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Poster
Limitations of Lazy Training of Two-layers Neural Network
Behrooz Ghorbani · Song Mei · Theodor Misiakiewicz · Andrea Montanari

Wed Dec 11 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #230
in Theory -- Learning Theory »

We study the supervised learning problem under either of the following two models: (1) Feature vectors xi are d-dimensional Gaussian and responses are yi = f*(xi) for f* an unknown quadratic function; (2) Feature vectors xi are distributed as a mixture of two d-dimensional centered Gaussians, and y_i's are the corresponding class labels. We use two-layers neural networks with quadratic activations, and compare three different learning regimes: the random features (RF) regime in which we only train the second-layer weights; the neural tangent (NT) regime in which we train a linearization of the neural network around its initialization; the fully trained neural network (NN) regime in which we train all the weights in the network. We prove that, even for the simple quadratic model of point (1), there is a potentially unbounded gap between the prediction risk achieved in these three training regimes, when the number of neurons is smaller than the ambient dimension. When the number of neurons is larger than the number of dimensions, the problem is significantly easier and both NT and NN learning achieve zero risk.

Keywords: Theory · Algorithms -> Kernel Methods; Theory -> Hardness of Learning and Approximations; Theory -> Learning Theory; Theory · Spaces of
[ Paper]  [ Slides] 

Author Information

Behrooz Ghorbani (Stanford University)
Song Mei (Stanford University)
Theodor Misiakiewicz (Stanford University)
Andrea Montanari (Stanford)

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