Norm-Based Generalization Bounds for Compositionally Sparse Neural Network
Name
CBMM-Memo-139.pdf
Size
1.2 MB
Format
Adobe PDF
Checksum (MD5)
ce16b15c52d27cc758e49faf20831919
Author(s)
Galanti, Tomer
Xu, Mengjia
Galanti, Liane
Poggio, Tomaso
Date Issued
February 14, 2023
Publisher
Center for Brains, Minds and Machines (CBMM)
Series/Report no.
CBMM Memo;139
Abstract
In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including convolutional neural networks. These bounds differ from previous ones, as they consider the norms of the convolutional filters instead of the norms of the associated Toeplitz matrices, independently of weight sharing between neurons.
As we show theoretically, these bounds may be orders of magnitude better than standard norm- based generalization bounds and empirically, they are almost non-vacuous in estimating generalization in various simple classification problems. Taken together, these results suggest that compositional sparsity of the underlying target function is critical to the success of deep neural networks.
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