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Deep symbolic regression for recurrence prediction

St├ęphane d'Ascoli · Pierre-Alexandre Kamienny · Guillaume Lample · Francois Charton

Hall E #433

Keywords: [ DL: Attention Mechanisms ] [ DL: Sequential Models, Time series ] [ APP: Time Series ] [ DL: Algorithms ] [ DL: Everything Else ]

Abstract: Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers or floats, a typical task in human IQ tests which has hardly been tackled in the machine learning literature. We evaluate our integer model on a subset of OEIS sequences, and show that it outperforms built-in Mathematica functions for recurrence prediction. We also demonstrate that our float model is able to yield informative approximations of out-of-vocabulary functions and constants, e.g. $\operatorname{bessel0}(x)\approx \frac{\sin(x)+\cos(x)}{\sqrt{\pi x}}$ and $1.644934\approx \pi^2/6$.

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