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Paper · 2009.08372 · 2020

A Principle of Least Action for the Training of Neural Networks

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 1 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
skander-karkar/LAP canonical 1 of 3
FunctionStatusWhere it lives
create_autoencoder Ran skander-karkar/LAP/utils.py
pointer only (licence: NONE) · get_code("65f72dfc4a9db1bf")
create_classifier Not yet run skander-karkar/LAP/utils.py
pointer only (licence: NONE) · get_code("b3f58f8ed60a82d6")
topkaccuracy Not yet run skander-karkar/LAP/utils.py
pointer only (licence: NONE) · get_code("7d5c66f6d4b651d5")

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Abstract

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.

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