media Hugging Face Forums · 1h ago · open_models

Preprint reveals geometric control of Transformer outputs via sphere-based analysis

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A preprint titled "Steer on a Sphere: Geometric Control of Transformer Outputs" analyzes the geometry of Transformer hidden states, finding they reside on a sphere defined by the per-layer RMSNorm scale rather than the dimension size. This radius varies significantly across architectures, such as DeepSeek-7B and Mistral-7B.

Key findings include tangent traversal, where one step along an LM-head direction reaches 91–98% of vocabulary rank 1, and "cow tipping," where specific tokens act as self-reinforcing fixed points that cause infinite repetition. The work also identifies defensive encoding vulnerabilities using triggers like NULL bytes and notes Lyapunov rate clustering near 0.5 for several architectures.

The author presents these geometric properties to explain specific Transformer behaviors, such as token locking and potential security implications for scrapers, while noting the geometric picture is approximate.

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