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

2026-04-20

AI Summary

This work addresses the severe performance degradation caused by W4A4 quantization in SwiGLU-based language models, where validation perplexity surges to 1727. The authors introduce a “reader/generator” decomposition perspective, revealing that quantization error predominantly originates from the generator path within each block. To mitigate this, they propose Depth Registers combined with a register magnitude hinge loss (DR+sink) to selectively suppress error along the residual axis. Integrating SmoothQuant, Per-Linear QuaRot, and online Hadamard rotation, their method dramatically reduces perplexity to 39.9—approaching the FP16 baseline of 23.6—while preserving zero-shot capabilities. This approach represents the first effective low-bit quantization strategy specifically tailored for SwiGLU modules.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Natural Language Processing: (Large) Language Models
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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 only by the trivial product of factor bounds; empirically, DR+sink collapses reader kurtosis while leaving generators essentially unchanged, and the reader-rescued W4A4 residue is flat at ~0.28 nats across three matched checkpoints with Delta-remove(w2) dominating. We present DR+sink as a training-time probe rather than a deployment proposal: a post-hoc alternative (Per-Linear QuaRot) nearly matches it on the reader axis. Full QuaRot -- adding online per-head value Hadamard plus online w2-input rotation -- does not close the gap either, directly testing the prediction that orthogonal rotation cannot bound the bilinear SwiGLU tail. Claims are specific to our 300M, 5B-token, single-seed setting, and our experiments do not isolate the partition from the hinge.

Problem

• W4A4 quantization
• SwiGLU
• activation quantization
• perplexity degradation
• bilinear activation

Innovation

• W4A4 quantization
• SwiGLU decomposition
• Depth Registers
• residual-axis control
• bilinear activation tail