Training Linear Neural Networks: Non-Local Convergence and Complexity Results

Jul 12, 2020

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Linear networks provide valuable insight into the workings of neural networks in general. In this paper, we improve the state of the art in (Bah et al., 2019) by identifying conditions under which gradient flow successfully trains a linear network, in spite of the non-strict saddle points present in the optimization landscape. We also improve the state of the art for computational complexity of training linear networks in (Arora et al., 2018a) by establishing non-local linear convergence rates for gradient flow. Crucially, these new results are not in the lazy training regime, cautioned against in (Chizat et al., 2019; Yehudai Shamir, 2019). Our results require the network to have a layer with one neuron, which corresponds to the popular spiked covariance model in statistics, and subsumes the important case of networks with a scalar output. Extending these results to all linear networks remains an open problem.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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