Controllable Neural Symbolic Regression

TL;DR

This paper introduces NSRwH, a neural symbolic regression method that incorporates user-defined prior knowledge to improve accuracy and control over predicted expressions, addressing limitations of existing NSR algorithms.

Contribution

The paper presents a novel neural symbolic regression approach that allows explicit integration of prior structural assumptions into the prediction process.

Findings

NSRwH outperforms unconditioned models in accuracy.

The method provides control over the structure of predicted expressions.

Experimental results validate the effectiveness of incorporating prior knowledge.

Abstract

In symbolic regression, the goal 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.