An ODE-based Sampler for Discrete Diffusion Models
Samson Gourevitch, Yazid Janati, Eric Moulines, Eric P. Xing, Alain Durmus, Giacomo Zanella
AI 速览：作者提出指数残差流（ERFs），为离散扩散模型构造类似概率流ODE的确定性采样框架，并证明其保持原扩散的边缘分布。
The marginals of a continuous diffusion model can be reproduced by a deterministic ordinary differential equation (ODE), known as the probability flow ODE, which provides a foundation for accelerated sampling and consistency distillation. In this paper we address the question whether an analogous formulation exists for discrete diffusion models and answer it affirmatively by introducing exponential residual flows (ERFs). Our framework augments the discrete state with a continuous residual variable for each token and position. These residuals evolve deterministically according to piecewise-defined ODEs whose vector fields depend on the current discrete state and the forward and backward rate matrices of the prescribed diffusion model. The discrete state changes whenever a residual reaches zero. We prove that this construction preserves the marginals of the original diffusion. We derive a practical discretization of our sampler and specialize it to masked and uniform diffusion. The deterministic trajectories of ERFs support consistency distillation and yield empirical improvements over previous approaches across a variety of benchmarks including code and text generation tasks.
Self-regularization and structural adaptation of NPMLE for Gaussian mixture models in all dimensions
Yanjun Han, Yandi Shen, Yihong Wu
AI 速览：作者证明：均值位于超立方体内的 d 维高斯混合模型，其 NPMLE 能以高概率自动拟合出 O((log n/log log n)^d) 个分量，并在有限混合数据下使拟合分量数依概率有界。
We establish structural properties of the nonparametric maximum likelihood estimator (NPMLE) for $d$-dimensional Gaussian mixtures whose means lie in a hypercube. We show that, with high probability, the NPMLE based on $n$ independent observations self-regularizes by fitting a mixture model with $O((\frac{\log n}{\log\log n})^d)$ components, achieving the optimal model complexity without explicit model selection. Furthermore, the NPMLE exhibits a structural adaptation property: For data drawn from a finite mixture, the number of fitted components is bounded in probability as $n\to\infty$. Our proof applies a multivariate Jensen-type bound to control the typical number of critical points of the KKT function associated with the first-order optimality conditions. The key step is to lower bound its gradient norm uniformly on complex spheres. We establish this lower bound by decomposing the KKT function into an empirical fluctuation term and a relative density estimation error term, combining small-ball probability estimates for the former with polynomial approximation and Hellinger error bounds for the latter.
Numerical Integration on Bounded Domains via Learned Reflected Diffusions
Kirill Korolev, Artur Goldman, Timofei Gritsaev, Tigran Ramazyan, Nikita Morozov
AI 速览：提出用反射扩散构造满足有界凸域约束的重要性采样提议分布，并训练神经得分模型逆转该过程以估计积分 Z。
We study high-dimensional integration on bounded convex domains. Given a non-negative integrand $r$, the goal is to estimate $Z=\int_{D}r(x)\,\mathrm dx$ on $D\subset\mathbb R^d$. Standard Quasi-Monte Carlo does not adapt its evaluation points to the integrand, while effective importance sampling requires a proposal that captures its concentration. Learned diffusion samplers can supply such a proposal, but existing methods are formulated on $\mathbb R^d$ and do not respect the domain constraint $x\in D$. We instead build the proposal from reflected dynamics that stay in $D$ by construction. A reflected diffusion progressively transforms the target distribution toward the uniform distribution on $D$, and a neural score model is trained to reverse this process. A change-of-measure formula for reflected diffusions yields a training objective without additional boundary terms and an unbiased importance-sampling estimator of $Z$. For non-smooth integrands, where reparameterization gradients may be undefined or uninformative, we derive a REINFORCE estimator of the training gradient using Gaussian proposal densities before reflection, without evaluating reflected transition densities or differentiating $r$. We evaluate on numerous synthetic targets and real-world problems, demonstrating strong performance of the proposed method, as well as favorable scaling with the dimension of the problem and the number of points used for the Monte Carlo estimate.
Rural Readiness: Domain Generalization with Adversarially Chosen Domains
Cynthia Dwork, Andisheh Ghasemi, Lunjia Hu
AI 速览：研究在源域由对抗性选择时，域泛化目标的样本复杂度，并发现允许模型与在99%源域上表现良好的假设竞争可显著降低样本需求。
Predictive models trained at well-resourced data-rich institutions often fail when deployed in new populations. Motivated by the goal of building clinical diagnosis and decision-making algorithms for data-scarce rural populations using the general knowledge learned from data-rich hospitals, we formulate the fundamental question of \emph{domain generalization with adversarially chosen domains}, which asks a learner to perform on any unseen target domain nearly as well as the worst hypothesis consistent with the evidence from the observed source domains. Assuming only that the hypothesis class contains a "universal" predictor with small error on all $k$ source domains, we characterize the sample complexity of this objective up to logarithmic factors. Letting $d$ denote the VC dimension of the hypothesis class, we find, somewhat surprisingly, that the sample complexity reduces significantly from $Ω(dk)$ to $O(d)$ under a small relaxation of the learning goal in which, roughly speaking, we allow the learned model to compete with hypotheses that perform well on 99% instead of 100% of the source domains. By applying this insight to the meta-distributional setting, in which source domains are selected according to a distribution on distributions, we obtain a corresponding improvement over known sample complexity upper bounds. We also study the effect of data access to the target domain and show that a small labeled sample from the target domain does not improve the worst-case sample complexity on the source domains.
Albert Gong, Annabelle Michael Carrell, Raaz Dwivedi, Lester Mackey
AI 速览：提出 Express 工具，将非因果注意力近似转化为因果近似，并结合 Thinformer 实现更优的因果注意力保证与高效实现。
We introduce a new tool, Express, for converting a non-causal attention approximation into a causal approximation with matching approximation guarantees. When combined with the state-of-the-art Thinformer approximation, Express improves upon the best known causal attention guarantees, delivering $\log^{3/2}(n)/s$ approximation error with only $O(s)$ memory and $O(s^2 \log^2(n))$ compression overhead for a sequence of length $n$. We pair these developments with an efficient I/O-aware Triton implementation, demonstrate substantial speedups over FlashAttention 2, and use Express to overcome four resource bottlenecks in the language modeling pipeline: long-context prefill, KV cache compression, long-form memory-constrained decoding, and long-form compute-constrained decoding.
From Many Models, One: Macroeconomic Forecasting with Reservoir Ensembles
Giovanni Ballarin, Lyudmila Grigoryeva, Yui Ching Li
AI 速览：该论文研究在线聚合算法（FTL与Hedge类）用于多频率回声状态网络（MFESN）集成，以提升美国季度GDP增长的宏观预测。
Model combination offers an alternative to selecting a single forecasting model, particularly when individual models are sensitive to random initialization and hyperparameter choices. We study online aggregation through Follow-the-Leader (FTL) and Hedge-type algorithms, with an application to ensembles of Multi-Frequency Echo State Networks (MFESNs) for macroeconomic forecasting. On the theoretical side, we derive Hoeffding- and Bernstein-type expected-regret bounds for FTL and decreasing Hedge under independent and $\varphi$-mixing expert losses. Under a positive gap between the best expert's expected loss and those of its competitors, the bounds are uniform in the number of forecasting rounds and exhibit logarithmic dependence on the number of experts. Monte Carlo experiments investigate the effects of temporal dependence and the separation between experts' expected losses. Empirically, we construct MFESN ensembles for forecasting U.S. quarterly GDP growth using mixed-frequency macroeconomic and financial indicators. The results show that adaptive aggregation, particularly FTL and AdaHedge, achieves substantial reductions in out-of-sample mean squared forecasting error relative to individual MFESN models and conventional forecast combinations.
Finite-Sample LTI System Identification from a Misspecified Finite Model Set
Nicolas Chatzikiriakos, Andrea Iannelli
AI 速览：研究真实LTI系统不在有限假设类内时，有限样本辨识的估计目标、失败概率下界及指数加权算法的鲁棒性上界。
We consider the problem of finite-sample identification of an unknown LTI system from a finite hypothesis class. In contrast to existing results that assume the hypothesis class contains the true system, we consider the misspecified setting, where the true system does not belong to the hypothesis class. We first characterize the resulting estimation target and its dependence on the data-generation scheme. We then establish a finite-sample lower bound on the failure probability that any identification algorithm must incur. Finally, we analyze the robustness of an existing exponential weighting-based identification algorithm to the misspecification and derive a finite-sample upper bound on its failure probability. Our results illustrate when using a misspecified finite hypothesis class can provide an advantage over identification without prior knowledge of the candidate systems.
Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
Lorenzo Tedesco, Francesco Finazzi
AI 速览：提出让大语言模型智能体根据样本自动选择条件分布模型并输出拟合程序，从而估计条件密度的方法（ADR）。
Artificial intelligence offers statisticians a new paradigm for modelling and analysing complex datasets. Agents based on large language models can reason about data and automate key stages of the statistical modelling workflow, from model fitting to validation. In this paper we propose a method that uses such an agent to estimate the conditional density of a response given a vector of covariates from an iid sample. The agent examines the sample, chooses a model for the conditional distribution of the response and the procedure to fit it, and returns the estimator as a short computer program. The program is built from a library of probability distributions. The returned law can therefore be a parametric distribution, a mixture or a multivariate factorization, with distribution parameters given by explicit formulas in the covariates. We call this approach agentic distributional regression (ADR). Unlike in the classical approach, the statistician no longer chooses the estimator, but asks an agent to build one. Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under assumptions on the number of admissible models and on the accuracy of the agent's fit, and an oracle inequality for the selection of a model among fitted candidates using independent validation data. Finally, assuming that, as the sample size grows, the agent selects the same smooth parametric model with probability tending to one and fits it accurately, we show that the estimated parameters are asymptotically normal. In simulation studies, on twelve real datasets and on a new dataset whose responses postdate the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the existing methods from the statistical literature with which it is compared.
Optimal Neural Estimation for High-Dimensional Nonparametric Regression under Multisource Covariate Shift
Chenghao Xu, Haotian Xu, Shivam Kumar, Daren Wang
AI 速览：研究多源协变量偏移下高维非参数回归，提出oracle加权神经估计并给出minimax最优收敛率，同时给出无需已知噪声方差与偏移参数的自适应方法。
We study high-dimensional nonparametric regression under multisource covariate shift, where $\mathrm J$ sources of training data share a common regression function but differ in their covariate distributions, sample sizes, and noise variances. Our goal is to combine these sources to estimate the regression function accurately under a target covariate distribution. We propose an oracle weighted neural estimator and establish its minimax optimality up to logarithmic factors through matching upper and lower bounds. The resulting rate is $\mathsf n_{\rm eff}^{-2p/(2p+K)}$, where $p$ and $K$ denote the effective smoothness and dimension of the regression function, and the effective sample size is \begin{align} \mathsf n_{\rm eff} =\sum_{j=1}^{\mathrm J} \frac{n_j}{(1+σ_{ρ,j})σ_{ε,j}^{2}}. \nonumber \end{align} Here, $n_j$ is the sample size of source $j$, $σ_{ε,j}^{2}$ is its noise variance, and $σ_{ρ,j}$ controls the deviation between the covariate distribution of source $j$ and the target covariate distribution. We also develop an adaptive procedure that requires no knowledge of source noise variances or covariate-shift parameters. Under suitable conditions, this procedure attains the oracle minimax rate up to logarithmic factors.
Statistical Inference for Matching Decisions via Matrix Completion under Dependent Missingness
Congyuan Duan, Wanteng Ma, Dong Xia, Kan Xu
AI 速览：针对匹配容量导致的观测条目依赖性问题，提出基于 Grassmannian 梯度下降的非凸矩阵补全方法，并构建去偏与投影框架，用于匹配决策的统计推断。
This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.
Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
Ilya Levin, Maksim Shuklin, Eric Moulines, Paul Mangold, Sergey Samsonov
AI 速览：该论文为联邦线性随机逼近建立Berry-Esseen型界与联邦高斯近似，并据此提出一种无需显式估计渐近协方差矩阵的在线乘子自助推断方法。
In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated Gaussian approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2025] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for inference on the last iterate, which avoids explicit estimation of the asymptotic covariance matrix, and obtain non-asymptotic validity guarantees for this procedure.
Hongqi Chen, Chengwang Liao, Ziwei Mei, Zhentao Shi
LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we establish two asymptotic results: (i) a local oracle property for the penalized regression, and (ii) a global oracle property for regressions with a penalty-level constraint. In particular, the latter guarantees a global solution that consistently estimates the true coefficients and enjoys oracle prediction performance. Simulation studies and an application to predicting the euro area unemployment rate show that FCP improves variable selection and out-of-sample prediction relative to LASSO.
Synthetic data are widely used for training modern AI systems. However, their statistical understanding remains limited. It is well recognized in statistics that repeated self-training on synthetic data can amplify errors inherited from pre-trained models, leading to model collapse. Verification plays a crucial role in selecting high-quality synthetic data to help prevent model collapse and improve model performance. We study verified self-training in a linear regression framework, where a pre-trained estimator generates synthetic data with injected generation noise and a verifier selects samples according to a verification threshold. Post-training on the accepted samples updates either all coordinates (full fine-tuning) or only an active subset (partial fine-tuning). Our analysis reveals three potentially counterintuitive effects. We establish that tighter verification does not always lead to lower prediction risk. We also find that a suitable level of injected generation noise can reduce prediction risk, while excessive noise can increase it. Moreover, full and partial fine-tuning can respond differently to the same verification rule, since pre-training error in the frozen coordinates affects both sample selection and post-training risk. We analyze these effects by deriving finite sample risk bounds for four separate regimes determined by the relative scales of the verification threshold, generation noise, and pre-training error. The bounds precisely characterize how verification affects prediction risk across these regimes. In particular, we quantify how the generation noise, the effective accepted sample size, and the covariance of the accepted covariates affect prediction risk. The analysis extends to iterative verified full fine-tuning, where sufficiently tight verification reduces the initial error contribution at a geometric rate.
Artificial intelligence (AI) models can accelerate cell-type annotation in digital pathology, but safely scaling their use requires determining, with error control, which model-generated labels can be accepted without expert review. This is challenging in evolving workflows because cell morphology and type composition may change across tissue regions and slides, making one-time calibration unreliable. We propose Conformal Annotation with Randomized Expert review under Distribution shift (CARED), a distribution-free framework that leverages randomized expert audit to achieve long-run error control for AI-assisted annotation under distribution shift. For each incoming batch, CARED uniformly selects a subset of cases for expert review and uses the acquired labels to calibrate later decisions. Among unreviewed cases, CARED determines a subset of them to safely skip expert labeling, while suggesting candidate labels for the others for downstream resolution. We prove that this workflow provides long-run control of cumulative error over both the full stream and the cells outside of the audit sample, without stationarity or exchangeability assumptions. We further enhance the framework by introducing class-conditional guarantees to ensure error control within important but rare cell types, together with a utility module to target more automatic resolutions, smaller candidate sets, and greater biological coherence, without compromising validity. Experiments on pancreas, lung, and ovary annotation streams, together with a stream constructed from real expert annotations, show that CARED controls the cumulative errors while a substantial fraction of cells (up to 70%) bypass expert review.
Vanilla gradient methods are often highly sensitive to the choice of stepsize, which typically requires manual tuning. Adaptive methods alleviate this issue, with AdaGrad being a prominent example. In this work, we first show that, in composite convex optimization, AdaGrad may fail to exploit the Hölder-smoothness of the differentiable term, as its stepsizes may decrease too rapidly, leading to convergence rates arbitrarily close to the nonsmooth $\mathcal O(n^{-1/2})$ rate. Motivated by this limitation, we study AdaGrad-Diff, a block-wise extension of the UniSgd method considered by \cite{rodomanov2024universality}, which accumulates successive gradient differences rather than gradients themselves. In the deterministic Lipschitz-smooth setting, we prove summability of squared gradient differences without assuming bounded iterates, yielding weak convergence to a minimizer in Hilbert spaces. Moreover, we show that, under $ν$-Hölder-smoothness, stepsizes decay no faster than $n^{-(1-ν)/2}$, thereby avoiding AdaGrad's failure mechanism and recovering the standard $\mathcal O(n^{-(1+ν)/2})$ rate. The same approach recovers known stochastic convergence rates under a unified condition covering bounded variance and interpolation. Numerical experiments demonstrate that the proposed method is more robust than AdaGrad in several practically relevant settings.
Recent advances in Time Series Foundation Models (TSFMs) increasingly rely on axial attention mechanisms, but despite their empirical success, the theoretical properties of axial attention remain largely unexplored. To bridge this gap, we extend the Single Location Regression framework introduced in Marion et al. [2025] to 2D structured data, in order to study sparse information settings where a target depends on a small number of tokens. We formulate an analytically tractable axial attention-type predictor and rigorously analyze its statistical properties and training dynamics. We prove that under a specific asymptotic regime and with knowledge of the underlying oracle parameters, our predictor achieves Bayes optimality, whereas a class of semi-linear simplifications strictly fails to do so, underlining the role of the inner non-linearity. We prove that for a specific temperature scaling, Projected Gradient Descent converges globally to the optimal oracle parameters. Extensive numerical experiments validate our theoretical findings and highlight the critical role of inverse temperature scheduling in empirical convergence.
Gayane Taturyan, Charlotte Laclau, Stephan Clémençon
We study the problem of fair ranking in recommender systems. We provide a formal probabilistic framework in which ranking policies are distributions over permutations, and the utility of a user is the exposure given to the items they interact with, relative to that of an ideal ranking. We consider utility parity across user groups, as well as its category-aware refinement, conditional utility parity, which requires parity within each category of items. Following a recent view of fairness as distributional stability, we show that both criteria are equivalent to the stability of the utility under changes in the composition of user groups. Optimizing over mixtures of ranking policies leads to a second-order cone program, for which we provide generalization bounds. A numerical study validates our theoretical findings.
We consider the problem of dynamically selecting among competing strategies using observable predictors. To mitigate estimation noise and excessive switching, we regularise the estimated policy with a switching cost, which may exceed actual transaction costs when these are too small to provide sufficient regularisation. Since switching costs make current choices affect future decisions, we formulate the problem using dynamic programming. The optimal policy is estimated using a reinforcement learning algorithm based on iterated regressions, making the procedure simple to implement. We apply the method to monthly rotation among momentum, value, profitability, and defensive U.S. equity factors over a sample of about 60 years. Using a parsimonious set of state variables, the estimated policy outperforms both the myopic dynamic policy and the best fixed factor in hindsight in out-of-sample evaluation. Under weak conditions, we show theoretically that the decision rule estimated from empirical data is asymptotically consistent for the unknown optimal decision rule. Simulation results illustrate the finite-sample relevance of these asymptotic results.
Guy Zamir, Victor Boone, Matthew Zurek, Yudong Chen
In this paper, we study the regret minimization problem in episodic tabular MDPs. Our algorithm achieves the first expected regret bound scaling as $\sqrt{H^3 S A K}$ for sufficiently large $K$, where $H$ is the episode length, $K$ is the number of episodes, and $S$ and $A$ are the numbers of states and actions, respectively. Our method is the first to match the minimax lower bound \emph{without extra polylog factors}. We introduce a variant of UCBVI which does not maintain strictly optimistic estimates, and uses MOSS-style exploration bonuses whose logarithmic terms adapt to both visit counts and estimated variances. A key challenge is controlling the propagation of errors caused by under-optimism, which we accomplish in an occupancy-weighted way, avoiding logarithmic overhead that would be incurred by uniform-over-rows concentration. Our analysis develops time-uniform and variance-aware concentration bounds that may be of independent interest. As a corollary we also develop an algorithm for $(\varepsilon, δ)$-PAC best-policy identification, which is the first to match the $Ω\big(H^3 SA\log(\frac{1}δ)\varepsilon^{-2}\big)$ minimax lower bound up to constants in some regimes.
Self-supervised contrastive learning (SSCL) learns representations by contrasting augmented views of the same sample, but it can exhibit feature suppression, where dominant or easy-to-learn factors suppress other class-relevant signals, degrading the performance of representations, particularly in high-dimensional data with heterogeneous features. We introduce Fisher Contrastive Learning (FCL), which uses a regularized Fisher trace criterion to address feature suppression. FCL learns embeddings by maximizing the discriminative strength of Fisher discriminant functions, producing representations that preserve class-relevant information implied by the augmentation process. We prove that the representations learned by FCL could alleviate the feature suppression effects. We demonstrate FCL on simulated benchmarks designed to induce feature suppression and on a real-world biomedical application, pretraining on large white blood cell microscopy image dataset and transfer learning for diagnosis of acute promyelocytic leukemia in an external cohort. In all experiments, FCL outperforms the self-supervised baselines and yields more robust and discriminative representations.
We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures remains challenging due to highly nonconvex and often ill-conditioned optimization landscapes. In contrast, for relatively shallow networks, most notably certain one-hidden-layer ReLU models, training admits convex reformulations with global guarantees under appropriate settings, motivating learning paradigms that improve stability while scaling to depth. MGDL builds on this insight by training deep networks grade by grade: previously learned grades are frozen, and each newly added grade-wise subnetwork is composed on top of the previously learned grades and trained to fit the residual left by the current approximation, yielding a structured and interpretable hierarchical refinement process. We develop an operator-theoretic foundation for MGDL and prove that, for any continuous target function defined on a hypercube, there exists a fixed-width multigrade ReLU scheme whose residuals are pointwise nonincreasing in magnitude and converge uniformly to zero, with strict $L^p$-norm decay at every nontrivial grade for $p\in [1,\infty)$. To the best of our knowledge, this work provides the first rigorous constructive approximation guarantee showing that a grade-wise residual refinement scheme can achieve vanishing error in a fixed-width multigrade ReLU architecture.
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different perspective by connecting Flow Matching to kernel density estimation. We first verify that the kernel density estimator matches the optimal rate of convergence in Wasserstein distance up to logarithmic factors, improving existing bounds for the Gaussian kernel. Based on this result, we prove that for sufficiently large networks, Flow Matching achieves the optimal rate up to logarithmic factors. If the target distribution lies on a lower-dimensional manifold, we show that the kernel density estimator profits from the smaller intrinsic dimension on a small tube around the manifold. The faster rate also applies to Flow Matching, providing a theoretical foundation for its empirical success in high-dimensional settings.
Raphael Kim, Michele Santacatterina, Ramin Zabih, Keith Barnatchez
Reinforcement learning (RL) is increasingly used to train robust, adaptable systems across healthcare, e-commerce, and robotics. In these settings, legal, ethical, or logistical concerns may preclude certain key variables that drive decisions from being collected during deployment time. This gives rise to a setting known as runtime confounding: the logged data hold full observability, but deployment time lacks knowledge of certain variables, known as runtime confounders. Unlike single timepoint and non-adaptive settings, runtime confounding under reinforcement learning has the potential to propagate over time, as earlier decisions affect future states, observations, and action assignments, leading to biased learning. We address these problems with three contributions: we (1) develop policy learning algorithms under runtime-confounding, (2) develop semi-parametric efficient off-policy estimation procedures, and (3) provide diagnostics for understanding the price of runtime confounding.
Despite their practical significance, modern AI systems pose significant societal risks, including toxicity, malicious use, and misinformation. Their mitigation depends not only on technical feasibility but also on the incentives of firms that develop and deploy these systems. We show how profit maximization shapes safety investment in an AI supply chain with an upstream LLM provider and several competing downstream firms. In our game-theoretic model, we derive the market-driven level of safety investment and compare it with the levels that maximize industry profit and market welfare. We find that downstream competition generally induces downstream firms to invest more in safety than the industry-profit-optimal level. By contrast, the upstream provider may underinvest relative to these benchmarks because it is not fully compensated for the surplus from safety investments. Finally, we analyze how different regulatory interventions affect the participants' incentives and profits, and the resulting levels of model safety.
Federico Pavesi, Noémie Jaquier, Antonio Candelieri
Probabilistic meshless methods solve partial differential equations (PDEs) by placing a Gaussian process prior on the solution and conditioning it on the PDE at a finite set of collocation nodes. The posterior provides both an approximation of the solution and a Bayesian quantification of its error. While these methods are well established on Euclidean domains, their extension to manifolds lacks, to our knowledge, any convergence analysis. We extend them to compact manifolds and study their convergence in two settings. First, for known manifolds whose Laplace-Beltrami eigenpairs are available, the prior can be evaluated exactly, but the PDE operator generally cannot be applied to it in closed form. We replace this operator by a standard generalized finite difference discretization on a point cloud sampled from the manifold, and show that the resulting method is consistent at the points of the cloud, at a rate governed by their fill distance. Second, for implicit manifolds, known only through a point cloud, both the prior and the operator must be approximated. We propose a new generalized finite difference scheme with a free stencil radius, and show that it retains the consistency of the standard construction while controlling the growth of its coefficients, and that an appropriate radius yields uniform convergence of the discrete Gram matrix. In both settings, we derive error bounds for the posterior mean which separate the collocation error intrinsic to the method from the error due to approximating the operator and, for implicit manifolds, the prior. Experiments on the circle, the sphere and the flat torus confirm our theoretical claims. On real-world cortical thickness data, our approach attains the accuracy of established discretizations, while conditioning on fewer than a tenth of the observations and providing a credible interval at every vertex.
Oumaïma Bounhar, Thomas Chêne, Ghaya Rekaya-Ben Othman, Oussama Damen
Reconfigurable Intelligent Surfaces (RIS) are a promising solution for improving millimeter-wave (mmWave) communications by controlling signal propagation. Yet, selecting the optimal RIS configuration remains challenging due to the high-dimensional search space and signaling overhead. We propose a Deep Reinforcement Learning (DRL) framework for blind passive beamforming, where a Deep Q-Learning (DQL) agent learns an adaptive policy to select near-optimal RIS configurations while sounding only few codewords, without channel state information. Results show that our approach outperforms Q-Learning (QL) and conventional baselines in convergence, performance, and overhead reduction.
Accelerated dynamics methods, such as parallel replica dynamics, require estimates of the decorrelation time, after which a process trapped in one of its metastable states is distributed according to the quasi-stationary distribution (QSD). In a method proposed by Binder, Lelièvre and Simpson, decorrelation times are defined by coupling a particle approximation of the non-linear conditioned probability flow of the process with MCMC-inspired diagnostics. We explore an alternative to MCMC diagnostics, based on coarse-graining of non-linear probability flows and simulation-based inference. We first develop a coarse-graining framework for killed Markov jump processes conditioned on survival, proving uniform-in-time, non-asymptotic estimates approximating the non-linear probability flow of the true process by the non-linear flow of a surrogate process, defined with a collective variable. The framework does not assume reversibility of the true process, and also gives bounds which scale explicitly in an adiabatic regime. Motivated by these results, we then construct a quasi-stationarity diagnostic using simulation-based inference: a recurrent neural network (RNN), trained on particle approximations of non-linear effective flows, estimates posterior probabilities of decorrelation. The learned diagnostic is then transferred to collective-variable traces of high-dimensional particle approximations. We investigate the behavior and robustness of this diagnostic on a set of numerical experiments, comparing it to the MCMC diagnostic of Binder et al.\ on both synthetic examples and a molecular system, in and out of its training prior distribution. When its prior assumptions hold, the RNN diagnostic outperforms the MCMC diagnostic in ROC analysis, is less conservative, fails less often, and has an interpretable decision threshold.
Michele Caprio, David Stutz, Shuo Li, Arnaud Doucet
An open question in \emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.
Shirley Xiaoqi Liu, Florence Regol, Antonios Valkanas, Patrick Rebeschini, Mark Coates
Adaptive inference systems balance accuracy and inference cost by routing inputs to models with varying capabilities. Although jointly training models and routers is empirically more sample-efficient than training them separately, principled losses for joint training remain underexplored. We address this gap in a classification setting by proposing cost-sensitive hinge losses for jointly training classifiers with single-stage or cascade routers. Single-stage routers directly select a model per input, whereas cascade routers sequentially decide at each stage whether to predict with the current model or defer to the next stage, which uses a more accurate but more costly model. For both settings, we prove linear calibration bounds establishing Bayes consistency: minimizing the hinge risk recovers the Bayes-optimal risk under the target cost-sensitive zero-one loss. Moreover, since routers can require more labeled data to train than classifiers, we propose a novel post-training prediction-powered inference (PPI) procedure that uses unlabeled data to refine a trained single-stage router. Experiments on synthetic and real datasets demonstrate that the proposed hinge losses are effective for joint training and that PPI can correct routing errors when labeled data is scarce.
Ernesto Araya, Gitta Kutyniok, Weilin Li, Johannes Maly, Manjot Singh
In this work, we formalize the concept of intrinsic dimension of objective landscapes introduced in Li et al. (2018), which measures the structural complexity of learning problems by training along randomly generated subspaces. We define the intrinsic dimension of a set $Θ\subset\mathbb{R}^p$ as the minimal dimension $d_{\mathrm{int}}(Θ)$ such that a random plane of dimension $d_{\mathrm{int}}(Θ)$ in $\mathbb{R}^p$ intersects $Θ$ with probability one. We show that it is a generalized notion of co-dimension that depends on the global geometry of $Θ$. We study mathematical properties of the intrinsic dimension and develop techniques to estimate the intrinsic dimension of sets $Θ$ that arise in learning problems. More specifically, we derive upper and/or lower bounds where $Θ$ is the set of optimal parameters in student-teacher settings with shallow and deep ReLU networks, including finite and infinite sample cases, and with and without regularization. We discuss how our theory leads to novel types of generalization bounds, thereby showing that the intrinsic dimension is a measure of learning complexity. Our results connect techniques from seemingly different areas of machine learning research such as classification of symmetries of ReLU networks and stochastic geometry.