February 2026

arXiv:2509.22122v2 Announce Type: replace-cross Abstract: This study considers the estimation of the direct bias-correction term for estimating the average treatment effect (ATE). Let ${(X_i, D_i, Y_i)}_{i=1}^{n}$ be the observations, where $X_i$ denotes $K$-dimensional covariates, $D_i in {0, 1}$ denotes a binary treatment assignment indicator, and $Y_i$ denotes an outcome. In ATE estimation, $h_0(D_i, X_i) = frac{1[D_i = 1]}{e_0(X_i)} – frac{1[D_i = 0]}{1 – e_0(X_i)}$ is called the bias-correction term, where $e_0(X_i)$ is the propensity score. The bias-correction term […]

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arXiv:2509.21906v2 Announce Type: replace-cross Abstract: Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error analysis remain largely unexplored. In this work, we develop a unified framework grounded in stochastic calculus theory to systematically investigate the theoretical properties of discrete flow models. Specifically, by leveraging a Girsanov-type theorem for the path measures of two continuous-time Markov chains […]

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arXiv:2506.08337v2 Announce Type: replace-cross Abstract: Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In this work, we present a simplified framework for analyzing the Euler–Maruyama discretization of variance-preserving SDEs (VP-SDEs). Using Gr”onwall’s inequality, we derive a convergence rate of $O(T^{-1/2})$ under standard Lipschitz assumptions, streamlining prior analyses. We then demonstrate that the standard Gaussian noise can be replaced by computationally […]

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arXiv:2506.06446v2 Announce Type: replace-cross Abstract: Providers of LLM-as-a-service have predominantly adopted a simple pricing model: users pay a fixed price per token. Consequently, one may think that the price two different users would pay for the same output string under the same input prompt is the same. In our work, we show that, surprisingly, this is not (always) true. We find empirical evidence that, particularly for non-english outputs, both proprietary and open-weights LLMs often generate the same (output) […]

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arXiv:2506.06185v2 Announce Type: replace-cross Abstract: We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model architectures, conditional and unconditional sampling, and even other generative models such as VAEs and Normalizing Flows. To explain it, we combine experiments and theory and propose a textit{symmetry conjecture} that the learned score function is approximately affine antisymmetric (odd symmetry up to a […]

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arXiv:2505.19589v3 Announce Type: replace-cross Abstract: Estimating causal effects from observational data is essential in fields such as medicine, economics and social sciences, where privacy concerns are paramount. We propose a general, model-agnostic framework for differentially private estimation of average treatment effects (ATE) that avoids strong structural assumptions on the data-generating process or the models used to estimate propensity scores and conditional outcomes. In contrast to prior work, which enforces differential privacy by directly privatizing these nuisance components, our […]

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arXiv:2505.17965v2 Announce Type: replace-cross Abstract: The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias component and study the extent to which SGD can match the optimal convergence behavior of deterministic gradient descent. Assuming only (strong) convexity and smoothness of the objective, we derive new bounds that are bias-optimal, in the sense that the bias term coincides with the […]

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arXiv:2505.11325v3 Announce Type: replace-cross Abstract: Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular data sets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian ideas, they do not provide any uncertainty quantification for predictive means, quantiles, or similar quantities. We propose a principled and efficient sampling procedure to construct Bayesian posteriors for such estimates based on Martingale posteriors, and prove its convergence. Several simulated […]

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arXiv:2601.07144v2 Announce Type: replace Abstract: Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, […]

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arXiv:2601.05219v2 Announce Type: replace Abstract: One-shot prediction enables rapid adaptation of pretrained foundation models to new tasks using only one labeled example, but lacks principled uncertainty quantification. While conformal prediction provides finite-sample coverage guarantees, standard split conformal methods are inefficient in the one-shot setting due to data splitting and reliance on a single predictor. We propose Conformal Aggregation of One-Shot Predictors (CAOS), a conformal framework that adaptively aggregates multiple one-shot predictors and uses a leave-one-out calibration scheme to […]

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