The Transformer as a Polar State Estimator
We show that the core components of the Transformer---attention, residual connections, and normalization---arise naturally from a single geometric state estimation problem. Modeling the latent state in polar coordinates naturally separates radial and hyperspherical dynamics, yielding a precision-weighted filtering procedure in which normalization enforces the hyperspherical constraint, attention aggregates directional evidence, and the residual connection implements an incremental state update. The standard Transformer block with rotary positional encodings is recovered by discarding the geometric correction terms of the resulting state estimator, showing that its architecture follows fro...
| Authors | Peter Racioppo |
|---|---|
| Primary category | cs.LG |
| Published | 10 May 2026 |
| Last updated at source | 7 September 2026 |
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