Stream separation improves Bregman conditioning in transformers
Linear methods for steering transformer representations, including probing, activation engineering, and concept erasure, implicitly assume the geometry of representation space is Euclidean. Park et al. [Park et al., 2026] showed that softmax induces a curved Bregman geometry whose metric tensor is the Hessian of the log-normalizer, $H(λ) = Cov[γ | λ]$. Ignoring this curvature causes Euclidean steering to leak probability mass to unintended tokens. Their analysis applies at the output layer. We measure this Hessian at intermediate layers in a controlled 2x2 design crossing stream separation with per-layer supervision (vocabulary decoding loss at each layer), all at matched vocabulary and p...
| Authors | James Clayton Kerce |
|---|---|
| Primary category | cs.LG |
| Published | 22 March 2026 |
| Last updated at source | 22 March 2026 |
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