PHEW : Constructing Sparse Networks that Learn Fast and Generalize Well without Training Data
Shreyas Malakarjun Patil, Constantine Dovrolis
Abstract
Methods that sparsify a network at initialization are important in practice because they greatly improve the efficiency of both learning and inference. Our work is based on a recently proposed decomposition of the Neural Tangent Kernel (NTK) that has decoupled the dynamics of the training process into a data-dependent component and an architecture-dependent kernel {–} the latter referred to as Path Kernel. That work has shown how to design sparse neural networks for faster convergence, without any training data, using the Synflow-L2 algorithm. We first show that even though Synflow-L2 is optimal in terms of convergence, for a given network density, it results in sub-networks with “bottleneck” (narrow) layers {–} leading to poor performance as compared to other data-agnostic methods that use the same number of parameters. Then we propose a new method to construct sparse networks, without any training data, referred to as Paths with Higher-Edge Weights (PHEW). PHEW is a probabilistic network formation method based on biased random walks that only depends on the initial weights. It has similar path kernel properties as Synflow-L2 but it generates much wider layers, resulting in better generalization and performance. PHEW achieves significant improvements over the data-independent SynFlow and SynFlow-L2 methods at a wide range of network densities.
BibTeX
@InProceedings{pmlr-v139-patil21a,
title = {PHEW : Constructing Sparse Networks that Learn Fast and Generalize Well without Training Data},
author = {Patil, Shreyas Malakarjun and Dovrolis, Constantine},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {8432--8442},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/patil21a/patil21a.pdf},
url = {https://proceedings.mlr.press/v139/patil21a.html},
abstract = {Methods that sparsify a network at initialization are important in practice because they greatly improve the efficiency of both learning and inference. Our work is based on a recently proposed decomposition of the Neural Tangent Kernel (NTK) that has decoupled the dynamics of the training process into a data-dependent component and an architecture-dependent kernel {–} the latter referred to as Path Kernel. That work has shown how to design sparse neural networks for faster convergence, without any training data, using the Synflow-L2 algorithm. We first show that even though Synflow-L2 is optimal in terms of convergence, for a given network density, it results in sub-networks with “bottleneck” (narrow) layers {–} leading to poor performance as compared to other data-agnostic methods that use the same number of parameters. Then we propose a new method to construct sparse networks, without any training data, referred to as Paths with Higher-Edge Weights (PHEW). PHEW is a probabilistic network formation method based on biased random walks that only depends on the initial weights. It has similar path kernel properties as Synflow-L2 but it generates much wider layers, resulting in better generalization and performance. PHEW achieves significant improvements over the data-independent SynFlow and SynFlow-L2 methods at a wide range of network densities.}
}