What can linear attention learn from nonlinear teachers in-context?
Linear attention is a tractable model for understanding the mechanisms governing in-context learning in transformers. For linear regression tasks, recent asymptotic analyses have characterised its learning and generalisation behaviour. We extend this theory to nonlinear single-index targets, $y=f(x^\top w)+\varepsilon $. Our main result establishes a nonlinearity-noise equivalence: linear attention extracts only the linear Hermite component of $f$, while the remaining nonlinear structure contributes to the generalisation error as effective noise. This reduction allows results from the corresponding linear theory to be transferred to nonlinear tasks. We illustrate its implications for fini...
| Authors | Mary Letey, Arman Rysmakhanov, Yue M. Lu et al. |
|---|---|
| Primary category | stat.ML |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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