BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction
2026-06-03 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors address the problem of solving geometry questions using artificial intelligence, which is tricky because current methods either lack flexibility or make mistakes easily. They note that previous systems pass information in only one direction—from a neural network to a symbolic solver—without checking back, which can cause errors. To improve this, the authors created BiNSGPS, a system where a language model and a symbolic solver communicate back and forth. This interaction helps fix mistakes early and supports solving harder problems by sharing feedback.
geometry problem solvingartificial intelligencesymbolic methodsneural methodsneuro-symbolic systemslarge language models (LLM)bidirectional interactionsymbolic solvermachine learning feedback loops
Authors
Qi Wang, Peijie Wang, Fei Yin, Cheng-Lin Liu
Abstract
Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions.