Deep symbolic regression for recurrence prediction

Stéphane D’Ascoli, Pierre-Alexandre Kamienny, Guillaume Lample, Francois Charton
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:4520-4536, 2022.

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 $1.644934\approx \pi^2/6$.

Cite this Paper

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 $1.644934\approx \pi^2/6$.} }
Endnote
%0 Conference Paper %T Deep symbolic regression for recurrence prediction %A Stéphane D’Ascoli %A Pierre-Alexandre Kamienny %A Guillaume Lample %A Francois Charton %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-d-ascoli22a %I PMLR %P 4520--4536 %U https://proceedings.mlr.press/v162/d-ascoli22a.html %V 162 %X 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 $1.644934\approx \pi^2/6$.
APA
D’Ascoli, S., Kamienny, P., Lample, G. & Charton, F.. (2022). Deep symbolic regression for recurrence prediction. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:4520-4536 Available from https://proceedings.mlr.press/v162/d-ascoli22a.html.

Related Material