Tag: interpolation
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On damage of interpolation to adversarial robustness in regression
On damage of interpolation to adversarial robustness in regression arXiv:2601.16070v1 Announce Type: new Abstract: Deep neural networks (DNNs) typically involve a large number of parameters and are trained to achieve zero or near-zero training error. Despite such interpolation, they often exhibit strong generalization performance on unseen data, a phenomenon that has motivated extensive theoretical investigations.…
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Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators arXiv:2512.24106v1 Announce Type: new Abstract: In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well…
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Sobolev norm inconsistency of kernel interpolation
Sobolev norm inconsistency of kernel interpolation arXiv:2504.20617v1 Announce Type: new Abstract: We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis…