A Mathematical Model for Curriculum Learning for Parities
This work addresses the lack of theoretical understanding in curriculum learning for machine learning researchers, though it is incremental as it builds on existing empirical analyses.
The authors tackled the problem of providing mathematical justification for curriculum learning by introducing a model for learning k-parities on d bits with neural networks trained by SGD, showing that a wise choice of training examples reduces computational cost significantly compared to uniform distribution, but found it not beneficial for Hamming mixtures.
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.