FactorLibrary: From Polynomials to Circuits via Recursive Subgoals

📰 ArXiv cs.AI

Learn how FactorLibrary uses reinforcement learning to find minimal arithmetic circuits for polynomials over finite fields, and apply this to your own problems

advanced Published 25 Jun 2026

Action Steps

Formulate your problem as a reinforcement learning problem using both bottom-up and top-down approaches
Implement FactorLibrary to store and reuse factorizable subexpressions as subgoals
Train a reinforcement learning model using FactorLibrary to find minimal arithmetic circuits
Apply the learned circuits to your specific problem domain
Evaluate and refine the performance of the FactorLibrary approach

Who Needs to Know This

Researchers and engineers working on algebraic complexity theory, reinforcement learning, and circuit optimization will benefit from this approach, as it provides a new way to tackle combinatorially hard problems

Key Insight

💡 Using reinforcement learning with a library of reusable subgoals can efficiently solve combinatorially hard problems in algebraic complexity theory

Key Takeaways

Learn how FactorLibrary uses reinforcement learning to find minimal arithmetic circuits for polynomials over finite fields, and apply this to your own problems

Full Article

Title: FactorLibrary: From Polynomials to Circuits via Recursive Subgoals

Abstract:
arXiv:2606.25394v1 Announce Type: cross Abstract: Finding minimal arithmetic circuits for polynomials over finite fields is a combinatorially hard problem central to algebraic complexity theory. We formulate it as a reinforcement learning problem in two directions, bottom-up and top-down. To address the challenge of a fast-growing combinatorial search space, we introduce FactorLibrary, which stores factorizable subexpressions that serve as reusable subgoals across training episodes. We trained a

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