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MorphingNet advances symbolic regression by treating function forms as continuous trainable parameters, enabling the network to seamlessly transition between mathematical operations like exponentials and sinusoids during optimization. This approach transforms formula discovery into a dense linear algebra problem, offering significant speedups over traditional search methods while maintaining high accuracy on scientific benchmarks. By eliminating the need for fixed operator libraries, this method provides a novel paradigm for extracting interpretable equations directly from data.
MorphingNet: Symbolic Regression Where the Network Is the Formula
arXiv:2610.19942v1 Announce Type: new Abstract: We introduce MorphingNet, a network for symbolic regression (SR) whose units change their function continuously. Instead of searching over expressions built from a fixed operator library, MorphingNet trains the form of each function as a parameter, so SR becomes one continuous optimization problem. Its units are either pole-free rational functions or complex exponential--logarithm functions, which move between exponentials, sinusoids, damped oscillations, power laws and logarithms as their parameters change. The network is a readable formula at every step of training, and no operator library is needed to train it; a structure-recovery step afterwards rewrites the trained formula into short elementary expressions. Training is dense linear algebra, so it is GPU-friendly and scales to large data. MorphingNet achieves state-of-the-art accuracy on SRBench, recovers most generating formulas on synthetic benchmarks, and on large data is up to two orders of magnitude faster than the strongest search method. By turning the search for a formula into the training of a network, MorphingNet offers a new paradigm for SR and for scientific discovery from data.
Abstract:We introduce MorphingNet, a network for symbolic regression (SR) whose units change their function continuously. Instead of searching over expressions built from a fixed operator library, MorphingNet trains the form of each function as a parameter, so SR becomes one continuous optimization problem. Its units are either pole-free rational functions or complex exponential--logarithm functions, which move between exponentials, sinusoids, damped oscillations, power laws and logarithms as their parameters change. The network is a readable formula at every step of training, and no operator library is needed to train it; a structure-recovery step afterwards rewrites the trained formula into short elementary expressions. Training is dense linear algebra, so it is GPU-friendly and scales to large data. MorphingNet achieves state-of-the-art accuracy on SRBench, recovers most generating formulas on synthetic benchmarks, and on large data is up to two orders of magnitude faster than the strongest search method. By turning the search for a formula into the training of a network, MorphingNet offers a new paradigm for SR and for scientific discovery from data.
Machine Learning (cs.LG)
arXiv:2610.19942 [cs.LG]
(or arXiv:2610.19942v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.19942 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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