Controllable Neural Symbolic Regression

Tommaso Bendinelli, Luca Biggio, Pierre-Alexandre Kamienny
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:2063-2077, 2023.

Abstract

In symbolic regression, the objective is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-bendinelli23a, title = {Controllable Neural Symbolic Regression}, author = {Bendinelli, Tommaso and Biggio, Luca and Kamienny, Pierre-Alexandre}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {2063--2077}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/bendinelli23a/bendinelli23a.pdf}, url = {https://proceedings.mlr.press/v202/bendinelli23a.html}, abstract = {In symbolic regression, the objective is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.} }
Endnote
%0 Conference Paper %T Controllable Neural Symbolic Regression %A Tommaso Bendinelli %A Luca Biggio %A Pierre-Alexandre Kamienny %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-bendinelli23a %I PMLR %P 2063--2077 %U https://proceedings.mlr.press/v202/bendinelli23a.html %V 202 %X In symbolic regression, the objective is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.
APA
Bendinelli, T., Biggio, L. & Kamienny, P.. (2023). Controllable Neural Symbolic Regression. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:2063-2077 Available from https://proceedings.mlr.press/v202/bendinelli23a.html.

Related Material