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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Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
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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.