A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We formally define the notion of incremental learning dynamics and derive the conditions on depth and initialization for which this phenomenon arises in deep linear models. Our main theoretical contribution is a dynamical depth separation result, proving that while shallow models can exhibit incremental learning dynamics, they require the initialization to be exponentially small for these dynamics to present themselves. However, once the model becomes deeper, the dependence becomes polynomial and incremental learning can arise in more natural settings. We complement our theoretical findings by experimenting with deep matrix sensing, quadratic neural networks and with binary classification using diagonal and convolutional linear networks, showing all of these models exhibit incremental learning.
|Published - 2020
|8th International Conference on Learning Representations, ICLR 2020 - Addis Ababa, Ethiopia
Duration: 30 Apr 2020 → …
|8th International Conference on Learning Representations, ICLR 2020
|30/04/20 → …
Bibliographical noteFunding Information:
This research is supported by the European Research Council (TheoryDL project).
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