Tag: general
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A general technique for approximating high-dimensional empirical kernel matrices
A general technique for approximating high-dimensional empirical kernel matrices arXiv:2511.03892v1 Announce Type: new Abstract: We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(cdot,cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative Khintchine inequality to obtain upper and lower bounds…
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A General Constructive Upper Bound on Shallow Neural Nets Complexity
A General Constructive Upper Bound on Shallow Neural Nets Complexity arXiv:2510.06372v1 Announce Type: new Abstract: We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem,…
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A General-Purpose Theorem for High-Probability Bounds of Stochastic Approximation with Polyak Averaging
A General-Purpose Theorem for High-Probability Bounds of Stochastic Approximation with Polyak Averaging arXiv:2505.21796v1 Announce Type: new Abstract: Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this paper, we present a general framework for establishing…
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Local minima of the empirical risk in high dimension: General theorems and convex examples
Local minima of the empirical risk in high dimension: General theorems and convex examples arXiv:2502.01953v1 Announce Type: new Abstract: We consider a general model for high-dimensional empirical risk minimization whereby the data $mathbf{x}_i$ are $d$-dimensional isotropic Gaussian vectors, the model is parametrized by $mathbf{Theta}inmathbb{R}^{dtimes k}$, and the loss depends on the data via the projection…