February 2026

arXiv:2602.19473v2 Announce Type: replace-cross Abstract: Quantifying distributional separation across groups is fundamental in statistical learning and scientific discovery, yet most classical discrepancy measures are tailored to two-group comparisons. We generalize the underlap coefficient (UNL), a multi-group separation measure, to multivariate variables. We establish key properties of the UNL and provide an explicit connection to total variation. We further interpret the UNL as a dependence measure between a group label and variables of interest and compare it with mutual […]

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arXiv:2512.25017v2 Announce Type: replace-cross Abstract: The aim of this article is to provide a firm mathematical foundation for the application of deep gradient flow methods (DGFMs) for the solution of (high-dimensional) partial differential equations (PDEs). We decompose the generalization error of DGFMs into an approximation and a training error. We first show that the solution of PDEs that satisfy reasonable and verifiable assumptions can be approximated by neural networks, thus the approximation error tends to zero as the […]

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arXiv:2507.14206v2 Announce Type: replace-cross Abstract: Electrocardiogram~(ECG), a key bioelectrical time-series signal, is crucial for assessing cardiac health and diagnosing various diseases. Given its time-series format, ECG data is often incorporated into pre-training datasets for large-scale time-series model training. However, existing studies often overlook its unique characteristics and specialized downstream applications, which differ significantly from other time-series data, leading to an incomplete understanding of its properties. In this paper, we present an in-depth investigation of ECG signals and establish […]

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arXiv:2211.02003v3 Announce Type: replace-cross Abstract: Distributed differentially private learning techniques enable a large number of users to jointly learn a model without having to first centrally collect the training data. At the same time, neither the communication between the users nor the resulting model shall leak information about the training data. This kind of learning technique can be deployed to edge devices if it can be scaled up to a large number of users, particularly if the communication […]

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arXiv:2511.01734v3 Announce Type: replace Abstract: We provide the first proof of learning rate transfer with width in a linear multi-layer perceptron (MLP) parametrized with $mu$P, a neural network parameterization designed to “maximize” feature learning in the infinite-width limit. We show that under $mu P$, the optimal learning rate converges to a emph{non-zero constant} as width goes to infinity, providing a theoretical explanation to learning rate transfer. In contrast, we show that this property fails to hold under alternative […]

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arXiv:2510.21686v2 Announce Type: replace Abstract: We introduce a framework for generating highly multimodal datasets with explicitly calculable mutual information (MI) between modalities. This enables the construction of benchmark datasets that provide a novel testbed for systematic studies of mutual information estimators and multimodal self-supervised learning (SSL) techniques. Our framework constructs realistic datasets with known MI using a flow-based generative model and a structured causal framework for generating correlated latent variables. We benchmark a suite of MI estimators on […]

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arXiv:2510.11789v2 Announce Type: replace Abstract: We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a nonlinear activation function. We prove that the minimax rate is $M^{-frac{2beta}{2beta+1}}$, where $M$ is the sample size and $beta$ is the H”older smoothness of the activation function. Importantly, this rate is independent of the embedding dimension $d$, the number of tokens $N$, and the rank $r$ of the weight matrix, provided […]

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arXiv:2404.07849v2 Announce Type: replace Abstract: This work demonstrates that applying a fixed-effect multiple linear regression (MLR) model to an overparameterized dataset is mathematically equivalent to fitting a hyper-curve parameterized by a single scalar. This reformulation shifts the focus from global coefficients to individual predictors, allowing each to be modeled as a function of a common parameter. We prove that this overparameterized linear framework can yield exact predictions even when the underlying data contains nonlinear dependencies that violate classical […]

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arXiv:2602.22083v1 Announce Type: cross Abstract: A class of causal effect functionals requires integration over conditional densities of continuous variables, as in mediation effects and nonparametric identification in causal graphical models. Estimating such densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even under correct identification. Under smoothness conditions, […]

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arXiv:2602.22003v1 Announce Type: cross Abstract: In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein geodesic between a source and target distribution, along with the associated velocity field. Building on the dynamical formulation of the optimal transport (OT) problem, we recast the constrained optimization as a minimax problem, using deep neural networks to approximate the relevant […]

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