What makes math problems hard for reinforcement learning: a case study
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies.
Code (1)
Tasks
MathReinforcement Learning (RL)Similar Papers 제목 키워드 기반
What Makes Math Word Problems Challenging for LLMs?
This paper investigates the question of what makes math word problems (MWPs) in English challenging for large language models (LLMs). We conduct an in-depth analysis of the key linguistic and mathematical characteristics…
MathPeano: Learning Formal Mathematical Reasoning
General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables …
Automated Theorem ProvingMathematical ReasoningvalidReinforcement Learning Assisted Recursive QAOA
Variational quantum algorithms such as the Quantum Approximation Optimization Algorithm (QAOA) in recent years have gained popularity as they provide the hope of using NISQ devices to tackle hard combinatorial optimizati…
Combinatorial Optimizationreinforcement-learningReinforcement LearningReinforcement Learning (RL)Bad-Policy Density: A Measure of Reinforcement Learning Hardness
Reinforcement learning is hard in general. Yet, in many specific environments, learning is easy. What makes learning easy in one environment, but difficult in another? We address this question by proposing a simple measu…
reinforcement-learningReinforcement LearningReinforcement Learning (RL)LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions
Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. I…
LEMMAMathematical ReasoningVocal Bursts Intensity Prediction