Depth Registers Unlock W4A4 on SwiGLU: A Reader/Generator Decomposition
Ziyang Liu

TL;DR
This paper investigates post-training quantization of a SwiGLU language model, introducing Depth Registers with hinge loss to significantly reduce quantization error and analyze the impact of different input-activation sites.
Contribution
It proposes Depth Registers with hinge loss as a training-time intervention to improve W4A4 quantization in SwiGLU models, revealing the roles of residual-axis readers and generators.
Findings
Residual-axis control bounds readers tightly but not generators.
DR+sink reduces quantization error by about 14x.
Residual ~2 PPL gap to FP16 is mainly due to w2 input.
Abstract
We study post-training W4A4 quantization in a controlled 300M-parameter SwiGLU decoder-only language model trained on 5B tokens of FineWeb-Edu, and ask which input-activation sites dominate the error. Naive round-to-nearest W4A4 collapses validation perplexity from FP16 23.6 to 1727. A simple residual-axis training-time intervention -- Depth Registers with a register-magnitude hinge loss (DR+sink) -- reduces this to 119 (about 14x) at matched FP16 PPL and matched zero-shot capacity, and composes with SmoothQuant to 39.9 PPL. The residual ~2 PPL gap to FP16 is the diagnostic core. We decompose W4A4 damage by input-activation site: the five trainable linears in a SwiGLU block split into residual-axis readers (qkv, w1, w3) and block-internal generators (o_proj, w2). Elementary norm arguments show residual-axis magnitude control bounds readers tightly but leaves w2's bilinear input bounded…
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