Neural-Symbolic Consensus: Eradicating Logical and Physical Hallucinations in Large Language Models via Formal Invariant Injection

This article introduces the groundbreaking hybrid architecture of Neural-Symbolic Consensus, which fundamentally eliminates hallucination issues in large language models' logical reasoning and physical simulation by injecting mathematical invariants and physical laws into neural network training. This framework combines the expressive power of neural networks with the strict rules of symbolic reasoning, providing a new solution for AI reliability.

Current mainstream large language models (such as GPT-4, Claude) rely on probabilistic statistical reasoning and lack an inherent 'logical compass', hence being called 'stochastic parrots'. They tend to generate hallucinations when dealing with complex mathematical calculations, logical reasoning, or physical simulations: examples include inconsistent results when swapping the order of large number multiplication, inventing non-existent database customer IDs, and predicting trajectories that violate Newton's laws.

The Neural-Symbolic Consensus framework combines neural networks (perception and pattern recognition) with symbolic systems (logical verification and constraint enforcement). The core is 'invariant injection'—embedding mathematical/physical invariants as training constraints into the model. Technical components include: the neural perception model JointPerceptionModel built with PyTorch, the symbolic reasoning component DatabaseSandbox (database sandbox), and the hybrid monitoring component (NeuroSymbolicCoddLoss loss function and LatentSpaceInspector).

The effect is validated through four cases: 1. Algebraic Commutative Law: Consistent results when swapping the order of large number multiplication, with Frobenius divergence of 0; 2. Database Integrity: Orphan ID violation rate reduced from 33% to 0%; 3. Relational Independence: Enforcing the Fourth Normal Form, with multi-valued dependency divergence approaching 0; 4. Physical Laws: Mean squared error of object falling simulation plummets to 0, complying with Newton's laws.

The experiment uses out-of-distribution (OOD) data (large prime tensors) and active corruption scenarios (injecting 33% incorrect IDs); the architecture uses a feedforward neural network + composite loss function; the 'Obsidian Tree' mechanism is introduced to dynamically modify symbolic constraints, ensuring the model's generalization ability instead of memorizing static examples.

This framework marks an important milestone in AI reliability research and can be deployed in trustworthy AI systems (financial transactions, autonomous driving, medical reasoning, etc.). In the future, it can be extended to fields such as chemical molecular design, legal reasoning, and engineering design, becoming an AI design philosophy of 'both intelligent and rule-abiding'.