We establish convergence of DC-LA to the target distribution $\pi$, up to discretization and smoothing errors, in the $q$-Wasserstein distance for all $q \in \mathbb{N}^*$, under the assumption that $V$ is distant dissipative. Our results improve previous work on non-log-concave sampling in terms of a more general framework and assumptions. Numerical experiments show that DC-LA produces accurate distributions in synthetic settings and provides qualitatively reasonable uncertainty quantification in a real-world Computed Tomography application.

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but possibly nonsmooth objective function. To deal with the constraints that are not easy to project on, we use a randomized feasibility algorithm with Polyak steps and a random number of sampled constraints per iteration, while taking (sub)gradient steps to minimize the objective function. For case (i), we prove linear convergence in expectation of the objective function values to any prescribed tolerance using an adaptive stepsize. For case (ii), we develop a fully problem parameter-free and adaptive stepsize scheme that yields an $O(1/\sqrt{T})$ worst-case rate in expectation. The infeasibility of the iterates decreases geometrically with the number of feasibility updates almost surely, while for the averaged iterates, we establish an expected lower bound on the function values relative to the optimal value that depends on the distribution for the random number of sampled constraints. For certain choices of sample-size growth, optimal rates are achieved. Finally, simulations on a Quadratically Constrained Quadratic Programming (QCQP) problem, Support Vector Machines (SVM), and logistic regression with group fairness constraints demonstrate the computational efficiency of our algorithm compared to other state-of-the-art methods.

The forest matrix of a signed graph plays an important role in network science and social opinion dynamics, yet existing algorithms are mainly designed for unsigned graphs and are difficult to extend to signed graphs. In this paper, we study the problem of efficiently estimating the forest matrix of signed graphs with \(n\) nodes and introduce the signed forest matrix theorem, which establishes the relationship between generalized spanning converging forests and the forest matrix. Based on this result, we propose a novel algorithm \textsc{GSCF}, built on a variant of loop-erased random walks, to generate generalized spanning converging forests in expected \(O(n)\) time. We further develop two sampling algorithms, \textsc{FMDE} and \textsc{FMDE+}, for estimating the diagonal of the forest matrix, both with time complexity \(O(ln)\), where \(l\) is the number of samples. Extensive experiments on various signed graphs show that our methods achieve high estimation accuracy, significantly improve computational efficiency, and scale to graphs with over twenty million nodes. Our source code is publicly available on \url{https://github.com/HaoxinSun98/SignedForestDiagonal}.

Sampling from distributions with bounded supports is a fundamental challenge in constrained statistical inference. Reflective Hamiltonian Monte Carlo (ReHMC) provides a useful sampling approach for this setting. However, it relies on convexity assumptions on the support and lacks non-asymptotic theoretical guarantees such as mixing-time bounds. To bridge this gap, we propose a convex-container plus thinning framework that is applicable to arbitrary target densities with bounded support. We establish the first non-asymptotic total-variation mixing-time bounds for ReHMC, achieving a polynomial dimension dependence of $O(d^2)$ for $L$-smooth targets, though with exponential dependence on smoothness parameters. Under an additional $m$-strong convexity assumption, we derive a sharper bound that eliminates this exponential dependence. We further apply this approach to sampling on the Stiefel manifold via a well-conditioned polar reparameterization and demonstrate improved numerical stability and sampling efficiency in simulation studies.