A Geometric Analysis of Sign-Magnitude Asymmetry in a ReLU + RMSNorm Block under Ternary Quantization
Pre-norm Transformers with RMSNorm tolerate ternary {-1,0,+1} weight quantization with surprisingly small loss (Ma et al., 2024). We give a geometric explanation via sign-magnitude decomposition of weight perturbations. In a two-layer ReLU + RMSNorm model with i.i.d. Gaussian weights, sign-flips produce $π/(π-2) \approx 2.75$ times more transverse output energy than sign-preserving magnitude perturbations of equal Frobenius norm, as the flip rate $p \to 0$ (Theorem 3). The mechanism: ReLU creates a hidden-space directional asymmetry between the two perturbation types, which RMSNorm's transverse-projection Fréchet derivative selectively exposes. Sign-quantization error is itself a sign-pre...
| Authors | Lei Dong |
|---|---|
| Primary category | cs.LG |
| Published | 18 May 2026 |
| Last updated at source | 18 May 2026 |
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