Hallucinations in Chain-of-Thought (CoT) reasoning can be detected as 'topological phase transitions' where the logical invariant of the reasoning trace collapses.

Motivation

Current hallucination detection relies on uncertainty estimation or consistency checks, which are themselves probabilistic. If reasoning is a topological phase, a logical error (hallucination) should manifest as a sharp discontinuity or a break in the symmetry protection, offering a deterministic signal for detecting errors in generated text.

Proposed Method

Treat the hidden states of an LLM generating a CoT sequence as a trajectory on a manifold. Train a binary classifier (discriminator) based on the Holonomic formulation to calculate the 'Berry phase' (geometric phase) of the trajectory. Test if valid reasoning preserves a specific topological invariant while hallucinations result in a phase slip. Apply this as a reward model in RLHF to penalize topologically trivial (illogical) outputs.

Expected Contribution

A theoretically grounded, deterministic metric for hallucination detection that moves beyond statistical probability, potentially solving the reliability issues in autonomous agents.

Required Resources

High-quality CoT datasets with annotated errors, mathematical expertise in topology/physics, standard ML training infrastructure.

Source Paper

Robust Reasoning as a Symmetry-Protected Topological Phase

View Paper Details →