Faster Directional Convergence of Linear Neural Networks under Spherically Symmetric Data

Part of Advances in Neural Information Processing Systems 34 (NeurIPS 2021)

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Dachao Lin, Ruoyu Sun, Zhihua Zhang


In this paper, we study gradient methods for training deep linear neural networks with binary cross-entropy loss. In particular, we show global directional convergence guarantees from a polynomial rate to a linear rate for (deep) linear networks with spherically symmetric data distribution, which can be viewed as a specific zero-margin dataset. Our results do not require the assumptions in other works such as small initial loss, presumed convergence of weight direction, or overparameterization. We also characterize our findings in experiments.