Training invariances and the low-rank phenomenon: beyond linear networks.

Wednesday, April 6, 2022 - 4:00pm to 4:30pm

Event Calendar Category

LIDS & Stats Tea

Speaker Name

Thien Le



Building and Room Number

LIDS Lounge


The implicit bias induced by the training of neural networks has become a topic of rigorous study. In the limit of gradient flow and gradient descent with appropriate step size, it has been shown that when one trains a deep linear network with logistic or exponential loss on linearly separable data, the weights converge to rank-1matrices. In this paper, we extend this theoretical result to the last few linear layers of the much wider class of nonlinear ReLU-activated feedforward networks containing fully-connected layers and skip connections. Similar to the linear case, the proof relies on specific local training invariances, sometimes referred to as alignment, which we show to hold for submatrices where neurons are stably-activated in all training examples, and it reflects empirical results in the literature. We also show this is not true in general for the full matrix of ReLU fully-connected layers. Our proof relies on a specific decomposition of the network into a multilinear function and another ReLU network whose weights are constant under a certain parameter directional convergence.


Thien Le is a third-year PhD graduate student in EECS under prof Stefanie Jegelka. Before MIT, he obtained his bachelor in Mathematics & Computer Science from UIUC in 2019. His research direction is currently in theoretical foundations of machine learning, especially deep learning, but he is also interested in theoretical aspects of computational biology.