Sparsity-depth Tradeoff in Infinitely Wide Deep Neural Networks
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Abstract (arXiv)
We investigate how sparse neural activity affects the generalization performance of a deep Bayesian neural network at the large width limit. To this end, we derive a neural network Gaussian Process (NNGP) kernel with rectified linear unit (ReLU) activation and a predetermined fraction of active neurons. Using the NNGP kernel, we observe that the sparser networks outperform the non-sparse networks at shallow depths on a variety of datasets. We validate this observation by extending the existing theory on the generalization error of kernel-ridge regression.
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References · 13
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- 2017Deep Neural Networks as Gaussian Processescited by 617
- 2016Exponential expressivity in deep neural networks through transient chaoscited by 260
- 2020Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networkscited by 200
- 2016Deep Information Propagationcited by 194
- 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
- 2020Finite Versus Infinite Neural Networks: an Empirical Studycited by 156
- 2020Deep Equals Shallow for ReLU Networks in Kernel Regimescited by 83
- 2020Exact posterior distributions of wide Bayesian neural networkscited by 29
- 2021Out-of-Distribution Generalization in Kernel Regressioncited by 21
- 2021Uniform Generalization Bounds for Overparameterized Neural Networkscited by 21
- 2019Asymptotic learning curves of kernel methods: empirical data v.s. Teacher-Student paradigmcited by 20
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