Reinforcement Learning for Symbolic Equation Solving
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Reinforcement Learning for Symbolic Equation Solving
Abstract:We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials, trigonometric) and a controlled class of restricted-open families requiring a change of variables (CoV) such as completing the square. We cast algebra as an MDP with a dynamic action space and a tree-structured policy (TreeMLP). The main policy learns from reward alone with no supervised solution traces; the CoV substitution comes from a supervised generator interchangeable with a CAS call. On closed equations the agent matches the prior best on CommonCore (0.93 greedy vs. ConPoLe's 0.925) under a single policy. On four hand-designed restricted-open families (quadratic, cubic, quartic, exponential) it reaches 0.79 beam / 0.67 greedy, exceeding the strongest non-learned search (A-star, 0.64). Learned CoV timing has content only on the exponential family, the one requiring a nested CoV, where a natural rule solves none of the held-out equations while the policy solves 75% from reward alone. At 10x scale a sharp seed-level bimodality emerges; a UCB learning-progress curriculum shows a non-significant positive trend toward mitigating it. We do not claim general open-equation solving: every open-equation result is confined to these four controlled families.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2608.30162 [cs.LG] |
| (or arXiv:2608.30162v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.30162
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems
Sep 14
-
Physics-Informed Conformal Prediction: Embedding PDE Consistency into Distribution-Free Uncertainty Quantification for Neural Operators
Sep 14
-
Fed-Equilibrium Framework for Topological Pareto Control in Robust and Fair Clinical Federated Learning
Sep 14
-
Efficient AI Model Deployment Using Quantization Analysis Tool
Sep 14
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.