April 2026

arXiv:2604.23260v1 Announce Type: new Abstract: An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular, sharpened ReLU integral representation, which involves a harmonic extension and a projection. The bounds demonstrate that functions can be approximated with $L^{2}(mathcal{D})$ errors that do not depend explicitly on dimension or degree, but rather the coefficients of their monomial expansions and the distribution $mathcal{D}$.

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arXiv:2604.23260v1 Announce Type: new Abstract: An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular, sharpened ReLU integral representation, which involves a harmonic extension and a projection. The bounds demonstrate that functions can be approximated with $L^{2}(mathcal{D})$ errors that do not depend explicitly on dimension or degree, but rather the coefficients of their monomial expansions and the distribution $mathcal{D}$.

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arXiv:2604.23212v1 Announce Type: new Abstract: Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of spectral algorithms in the large-dimensional setting where the sample size and dimension are of comparable order, i.e., $n asymp d^{gamma}$ for some $gamma>0$. We first consider inner-product kernels on the sphere $mathbb{S}^{d-1}$ and establish a sharp asymptotic characterization of the excess risk […]

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arXiv:2604.23212v1 Announce Type: new Abstract: Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of spectral algorithms in the large-dimensional setting where the sample size and dimension are of comparable order, i.e., $n asymp d^{gamma}$ for some $gamma>0$. We first consider inner-product kernels on the sphere $mathbb{S}^{d-1}$ and establish a sharp asymptotic characterization of the excess risk […]

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arXiv:2604.23107v1 Announce Type: new Abstract: Causal effect estimation from observational data requires careful adjustment for confounding. Classical estimators such as inverse probability weighting and augmented inverse probability weighting are effective under favorable model specification, but may become unstable when treatment assignment and outcome mechanisms are complex, non-linear, and high-dimensional. Machine learning and representation learning approaches improve flexibility, yet joint training can allow outcome-related information to influence treatment-side representations, which is undesirable from a causal perspective. We propose MOCA […]

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arXiv:2604.23107v1 Announce Type: new Abstract: Causal effect estimation from observational data requires careful adjustment for confounding. Classical estimators such as inverse probability weighting and augmented inverse probability weighting are effective under favorable model specification, but may become unstable when treatment assignment and outcome mechanisms are complex, non-linear, and high-dimensional. Machine learning and representation learning approaches improve flexibility, yet joint training can allow outcome-related information to influence treatment-side representations, which is undesirable from a causal perspective. We propose MOCA […]

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arXiv:2604.23083v1 Announce Type: new Abstract: Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Automatic selection of the number of components is established with the introduction of the […]

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arXiv:2604.23083v1 Announce Type: new Abstract: Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Automatic selection of the number of components is established with the introduction of the […]

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arXiv:2604.22967v1 Announce Type: new Abstract: Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO’s local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To […]

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