Predictive Geometry of Hidden Trajectories in Transformers
Decoder-only transformers are trained only through a terminal next-token prediction loss, yet this loss constrains every intermediate hidden state through the fixed downstream computation. We formalize this constraint by studying layerwise loss-to-go functions: the terminal loss obtained by continuing a candidate hidden state through the remaining transformer blocks. Around successful validation trajectories, we show that the local second-order geometry of these functions is governed, up to low-loss residual terms, by a pullback Fisher operator on hidden-state space. Its spectrum identifies output-sensitive directions and approximately prediction-null directions, yielding a local observab...
| Authors | Timur Mudarisov, Mikhail Burtsev, Tatiana Petrova et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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