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On the theoretical limit of gradient descent for Simple Recurrent Neural Networks with finite precision | ||
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Volodimir Mitarchuk · Rémi Emonet · Remi Eyraud · Amaury Habrard | ||
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Despite their great practical successes, the understanding of neural network behavior is still | ||
a topical research issue. In particular, the class of functions learnable in the context of a | ||
finite precision configuration is an open question. In this paper, we propose to study the | ||
limits of gradient descent when such a configuration is set for the class of Simple Recurrent | ||
Networks (SRN). We exhibit conditions under which the gradient descend will provably fail. | ||
We also design a class of SRN based on Deterministic finite State Automata (DFA) that | ||
fulfills the failure requirements. The definition of this class is constructive: we propose an | ||
algorithm that, from any DFA, constructs a SRN that computes exactly the same function, | ||
a result of interest by its own. | ||
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