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Convexifying Sparse Interpolation with Infinitely Wide Neural Networks An Atomic Norm Approach

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Document pages: 5 pages

Abstract: This work examines the problem of exact data interpolation via sparse (neuroncount), infinitely wide, single hidden layer neural networks with leakyrectified linear unit activations. Using the atomic norm framework of[Chandrasekaran et al., 2012], we derive simple characterizations of the convexhulls of the corresponding atomic sets for this problem under several differentconstraints on the weights and biases of the network, thus obtaining equivalentconvex formulations for these problems. A modest extension of our proposedframework to a binary classification problem is also presented. We explore theefficacy of the resulting formulations experimentally, and compare withnetworks trained via gradient descent.

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