Low-Rank Attention Residuals

Abstract

Attention Residuals (AttnRes) replace the fixed residual sum with depth-wise attention over previous sub-layer outputs in Large Language Models (LLMs), but use each output as both a full-dimensional key and value. This couples routing with representation and makes the cost of computing depth-routing scores scale with hidden width $d$. We propose Low-Rank Attention Residuals (LR-AttnRes), which keep full-dimensional residual values while using $r$-dimensional keys, with $r < d$, for routing. LR-AttnRes uses the last $r$ dimensions of each value as the routing key, reducing total residual-side FLOPs while still improving performance. Comprehensive sweeps across the number of blocks ($N$) and $r$ show that depth-wise routing can be effective with far fewer dimensions than the model width. At both $1$B and $4$B parameters with $r = d/4$, LR-AttnRes achieves lower final validation loss, higher average downstream accuracy, and higher measured training-step throughput than standard AttnRes. We also provide a fused kernel supporting standard and low-rank routing. We release all code, the kernel, and all trained models to facilitate future research.