BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction

BiNSGPS introduces a bidirectional neuro-symbolic framework that enables dynamic feedback loops between machine learning models and symbolic solvers for geometry problem-solving. Unlike traditional unidirectional approaches, this system allows the neural component to actively incorporate feedback and correct errors, addressing fundamental limitations in AI's ability to solve complex geometric reasoning tasks.

BiNSGPS represents a meaningful advance in addressing a core challenge within AI systems: the gap between neural networks' pattern-matching capabilities and symbolic reasoning's logical rigor. Geometry problem-solving has historically exposed the weaknesses of both paradigms independently—neural methods generate plausible but sometimes incorrect outputs, while symbolic approaches lack the contextual understanding and flexibility that machine learning models provide. The bidirectional interaction model proposed here attempts to bridge this divide through active feedback mechanisms, where symbolic constraints inform neural outputs in real-time rather than operating as a one-way pipeline. This architectural innovation directly addresses brittleness that emerges when early errors propagate uncorrected through traditional neuro-symbolic systems. The framework's capacity to dynamically rectify inconsistent representations and propose auxiliary hypotheses suggests meaningful progress toward more robust AI reasoning systems. For the broader AI research community, this work signals growing recognition that hybrid approaches require genuine two-way communication rather than sequential processing. The implications extend beyond geometry into domains requiring complex reasoning under formal constraints, including engineering, physics simulation, and automated theorem proving. Developers building reasoning-dependent applications may benefit from this framework's approach to error correction and conflict resolution. The research establishes that feedback mechanisms can substantially improve system reliability compared to unidirectional architectures, potentially influencing how future neuro-symbolic systems are designed across multiple application domains.

• →BiNSGPS enables bidirectional feedback between neural and symbolic components, eliminating unidirectional pipeline brittleness
• →The MLLM Adviser can dynamically correct formal representations and resolve symbolic conflicts in real-time
• →Hybrid neuro-symbolic systems with feedback mechanisms demonstrate superior error handling compared to sequential architectures
• →Geometry problem-solving serves as a testbed for broader reasoning tasks requiring formal constraint satisfaction
• →The framework addresses fundamental limitations where neural hallucinations and symbolic inflexibility both constrain AI performance