At the output layer only the rows of tokens that compete can move. The signal that backpropagation carries into the network is the drawn token’s output vector minus the sampler’s average, so it lies in the span of differences of those vectors and vanishes where the sampler is sure. A linear map that feeds the unembedding therefore gets an expected update of rank at most the number of competing tokens minus one, plus a leak set by the tail mass, and a LoRA of that rank carries the main part. Measured updates are numerically full rank yet spectrally concentrated; the optimizer and many steps account for the difference.