Efficient Neural Clause-Selection Reinforcement (2503.07792v2)

Abstract: Clause selection is arguably the most important choice point in saturation-based theorem proving. Framing it as a reinforcement learning (RL) task is a way to challenge the human-designed heuristics of state-of-the-art provers and to instead automatically evolve -- just from prover experiences -- their potentially optimal replacement. In this work, we present a neural network architecture for scoring clauses for clause selection that is powerful yet efficient to evaluate. Following RL principles to make design decisions, we integrate the network into the Vampire theorem prover and train it from successful proof attempts. An experiment on the diverse TPTP benchmark finds the neurally guided prover improve over a baseline strategy, from which it initially learns -- in terms of the number of in-training-unseen problems solved under a practically relevant, short CPU instruction limit -- by 20%.

Efficient Neural Clause-Selection Reinforcement: An Overview

The paper "Efficient Neural Clause-Selection Reinforcement" authored by Martin Suda presents a neural network architecture tailored to improve clause selection within saturation-based theorem proving. A key aspect of the paper is the framing of clause selection as a reinforcement learning task, aiming to replace human-designed heuristics in state-of-the-art provers with a potentially more optimal strategy evolved from prover experiences.

Core Contributions

1. Neural Architecture for Clause Scoring: The paper introduces a neural network architecture that efficiently scores clauses for selection during saturation, balancing power and evaluative efficiency. It's integrated into the Vampire theorem prover and trained using reinforcement learning principles from successful proof attempts.
2. Experimental Validation: Using the TPTP benchmark, the neurally guided prover demonstrated notable improvements, solving unseen problems during training with a \SI{20}{\percent} increase in efficiency compared to a baseline strategy.

Technical Approach

The approach starts by analyzing the clause selection heuristic as an RL agent, embedding a neural architecture into Vampire, a leading ATP system. The RL perspective motivates the design of an agent that learns clause selection strategies devoid of evolving state dependencies, providing a mostly uniform treatment of clauses independent of the dynamic state traditionally involved in saturation-based proving.

State and Actions

• "Stateless" Environment: The system assumes a "stateless" environment, focusing solely on immediate rewards, i.e., clauses that are part of the proof receive rewards while non-proof clauses do not. The neural model assigns a score to each passive clause, emphasizing efficient processing without reliance on complex state transitions throughout derivations.
• Clause Selection Mechanism: Actions are equated with selecting one clause from the passive set for activation; a core decision point in saturation loops. The neural architecture endeavors to optimally score these actions, with its efficacy validated against baseline heuristics.

Learning Strategy

The proposed RL-inspired learning operator derives from policy gradient methods, implementing a mechanism akin to REINFORCE. It utilizes the concept of logits normalized via softmax to construct a probabilistic view of clause selection, although the implementation of clause selection is deterministic for efficiency reasons.

Through iterative updates informed by traces of prior successful proofs, this operator incrementally refines the neural architecture's performance. Reflecting RL's trial-and-error learning, it captures each snapshot of clause selection within a trace as independent training data, permitting more granular learning compared to traditional supervised learning methods. The operator fosters generalization across diverse logic forms, particularly within the varied TPTP dataset.

Empirical Findings

The experimental setup employs the TPTP library's first-order problems, demonstrating that the trained neural model leads to substantial improvements over Vampire's default strategy. Even within the diverse TPTP context, traditionally challenging for ML-guided methods due to encoding variety, the new architecture robustly enhances problem-solving capability. The significant jump in performance not only showcases improved clause selection efficacy but also signifies the role of learned heuristics in surpassing any pre-established, human-centric strategies within theorem proving.

Future Outlook

The research opens prospects for exploring broader implications of using reinforcement learning in ATP systems:

• Strategy Schedules and Broader Integration: Beyond single-heuristic improvements, strategy schedules leveraging multiple RL-trained models could represent a strategic frontier in enhancing ATP systems' utility across diverse domains.
• Transfer Learning: Given the encouraging results within TPTP, there exists potential for the neural-guided approach to benefit theorem provers facing other benchmarks such as Mizar40, offering insights into cross-benchmark adaptability.

Conclusion

Martin Suda's framework pushes the frontier of ML for theorem proving, evolving from successful methodologies to fresh performance heights. By advancing the narrative around efficiency in neural clause selection, the research imparts substantial methodological innovations set to impact both theoretical constructs and practical applications within the field of automated theorem proving.