A Mathematical Model for Curriculum Learning for Parities

• URL: http://arxiv.org/abs/2301.13833v2
• Date: Tue, 23 Apr 2024 01:44:30 GMT
• Title: A Mathematical Model for Curriculum Learning for Parities
• Authors: Elisabetta Cornacchia, Elchanan Mossel,
• Abstract summary: We introduce a CL model for learning the class of k-parities on d bits of a binary string with a neural network trained by gradient descent. We show that a wise choice of training examples involving two or more product distributions, allows to reduce significantly the computational cost of learning this class of functions. We also show that for another class of functions - namely the Hamming mixtures' - CL strategies involving a bounded number of product distributions are not beneficial.
• Score: 8.522887729678637
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Curriculum learning (CL) - training using samples that are generated and presented in a meaningful order - was introduced in the machine learning context around a decade ago. While CL has been extensively used and analysed empirically, there has been very little mathematical justification for its advantages. We introduce a CL model for learning the class of k-parities on d bits of a binary string with a neural network trained by stochastic gradient descent (SGD). We show that a wise choice of training examples involving two or more product distributions, allows to reduce significantly the computational cost of learning this class of functions, compared to learning under the uniform distribution. Furthermore, we show that for another class of functions - namely the `Hamming mixtures' - CL strategies involving a bounded number of product distributions are not beneficial.

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