Learning Fast Monomial Orders for Gr"obner Basis Computations

arXiv:2602.02972 · cs.SC, cs.LG, math.AC, math.AG · Submitted 2026-02-03 · Read on arXiv

cs.SC, cs.LG, math.AC, math.AG

Submitted: 2026-02-03

Updated: 2026-08-28

Comments: added more experiments against baselines, corrected a few typos and cosmetics

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reinforcement Learning — 19× in this paper · explained in 4 episodes
• Actor — 15× in this paper · explained in 3 episodes
• Distillation — 10× in this paper · explained in 2 episodes
• Trace — 6× in this paper · explained in 2 episodes
• Symbolic Regression — 5× in this paper · explained in 5 episodes
• Benchmark — 4× in this paper · explained in 2 episodes
• Calibration — 4× in this paper · explained in 7 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Action Space — 3× in this paper · explained in 1 episode
• Deep Reinforcement Learning — 3× in this paper · explained in 2 episodes
• Reward Function — 3× in this paper · explained in 2 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Conservation Laws — 2× in this paper · explained in 3 episodes
• Gaussian Error Linear Unit — 2× in this paper
• Generalization — 2× in this paper · explained in 13 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Elias — 1× in this paper · explained in 2 episodes
• GNNs — 1× in this paper · explained in 2 episodes
• GRPO — 1× in this paper · explained in 6 episodes
• Graph Neural Networks (GNNs) — 1× in this paper · explained in 7 episodes
• Group Relative Policy Optimization (GRPO) — 1× in this paper · explained in 5 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Transformer Models — 1× in this paper · explained in 2 episodes

Sources

• Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl
• Parameter regions that give rise to 2[n/2]+1 positive steady states in the n-site phosphorylation system
• Gaussian Error Linear Units (GELUs)
• Predicting the cardinality and maximum degree of a reduced Gr\"obner basis
• Geometric Generality of Transformer-Based Gr\"obner Basis Computation
• Prioritized Experience Replay
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

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