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Theoretical Properties for Neural Networks with Weight Matrices of Low Displacement Rank
Liang Zhao · Siyu Liao · Yanzhi Wang · Zhe Li · Jian Tang · Bo Yuan

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #83

Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computational complexity while retaining high accuracy. This paper gives theoretical study on LDR neural networks. First, we prove the universal approximation property of LDR neural networks with a mild condition on the displacement operators. We then show that the error bounds of LDR neural networks are as efficient as general neural networks with both single-layer and multiple-layer structure. Finally, we propose back-propagation based training algorithm for general LDR neural networks.

Author Information

Liang Zhao (The City University of New York)
Siyu Liao
Yanzhi Wang
Zhe Li (Syracuse University)
Jian Tang (Syracuse University)
Bo Yuan (City College of New York, CUNY)

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