RT-Transformer: The Transformer Block as a Spherical State Estimator

We show that the core components of the Transformer block -- attention, residual connections, and normalization -- arise naturally from a single geometric estimation problem. Modeling the latent state as a direction on the hypersphere, with noise defined in the tangent plane at the current estimate, yields a precision-weighted directional inference procedure in which attention aggregates evidence, residual connections implement incremental state updates, and normalization retracts the updated state back onto the hypersphere. Together, these components follow from the geometry of the estimation problem rather than being introduced as independent architectural choices.