VaSST: Variational Inference for Symbolic Regression using Soft Symbolic Trees

Somjit Roy, Pritam Dey, Bani Mallick
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:5790-5844, 2026.

Abstract

Symbolic regression (SR) has gained recent traction in {AI}-driven scientific discovery for learning closed-form physical laws. Yet existing methods are dominated by heuristic search or data-intensive approaches that often assume low-noise regimes and lack principled uncertainty quantification, while fully probabilistic SR formulations remain scarce. We introduce a scalable probabilistic framework for SR, {VaSST}, based on variational inference. {VaSST} uses soft symbolic trees, a continuous relaxation of symbolic expression trees in which discrete operator and feature assignments are replaced by probability distributions over allowable components. This transforms combinatorial symbolic search through an astronomically large expression space into efficient gradient-based optimization while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling uncertainty quantification across plausible symbolic forms through posterior-aware symbolic model selection. On simulated experiments and the {Feynman} Symbolic Regression Database, {VaSST} achieves strong structural recovery and predictive accuracy compared to state-of-the-art competing SR methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-roy26a, title = {{VaSST}: Variational Inference for Symbolic Regression using Soft Symbolic Trees}, author = {Roy, Somjit and Dey, Pritam and Mallick, Bani}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {5790--5844}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/roy26a/roy26a.pdf}, url = {https://proceedings.mlr.press/v337/roy26a.html}, abstract = {Symbolic regression (SR) has gained recent traction in {AI}-driven scientific discovery for learning closed-form physical laws. Yet existing methods are dominated by heuristic search or data-intensive approaches that often assume low-noise regimes and lack principled uncertainty quantification, while fully probabilistic SR formulations remain scarce. We introduce a scalable probabilistic framework for SR, {VaSST}, based on variational inference. {VaSST} uses soft symbolic trees, a continuous relaxation of symbolic expression trees in which discrete operator and feature assignments are replaced by probability distributions over allowable components. This transforms combinatorial symbolic search through an astronomically large expression space into efficient gradient-based optimization while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling uncertainty quantification across plausible symbolic forms through posterior-aware symbolic model selection. On simulated experiments and the {Feynman} Symbolic Regression Database, {VaSST} achieves strong structural recovery and predictive accuracy compared to state-of-the-art competing SR methods.} }
Endnote
%0 Conference Paper %T VaSST: Variational Inference for Symbolic Regression using Soft Symbolic Trees %A Somjit Roy %A Pritam Dey %A Bani Mallick %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-roy26a %I PMLR %P 5790--5844 %U https://proceedings.mlr.press/v337/roy26a.html %V 337 %X Symbolic regression (SR) has gained recent traction in {AI}-driven scientific discovery for learning closed-form physical laws. Yet existing methods are dominated by heuristic search or data-intensive approaches that often assume low-noise regimes and lack principled uncertainty quantification, while fully probabilistic SR formulations remain scarce. We introduce a scalable probabilistic framework for SR, {VaSST}, based on variational inference. {VaSST} uses soft symbolic trees, a continuous relaxation of symbolic expression trees in which discrete operator and feature assignments are replaced by probability distributions over allowable components. This transforms combinatorial symbolic search through an astronomically large expression space into efficient gradient-based optimization while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling uncertainty quantification across plausible symbolic forms through posterior-aware symbolic model selection. On simulated experiments and the {Feynman} Symbolic Regression Database, {VaSST} achieves strong structural recovery and predictive accuracy compared to state-of-the-art competing SR methods.
APA
Roy, S., Dey, P. & Mallick, B.. (2026). VaSST: Variational Inference for Symbolic Regression using Soft Symbolic Trees. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:5790-5844 Available from https://proceedings.mlr.press/v337/roy26a.html.

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