Depth Laws for the Precision Floor of Trained Neural Networks: Amplification, Residual Scaling, and a Quantization-Aware Training Paradox
How many bits does a network need before its accuracy collapses, and how does this grow with depth? We study the precision floor, the perturbation level or bit-width at which accuracy falls halfway to chance, in MLPs, CNNs, Vision Transformers and nine pretrained language models, under post-training quantization (PTQ) and quantization- or noise-aware training (QAT). (i) A first-order theory sets the floor through one full-precision quantity, the predictive amplification $G$: $η_c=Λ/G$, and $G^2$ grows linearly in depth at a rate proportional to the squared residual branch scale. (ii) The predicted equality $α_{PTQ}=ρ$ of depth exponents holds within 95% intervals in twelve of thirteen tra...
| Authors | Ahmad S. Tarawneh |
|---|---|
| Primary category | cs.LG |
| Published | 25 September 2026 |
| Last updated at source | 25 September 2026 |
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