Natural language reasoning can be stabilized by enforcing approximate gauge symmetries corresponding to semantic equivalence classes (e.g., paraphrasing, entity swapping) via a 'Semantic Holonomy' loss.

Motivation

The original paper demonstrates robustness in discrete symbolic domains. However, natural language lacks exact symmetries; extending the topological protection to language requires defining 'soft' symmetries where paraphrased inputs preserve the topological sector of the latent state, preventing semantic drift.

Proposed Method

Develop a 'Topological Adapter' for a standard LLM (e.g., Llama-3). Construct a dataset of logical problems with massive surface-form variations (paraphrases). During fine-tuning, implement a loss function that minimizes the geometric phase (holonomy) accumulated when traversing a closed loop of semantic paraphrases in the latent space. Compare reasoning consistency against standard SFT baselines.

Expected Contribution

A methodology to transfer the 'infinite' extrapolation capabilities of SPT phases from symbolic logic to unstructured text, reducing reasoning incoherence in LLMs.

Required Resources

Access to open-weights LLMs, a large-scale synthetic dataset of paraphrased logical puzzles, and GPU resources for fine-tuning with custom loss functions.

Source Paper

Robust Reasoning as a Symmetry-Protected Topological Phase

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