New Low-Dimensional Structures in LLM Training Dynamics
orvieto_antonio · x · 2026-07-17
This preprint discusses the interpretable structures within the parameter space during LLM training.
The authors propose that under certain data symmetry conditions, a low-dimensional subspace emerges in the parameter space with self-consistent training dynamics. If training begins within this subspace, the trajectory remains contained within it. This allows the training process of "billion-parameter" models to be reduced and analyzed using a few pseudo-parameters.
The paper also emphasizes that this subspace is highly interpretable, with each coordinate corresponding to a specific mechanism. For instance, an induction head can be decomposed into 3 directions within this subspace. The author notes that this will make both theoretical analysis and experimental research much more tractable.
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