Unbiased Gradients, Moving Stability Boundaries: Exact Mini-Batch Geometry in Linear Self-Attention
Unbiased stochastic gradients can match the full gradient in expectation while changing finite-step stability. We study this effect in one-layer linear self-attention for in-context linear regression, where shared-mode mini-batch training reduces exactly to a random two-factor map. The full-batch map preserves an elliptic region, whereas sampled curvature and target correlation create batch-dependent stability boundaries. Their combined fluctuation is centered at the parameter-update level but induces a strictly outward drift of the full-batch boundary coordinate. We derive an exact one-step crossing criterion, adaptive concentration bounds, and conditional drift identities, and prove alm...
| Authors | Krishnakumar Balasubramanian |
|---|---|
| Primary category | stat.ML |
| Published | 20 May 2026 |
| Last updated at source | 21 September 2026 |
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