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Poster
Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers
Zeyuan Allen-Zhu · Yuanzhi Li · Yingyu Liang

Tue Dec 10 05:30 PM -- 07:30 PM (PST) @ East Exhibition Hall B + C #92
in Deep Learning -- Optimization for Deep Networks »

The fundamental learning theory behind neural networks remains largely open. What classes of functions can neural networks actually learn? Why doesn't the trained network overfit when it is overparameterized?

In this work, we prove that overparameterized neural networks can learn some notable concept classes, including two and three-layer networks with fewer parameters and smooth activations. Moreover, the learning can be simply done by SGD (stochastic gradient descent) or its variants in polynomial time using polynomially many samples. The sample complexity can also be almost independent of the number of parameters in the network.

On the technique side, our analysis goes beyond the so-called NTK (neural tangent kernel) linearization of neural networks in prior works. We establish a new notion of quadratic approximation of the neural network, and connect it to the SGD theory of escaping saddle points.

Keywords: Optimization for Deep Networks · Deep Learning
[ Paper]  [ Slides] 

Author Information

Zeyuan Allen-Zhu (Microsoft Research)
Yuanzhi Li (Princeton)
Yingyu Liang (University of Wisconsin Madison)

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