Lost in Backpropagation: The LM Head is a Gradient Bottleneck

ArXi:2603.10145v1 Announce Type: new The last layer of neural language models (LMs) projects output features of dimension $D$ to logits in dimension $V$, the size of the vocabulary, where usually $D \ll V$. This mismatch is known to raise risks of limited expressivity in neural LMs, creating a so-called softmax bottleneck. We show the softmax bottleneck is not only an expressivity bottleneck but also an optimization bottleneck. Backpropagating $V$-dimensional gradients through a rank-$D$ linear layer induces unavoidable compression, which alters the.