Embedding Holonomic Networks as a 'Reasoning Bottleneck' layer within frozen LLMs enables zero-shot logical extrapolation on unstructured text without retraining the base model.

Motivation

The paper identifies a trade-off: Holonomic Networks offer infinite logical recursion (topological protection) but lack semantic understanding, while Transformers have semantic richness but fail at long-tail logic. A hybrid architecture could bridge the transferability gap, utilizing the LLM for semantic parsing and the Holonomic Network for the actual logical execution.

Proposed Method

Construct a 'Semantic-to-Anyon' adapter architecture. 1) Use a frozen LLM (e.g., Llama-3) to encode natural language premises into vector embeddings. 2) Train a learnable projection layer to map these embeddings onto the non-Abelian state space of a Holonomic Network (mapping semantic concepts to 'quasiparticles'). 3) Perform reasoning via braiding operations in the Holonet. 4) Project the final topological state back to the LLM's vocabulary for decoding. Evaluate on the RuleTaker dataset, specifically testing on samples 10x longer than training examples.

Expected Contribution

A neuro-symbolic architecture that combines the linguistic versatility of Transformers with the 100x length generalization of topological phases, solving the 'transferability' issue highlighted in the impact report.

Required Resources

Access to open-weights LLMs, GPU cluster for training adapter layers, datasets for logical reasoning (RuleTaker, CLUTRR), and expertise in both geometric deep learning and NLP.

Source Paper

Robust Reasoning as a Symmetry-Protected Topological Phase

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