A Geometric Analysis of Sign-Magnitude Asymmetry in a ReLU + RMSNorm Block under Ternary Quantization

arXiv:2605.18933v1 Announce Type: new Abstract: 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 $\pi/(\pi-2) \approx 2.75$ 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 t

Source: arXiv cs.LG — read the full report at the original publisher.

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