Deep Divide-and-Reduce in Symbolic Regression
-cross Abstract: Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability.
Arxiv 2 versions
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Deep Divide-and-Reduce in Symbolic Regression
-cross Abstract: Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability. Most existing learning-based SR methods primarily optimize expressions from observations without explicitly exploiting their structural mathematical properties. AI Feynman introduced a complementary paradigm that leverages such properties to recursively decompose complex expressions, but its decomposition criteria cover only restricted structural forms and its treatment of nested composition can require brute-force search over candidate sub-expressions. Building on this paradigm, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a mathematically grounded framework that systematically generalizes expression decomposition and variable reduction. DDRSR extends translational symmetry to coefficient- and exponent-interfered forms, enables variable separation under overlapping variables and additive constant offsets, and generalizes the identification of nested compositional structures. We further characterize an intrinsic non-identifiability limitation of decomposition when no effective variable separation is induced. Experiments across multiple symbolic regression algorithms and benchmark datasets show that DDRSR identifies a broader range of decomposable structures than AI Feynman and overall improves downstream regression accuracy and exact-expression recovery.
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Deep Divide-and-Reduce in Symbolic Regression
-cross Abstract: Symbolic regression (SR) is the task of discovering underlying patterns from data and representing them using mathematical expressions. Current machine learning approaches to SR often lack a profound understanding of the intrinsic mathematical and physical principles governing these expressions. While the pioneering AI Feynman method leverages the mathematical properties underlying the data, its expression decomposition mechanism suffers from a narrow scope of applicability and is prone to failure on complex equations. Furthermore, its underlying mechanisms rely heavily on brute-force searches for sub-expressions, severely limiting its practical utility. Building on AI Feynman, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a principled extension derived from a formal analysis of a broader class of decomposition structures. DDRSR fundamentally broadens the applicability of expression decomposition and reduction and ensures both wider versatility and sound analytical grounding. Empirical evaluations demonstrate that these theoretical principles yield substantial advantages in both expression decomposition and downstream symbolic regression performance. Finally, we discuss the applicable scenarios and inherent limitations of this paradigm, alongside promising directions for future research.
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U.S. Navy. Naval Aerospace Medical Research Laboratory · Public domain · Wikimedia Commons · illustrativeWhat happened
-cross Abstract: Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability. Most existing learning-based SR methods primarily optimize expressions from observations without explicitly exploiting their structural mathematical properties. AI Feynman introduced a complementary paradigm that leverages such properties to recursively decompose complex expressions, but its decomposition criteria cover only restricted structural forms and its treatment of nested composition can require brute-force search over candidate sub-expressions.
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