GraphACT: An ACT-R-Inspired Verifier for Mathematical Reasoning

A fluent chain-of-thought (CoT) can contain local arithmetic errors. State of the art self-critique, extra sampling, and process-score driven architectures typically do not evaluate the calculation processes. GraphACT, our proposed ACT-R based evaluator-verifier architecture, provides a training-free loop around a frozen student generator (DeepSeek-R1-Distill-Qwen). While the generator produces an ordinary CoT; The ACT-R inspired verifier module - comprising a knowledge graph (ProofWiki) based declarative memory, a procedural checker (SymPy), a goal buffer, and a controller - extracts parseable equalities, checks them with SymPy, and either accepts the answer or calls the generator again with the failing identity named . A second generation-iteration is issued only when a violation occurs. Across a variety of databases (GSM8K, MATH-500, AIME), through different model sizes (1.5B, 14B and 32B) as the foundation of GraphACT and using greedy decoding, we were able to improve the first generation responses in all benchmarks after this verification loop. GraphACT uses fewer extra generator calls than the contemporary Self-Refine architecture on all of these traces. Ablation studies attribute this performance gain to the symbolic check and procedural intervention by the proposed architecture.