How much pre-training is enough to discover a good subnetwork?

• URL: http://arxiv.org/abs/2108.00259v3
• Date: Tue, 22 Aug 2023 18:13:50 GMT
• Title: How much pre-training is enough to discover a good subnetwork?
• Authors: Cameron R. Wolfe, Fangshuo Liao, Qihan Wang, Junhyung Lyle Kim, Anastasios Kyrillidis
• Abstract summary: We mathematically analyze the amount of dense network pre-training needed for a pruned network to perform well. We find a simple theoretical bound in the number of gradient descent pre-training iterations on a two-layer, fully-connected network. Experiments with larger datasets require more pre-training forworks obtained via pruning to perform well.
• Score: 10.699603774240853
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural network pruning is useful for discovering efficient, high-performing subnetworks within pre-trained, dense network architectures. More often than not, it involves a three-step process -- pre-training, pruning, and re-training -- that is computationally expensive, as the dense model must be fully pre-trained. While previous work has revealed through experiments the relationship between the amount of pre-training and the performance of the pruned network, a theoretical characterization of such dependency is still missing. Aiming to mathematically analyze the amount of dense network pre-training needed for a pruned network to perform well, we discover a simple theoretical bound in the number of gradient descent pre-training iterations on a two-layer, fully-connected network, beyond which pruning via greedy forward selection [61] yields a subnetwork that achieves good training error. Interestingly, this threshold is shown to be logarithmically dependent upon the size of the dataset, meaning that experiments with larger datasets require more pre-training for subnetworks obtained via pruning to perform well. Lastly, we empirically validate our theoretical results on a multi-layer perceptron trained on MNIST.

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