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Creators/Authors contains: "Nichani, Eshan"

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  1. ; ; ; ( , NeurIPS 2023)
  2. ; ; ; ( , NeurIPS 2023)
    We focus on the task of learning a single index model with respect to the isotropic Gaussian distribution in d dimensions. Prior work has shown that the sample complexity of learning the hidden direction is governed by the information exponent k of the link function. Ben Arous et al. showed that d^k samples suffice for learning and that this is tight for online SGD. However, the CSQ lowerbound for gradient based methods only shows that d^{k/2} samples are necessary. In this work, we close the gap between the upper and lower bounds by showing that online SGD on a smoothed loss learns the hidden direction with the correct number of samples. We also draw connections to statistical analyses of tensor PCA and to the implicit regularization effects of minibatch SGD on empirical losses. 
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