Learning two-layer neural networks with symmetric inputs

• Main Authors: GE, Rong, KUDITIPUDI, Rohith, LI, Zhize, WANG, Xiang
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2019
• Subjects: Neural network; Optimization; Symmetric inputs; Moment-of-moments; Databases and Information Systems; OS and Networks
• Online Access: https://ink.library.smu.edu.sg/sis_research/8676; https://ink.library.smu.edu.sg/context/sis_research/article/9679/viewcontent/ICLR19_symmetric.pdf
• Institution: Singapore Management University

We give a new algorithm for learning a two-layer neural network under a very general class of input distributions. Assuming there is a ground-truth two-layer network $y = A \sigma(Wx) + \xi$, where A, W are weight matrices, $\xi$ represents noise, and the number of neurons in the hidden layer is no larger than the input or output, our algorithm is guaranteed to recover the parameters A, W of the ground-truth network. The only requirement on the input x is that it is symmetric, which still allows highly complicated and structured input. Our algorithm is based on the method-of-moments framework and extends several results in tensor decompositions. We use spectral algorithms to avoid the complicated non-convex optimization in learning neural networks. Experiments show that our algorithm can robustly learn the ground-truth neural network with a small number of samples for many symmetric input distributions.