AlphaIntegrator: Transformer Action Search for Symbolic Integration Proofs

We present the first correct-by-construction learning-based system for step-by-step mathematical integration. The key idea is to learn a policy, represented by a GPT transformer model, which guides the search for the right mathematical integration rule, to be carried out by a symbolic solver. Concretely, we introduce a symbolic engine with axiomatically correct actions on mathematical expressions, as well as the first dataset for step-by-step integration. Our GPT-style transformer model, trained on this synthetic data, demonstrates strong generalization by surpassing its own data generator in accuracy and efficiency, using 50% fewer search steps. Our experimental results with SoTA LLMs also demonstrate that the standard approach of fine-tuning LLMs on a set of question-answer pairs is insufficient for solving this mathematical task. This motivates the importance of discovering creative methods for combining LLMs with symbolic reasoning engines, of which our work is an instance. Large language models (LLMs) based on the transformer architecture (Vaswani et al., 2023) have demonstrated remarkable abilities across diverse tasks, such as language translation, code generation, and engaging human-like conversations (OpenAI, 2024). However, applying these models to mathematics presents significant challenges. Their autoregressive nature makes them prone to hallucinations and errors during inference.