A Principle of Least Action for the Training of Neural Networks
| Autor: | Karkar, Skander, Ayed, Ibrahim, de Bézenac, Emmanuel, Gallinari, Patrick |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Neural networks have been achieving high generalization performance on many tasks despite being highly over-parameterized. Since classical statistical learning theory struggles to explain this behavior, much effort has recently been focused on uncovering the mechanisms behind it, in the hope of developing a more adequate theoretical framework and having a better control over the trained models. In this work, we adopt an alternate perspective, viewing the neural network as a dynamical system displacing input particles over time. We conduct a series of experiments and, by analyzing the network's behavior through its displacements, we show the presence of a low kinetic energy displacement bias in the transport map of the network, and link this bias with generalization performance. From this observation, we reformulate the learning problem as follows: finding neural networks which solve the task while transporting the data as efficiently as possible. This offers a novel formulation of the learning problem which allows us to provide regularity results for the solution network, based on Optimal Transport theory. From a practical viewpoint, this allows us to propose a new learning algorithm, which automatically adapts to the complexity of the given task, and leads to networks with a high generalization ability even in low data regimes. Comment: ECML PKDD 2020 |
| Databáze: | arXiv |
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