用拓扑保护机制让大模型推理更稳定，避免幻觉
Robust Reasoning as a Symmetry-Protected Topological Phase
- 将逻辑推理视为非阿贝尔任意子编织的拓扑相，取代脆弱的几何插值
- 在百万级符号任务中，新模型推断精度在100倍外推下仍保持完美
- 该方法依赖非阿贝尔规范对称性，适合追求高可靠推理的场景
大型语言模型易受语义噪声影响而产生逻辑不一致（即‘幻觉’）。我们提出当前架构处于‘度量相’，其因果顺序易受自发对称性破缺影响。本文将鲁棒推理识别为一种对称性保护的拓扑相，其中逻辑操作形式上等价于非阿贝尔任意子的编织，以稳健的拓扑不变量替代脆弱的几何插值。实验表明存在明显的拓扑相变：Transformer与RNN呈现无能隙衰减，而我们的全息网络展现出宏观‘质量间隙’，在临界噪声阈值以下保持恒定保真度。在$S_{10}$（3.6 × 10⁶状态）上的可变绑定任务中，该拓扑模型实现全息泛化——从训练长度$L=50$外推至$5000$仍保持完美保真度，与理论上无限因果视域一致；而Transformer则丧失逻辑一致性。消融研究显示，这种保护严格源于非阿贝尔规范对称性。这为逻辑推理提供了新的普适类证据，将因果稳定性与语义流形的拓扑结构相联系。
原文摘要 · Abstract (English)
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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