Robust Reasoning as a Symmetry-Protected Topological Phase

TL;DR

This paper introduces a topological framework for robust reasoning in neural networks, demonstrating that symmetry-protected topological phases can prevent logical hallucinations and improve generalization in symbolic tasks.

Contribution

It proposes a novel topological phase model for reasoning, showing how non-Abelian symmetry provides robustness against semantic noise in neural architectures.

Findings

Holonomic Network exhibits a macroscopic mass gap, maintaining fidelity under noise.

Topological model generalizes perfectly beyond training data, unlike Transformers.

Protection arises strictly from non-Abelian gauge symmetry.

Abstract

Large language models suffer from "hallucinations"-logical inconsistencies induced by semantic noise. We propose that current architectures operate in a "Metric Phase," where causal order is vulnerable to spontaneous symmetry breaking. Here, we identify robust inference as an effective Symmetry-Protected Topological phase, where logical operations are formally isomorphic to non-Abelian anyon braiding, replacing fragile geometric interpolation with robust topological invariants. Empirically, we demonstrate a sharp topological phase transition: while Transformers and RNNs exhibit gapless decay, our Holonomic Network reveals a macroscopic "mass gap," maintaining invariant fidelity below a critical noise threshold. Furthermore, in a variable-binding task on $S_{10}$ ($3.6 \times 10^6$ states) representing symbolic manipulation, we demonstrate holonomic generalization: the topological model maintains perfect fidelity extrapolating $100\times$ beyond training ($L=50 \to 5000$), consistent with a theoretically indefinite causal horizon, whereas Transformers lose logical coherence. Ablation studies indicate this protection emerges strictly from non-Abelian gauge symmetry. This provides strong evidence for a new universality class for logical reasoning, linking causal stability to the topology of the semantic manifold.