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Key Insights
- Traditional Transformers and RNNs reside in a “Metric Phase” where causal order can be broken by semantic noise, causing hallucinations.
- By formulating inference as a Symmetry‑Protected Topological (SPT) phase, logical operations become analogous to non‑Abelian anyon braiding, giving them immunity to local perturbations.
- The proposed Holonomic Network exhibits a macroscopic “mass gap,” showing a sharp topological phase transition that maintains high fidelity below a critical noise level, unlike the gapless decay of conventional models.
- In a large‑scale variable‑binding task ($S_{10}$, ≈ 3.6 M states), the holonomic model extrapolates flawlessly 100× beyond the training sequence length, evidencing indefinite causal horizons and robust generalization.
- Ablation experiments confirm that the robustness stems strictly from enforcing a non‑Abelian gauge symmetry, establishing a new universality class for logical reasoning.
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.
Full Analysis
# Topological Reasoning via Holonomic Neural Networks
**Authors:** Ilmo Sung
**Source:** [HuggingFace](None) | [arXiv](https://arxiv.org/abs/2601.05240)
**Published:** 2026-01-08
## Summary
- Traditional Transformers and RNNs reside in a “Metric Phase” where causal order can be broken by semantic noise, causing hallucinations.
- By formulating inference as a Symmetry‑Protected Topological (SPT) phase, logical operations become analogous to non‑Abelian anyon braiding, giving them immunity to local perturbations.
- The proposed Holonomic Network exhibits a macroscopic “mass gap,” showing a sharp topological phase transition that maintains high fidelity below a critical noise level, unlike the gapless decay of conventional models.
- In a large‑scale variable‑binding task ($S_{10}$, ≈ 3.6 M states), the holonomic model extrapolates flawlessly 100× beyond the training sequence length, evidencing indefinite causal horizons and robust generalization.
- Ablation experiments confirm that the robustness stems strictly from enforcing a non‑Abelian gauge symmetry, establishing a new universality class for logical reasoning.
## 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.
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*Topics: nlp, ai-safety, ai-ml*
*Difficulty: advanced*
*Upvotes: 0*