Deep symbolic regression for recurrence prediction
Stéphane D’Ascoli, Pierre-Alexandre Kamienny, Guillaume Lample, Francois Charton
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 $1.644934\approx \pi^2/6$.
BibTeX
@InProceedings{pmlr-v162-d-ascoli22a,
title = {Deep symbolic regression for recurrence prediction},
author = {D'Ascoli, St{\'e}phane and Kamienny, Pierre-Alexandre and Lample, Guillaume and Charton, Francois},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {4520--4536},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/d-ascoli22a/d-ascoli22a.pdf},
url = {https://proceedings.mlr.press/v162/d-ascoli22a.html},
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 $1.644934\approx \pi^2/6$.}
}