AISTATS 2026 论文列表

To ensure high quality outputs, it is important to quantify the epistemic uncertainty of diffusion models. Existing methods are often unreliable because they mix epistemic and aleatoric uncertainty. We introduce a method based on Fisher information that explicitly isolates epistemic variance, producing more reliable plausibility scores for generated data. To make this approach scalable, we propose FLARE (Fisher-Laplace Randomized Estimator), which approximates the Fisher information using a uniformly random subset of model parameters. Empirically, FLARE improves uncertainty estimation in synthetic time-series generation tasks, achieving more accurate and reliable filtering than other methods. Theoretically, we bound the convergence rate of our randomized approximation and provide analytic and empirical evidence that last-layer Laplace approximations are insufficient for this task.

Masked diffusion models (MDMs) have emerged as a promising approach for language modeling, yet they face a performance gap compared to autoregressive models (ARMs) and require more training iterations. In this work, we present the Auto-Regressive Masked Diffusion (ARMD) model, an architecture designed to close this gap by unifying the training efficiency of autoregressive models with the parallel generation capabilities of diffusion-based models. Our key insight is to reframe the masked diffusion process as a block-wise causal model. This perspective allows us to design a strictly causal, permutation-equivariant architecture that computes all conditional probabilities across multiple denoising steps in a single, parallel forward pass. The resulting architecture supports efficient, autoregressive-style decoding and a progressive permutation training scheme, allowing the model to learn both canonical left-to-right and random token orderings. Leveraging this flexibility, we introduce a novel strided parallel generation strategy that accelerates inference by generating tokens in parallel streams while maintaining global coherence. Empirical results demonstrate that ARMD achieves state-of-the-art performance on standard language modeling benchmarks, outperforming established diffusion baselines while requiring significantly fewer training steps. Furthermore, it establishes a new benchmark for parallel text generation, effectively bridging the performance gap between parallel and sequential decoding.

Transformers have shown impressive results in tabular data generation. However, they lack domain-specific inductive biases which are critical for preserving the intrinsic characteristics of tabular data. They also suffer from poor scalability and efficiency due to quadratic computational complexity. In this paper, we propose TabTreeFormer, a hybrid transformer architecture that integrates inductive biases of tree-based models (e.g., non-smoothness and non-rotational invariance) to effectively handle the discrete and weakly correlated features in tabular datasets. To improve numerical fidelity and capture multimodal distributions, we introduce a novel tokenizer that learns token sequences based on the complexity of tabular values. This reduces vocabulary size and sequence length, yielding more compact and efficient representations without sacrificing performance. We evaluate TabTreeFormer on nine diverse datasets, benchmarking against eight generative models. We show that TabTreeFormer consistently outperforms baselines in utility, fidelity, and privacy metrics with competitive efficiency. Notably, in scenarios prioritizing data utility over privacy and efficiency, the best variant of TabTreeFormer delivers a 44

We study repeated bidding in multi-unit discriminatory (pay-as-bid) auctions for a single bidder with per-round utility equal to value minus α times payment, where α∈[0,1] is a cost-of-capital parameter. The bidder aims to maximize cumulative utility over T rounds subject to a total budget B. The problem is challenging even without budgets: the action space is exponential in the bidder’s maximum demand M, and the valuation vector (context) varies over time. Exploiting a decomposition of utility across units, we develop polynomial-time learning algorithms based on shortest paths in a directed acyclic graph, obtaining sublinear regret under both full-information and bandit feedback. In the bandit setting, the regret is independent of the number of contexts due to complete cross-learning: observing the utility of the chosen action under the realized context reveals the utility for the same action under all counterfactual contexts. With budget constraints, when the average normalized per-round budget ρ=B/MT<1, we design a coupled primal-dual algorithm in which the DAG-based procedure uses dual-adjusted edge weights for primal updates, while online gradient descent updates the dual variable, yielding ρ-approximate sublinear regret. Finally, we give implementations whose per-round time and space are independent of the number of contexts, enabling scalability to large or even infinite context spaces.

The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex M-estimation or stochastic optimization problem is solvable in such an assumption-free setting, providing a precise dividing line between solvable and unsolvable problems. The conditions we identify show that Lipschitz continuity of the loss being minimized is not necessary for distribution free minimization, and they are also distinct from classical characterizations of learnability in machine learning.

We study the piecewise-stationary restless multi-armed bandit (PS-RMAB) problem, where each arm evolves as a Markov chain but mean rewards may change across unknown segments. To address the resulting exploration–detection delay trade-off, we propose a modular framework that integrates arbitrary RMAB base algorithms with change detection and a novel diminishing exploration mechanism. This design enables flexible plug-and-play use of existing solvers and detectors, while efficiently adapting to mean changes without prior knowledge of their number. To evaluate performance, we introduce a refined regret notion that measures the excess regret due to exploration and detection, benchmarked against an oracle that restarts the base algorithm at the true change points. Under this metric, we prove a regret bound of Õ(√(LMKT)), where L denotes the maximum mixing time of the Markov chains across all arms and segments, M the number of segments, K the number of arms, and T the horizon. Simulations confirm that our framework achieves regret close to that of the segment oracle and consistently outperforms base solvers that do not incorporate any mechanism to handle environmental hanges.

Reinforcement Learning (RL) has achieved tremendous success in recent years. However, the classical foundations of RL do not account for the risk sensitivity of the objective function, which is critical in various fields, including healthcare, finance, etc. A popular approach to incorporate risk sensitivity is to optimize a specific quantile of the cumulative reward distribution. In this paper, we develop UCB-QRL, an optimistic learning algorithm for the τ-quantile objective in finite-horizon Markov decision processes (MDPs). UCB-QRL is an iterative algorithm in which, at each iteration, we first estimate the underlying transition probability and then optimize the quantile value function over a confidence ball around this estimate. Here, we show that UCB-QRL yields high-probability regret bounds 𝒪((2/κ)^HH√(SATHlog(2SATH/δ))) in the episodic setting with S states, A actions, T episodes, and H horizons. Here, κ>0 is a problem-dependent constant that captures the sensitivity of the underlying MDP’s quantile value.

Continual learning (CL) is concerned with learning multiple tasks sequentially without forgetting previously learned tasks. Despite substantial empirical advances over recent years, the theoretical development of CL remains in its infancy. At the heart of developing CL theory lies the challenge that the data distribution varies across tasks, and we argue that properly addressing this challenge requires understanding this variation–dependency among tasks. To explicitly model task dependency, we consider nonlinear regression tasks and propose the assumption that these tasks are dependent in such a way that the data of the current task is a nonlinear transformation of previous data. With this model and under natural assumptions, we prove statistical recovery guarantees (more specifically, bounds on estimation errors) for several CL paradigms in practical use, including experience replay with data-independent regularization and data-independent weights that balance the losses of tasks, replay with data-dependent weights, and continual learning with data-dependent regularization (e.g., knowledge distillation). To the best of our knowledge, our bounds are informative in cases where prior work gives vacuous bounds.

We study the problem of constructing Steiner Minimal Trees (SMTs) in hyperbolic space. Exact SMT computation is NP-hard, and existing hyperbolic heuristics such as HyperSteiner are deterministic and often get trapped in locally suboptimal configurations. We introduce Randomized HyperSteiner (RHS), a stochastic Delaunay triangulation heuristic that incorporates randomness into the expansion process and refines candidate trees via Riemannian gradient descent optimization. Experiments on synthetic data sets and a real-world single-cell transcriptomic data show that RHS outperforms Minimum Spanning Tree (MST), Neighbour Joining, and vanilla HyperSteiner (HS). In near-boundary configurations, RHS can achieve a 32

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the target data when learning the flow from a simple source distribution like the standard Gaussian. This leads to inefficient learning, especially for many high-dimensional real-world datasets, which often reside in a low-dimensional manifold. To this end, we present , which provides efficient training strategies by conditioning on the features extracted from data using pretrained deep latent variable models. Through experiments on synthetic data from multi-modal distributions and widely used image benchmark datasets, we show that exhibits improved generation quality with significantly less training and computation than state-of-the-art flow matching models by adopting pretrained lightweight latent variable models. Beyond natural images, we consider generative modeling of spatial fields stemming from physical processes. Using a 2d Darcy flow dataset, we demonstrate that our approach generates more physically accurate samples than competing approaches. In addition, through latent space analysis, we demonstrate that our approach can be used for conditional image generation conditioned on latent features, which adds interpretability to the generation process.

We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods—such as plug-in and batch-means estimators—are available, they either require inaccessible second-order (Hessian) information or suffer from slow convergence. To address these challenges, we propose a novel, fully online de-biased covariance estimator that eliminates the need for second-order derivatives while significantly improving estimation accuracy. Our method employs a bias-reduction technique to achieve a convergence rate of n^(α-1)/2√(log n), outperforming existing Hessian-free alternatives.

The Key–Value (KV) cache is central to the efficiency of transformer-based large language models (LLMs), storing previously computed vectors to accelerate inference. Yet, as sequence length and batch size grow, the cache becomes a major memory bottleneck. Prior compression methods typically apply low-rank decomposition to keys alone or attempt to jointly embed queries and keys, but both approaches neglect that attention fundamentally depends on their inner products. In this work, we prove that such strategies are sub-optimal for approximating the attention matrix. We introduce KQ-SVD, a simple and computationally efficient method that directly performs an optimal low-rank decomposition of the attention matrix via a closed-form solution. By targeting the true source of redundancy, KQ-SVD preserves attention outputs with higher fidelity under compression. Extensive evaluations on LLaMA and Mistral models demonstrate that our approach consistently delivers superior projection quality.

Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of 𝒪(ϵ^-2). Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.

Developing trustworthy Machine Learning (ML) models requires their predicted probabilities to be well-calibrated, meaning they should reflect true-class frequencies. Among calibration notions in multiclass classification, strong calibration is the most stringent, as it requires all predicted probabilities to be simultaneously calibrated across all classes. However, existing approaches to multiclass calibration lack a notion of distance among inputs, which makes them vulnerable to proximity bias: predictions in sparse regions of the feature space are systematically miscalibrated. In this work, we address this main shortcoming by introducing a local perspective on multiclass calibration. First, we formally define multiclass local calibration and establish its relationship with strong calibration. Second, we theoretically analyze the pitfalls of existing evaluation metrics when applied to multiclass local calibration. Third, we propose a practical method to enhance local calibration in Neural Networks, which enforces alignment between predicted probabilities and local estimates of class frequencies using the Jensen-Shannon distance. Finally, we empirically validate our approach against existing multiclass calibration techniques.

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as is the case with text data. Sequential Monte Carlo (SMC) methods give a natural way of representing and updating this uncertainty over time, but have prohibitive memory requirements for large-scale problems. We propose a novel SMC algorithm that decomposes clustering problems into approximately independent subproblems, allowing a more compact representation of the algorithm state. Our approach is motivated by the knowledge base construction problem, and we show that our method is able to accurately and efficiently solve clustering problems in this setting and others where traditional SMC struggles.

We introduce a black-box interpretability framework that learns a verifiable constitution: a natural language summary of how changes to a prompt affect a model’s specific behavior, such as its alignment, correctness, or adherence to constraints. Our method leverages atomic concept edits (ACEs), which are targeted operations that add, remove, or replace an interpretable concept in the input prompt. By systematically applying ACEs and observing the resulting effects on model behavior across various tasks, our framework learns a causal mapping from edits to predictable outcomes. This learned constitution provides deep, generalizable insights into the model. Empirically, we validate our approach across diverse tasks, including mathematical reasoning and text-to-image alignment, for controlling and understanding model behavior. We found that for text-to-image generation, GPT-Image tends to focus on grammatical adherence, while Imagen 4 prioritizes atmospheric coherence. In mathematical reasoning, distractor variables confuse GPT-5 but leave Gemini 2.5 models and o4-mini largely unaffected. Moreover, our results show that the learned constitutions are highly effective for controlling model behavior, achieving an average of 1.86 times boost in success rate over methods that do not use constitutions.

Probabilities of causation are valuable concepts for explainable artificial intelligence (XAI) and personalized decision-making. Pearl (2009) defined the probabilities of causation from the viewpoint of "necessity", "sufficiency", and "necessity and sufficiency" in the context of structural causal models. In addition, Tian and Pearl (2000) and Kuroki and Cai (2011) provided the identification conditions of the probabilities of causation under the monotonicity assumption. However, these identification conditions are described based on "the joint probabilities of observed random variables" and/or "causal risks" without selection biases. Thus, they are not applicable to studies in the presence of confounding and selection biases. To address this problem, this paper provides novel identification conditions for the probabilities of causation by using (i) two proxy covariates and (ii) an instrumental variable and a proxy covariate. When the probabilities of causation can be evaluated through the proposed identification conditions, new plug-in estimators for these probabilities are presented. Finally, we illustrate the application of our results on a real-world dataset.

Pooling is a core operation in convolutional neural networks (CNNs), enabling spatial reduction and hierarchical abstraction. However, standard methods such as max or average pooling operate locally and often fail to capture global context, leading to under- or over-estimation of features. This limits performance on tasks requiring both fine localization and holistic understanding. To address this, we propose Top-k

While clients may join federated learning to improve performance on data they rarely observe locally, they often remain self-interested, expecting the global model to perform well on their own data. This motivates an objective that ensures all clients achieve a similar loss gap—the difference in performance between the global model and the best model they could train using only their local data. To this end, we propose EAGLE, a novel federated learning algorithm that explicitly regularizes the global model to minimize disparities in loss gaps across clients. Our approach is particularly effective in heterogeneous settings, where clients’ optimal local models may be misaligned. Unlike existing methods that encourage loss parity, potentially degrading performance for many clients, EAGLE targets fairness in relative improvements. We provide theoretical convergence guarantees for EAGLE under non-convex loss functions, and characterize how its iterates perform relative to the standard federated learning objective using a novel heterogeneity measure. Empirically, we demonstrate that EAGLE reduces the disparity in loss gaps among clients by prioritizing those furthest from their local optimal loss, while maintaining competitive utility in both convex and non-convex cases compared to strong baselines.