arXiv：cs.LG· Jincheng Gao, Jiahe Yi, Shuo Sun·· 10 小时前
MorphingNet：网络本身即公式的符号回归方法
MorphingNet: Symbolic Regression Where the Network Is the Formula
AI 导读
MorphingNet 是一种网络单元函数可连续变化的符号回归（SR）网络，将函数形式作为参数训练，把符号回归变成单一连续优化问题。其单元为无极点有理函数或复指数—对数函数，训练全程网络即可读作公式，无需固定算子库，训练为稠密线性代数、GPU 友好；在 SRBench 上取得 SOTA 精度，大规模数据上比最强搜索方法快最多两个数量级。
正文
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.
| Comments: | 15 pages, 1 figure, 9 tables |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.19942 [cs.LG] |
| (or arXiv:2610.19942v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19942 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jincheng Gao [view email]
[v1]
Wed, 14 Oct 2026 10:26:08 UTC (61 KB)
来源：arXiv：cs.LG · arxiv.org