Symmetries in next-token prediction targets induce corresponding geometric symmetries such as circulant matrices and equiangular tight frames in the optimal weights and embeddings of a layer-peeled LLM surrogate model.
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A geometric 1-form on token embeddings has curvature that couples to semantic world models in language models, as evidenced by clustering on chess board regions and piece importance.
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Uncovering Symmetry Transfer in Large Language Models via Layer-Peeled Optimization
Symmetries in next-token prediction targets induce corresponding geometric symmetries such as circulant matrices and equiangular tight frames in the optimal weights and embeddings of a layer-peeled LLM surrogate model.
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A geometric relation of the error introduced by sampling a language model's output distribution to its internal state
A geometric 1-form on token embeddings has curvature that couples to semantic world models in language models, as evidenced by clustering on chess board regions and piece importance.