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Creators/Authors contains: "Li, Zhize"

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  1. ; ; ( , Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS))
  2. ; ; ( , SIAM Journal on Mathematics of Data Science)
    Full Text Available 
  3. ; ; ; ( , International Conference on Learning Representations)
    We give a new algorithm for learning a two-layer neural network under a general class of input distributions. Assuming there is a ground-truth two-layer network y = Aσ(Wx) + ξ, where A,W are weight matrices, ξ 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. 
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    Accepted Manuscript Full Text Available
  4. ; ; ; ( , The 32’nd Annual Conference on Learning Theory (COLT 2019))
    Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary point (with small gradient and almost PSD hessian). In this paper, we show that Stabilized SVRG (a simple variant of SVRG) can find an \eps-second-order stationary point using only O(n^{2/3}/\eps^2+n/\eps^{1.5}) stochastic gradients. To our best knowledge, this is the first second-order guarantee for a simple variant of SVRG. The running time almost matches the known guarantees for finding \eps-first-order stationary points. 
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    Accepted Manuscript Full Text Available