Structural Sensitivity in Compressed Transformers: Relative Error Propagation and Layer Removal

Compressing transformer weights makes large language models cheaper to deploy. But each layer's compression introduces an error. These errors accumulate as the signal passes through later layers, and how they accumulate is not well understood. We measure this directly: at each layer, we take the ratio of output to input error, calling it rho. A value below one means the layer absorbs the error; above one means it grows. Computing rho on six transformers (117M to 8B parameters) yields three findings. (i) Errors at layer t scale downstream by the product of later rho values, predicting representation drift (Spearman r = -0.44, p < 10^-4). This explains why compressing early layers hurts more than late ones, and why depth-decreasing sparsity schedules outperform uniform ones. Across architecture families, however, model width and redundancy matter more than rho alone. (ii) Within a layer, naive pruning shows a ~600x spread in component sensitivity. Activation-aware pruning (Wanda) shrinks this to 3-7x; the ranking reverses across architectures, so fixed importance scores do not transfer. (iii) For depth pruning, ranking layers by how far rho is from one takes two forward passes. It beats ShortGPT's Block Influence with 1.6x lower perplexity at eight layers removed, and physical deletion delivers 1.22x wall-clock speed-up. A blend of the two criteria does best (perplexity 14.2, 60.0% downstream accuracy on LLaMA-2-7B). Twelve Lean 4 norm inequalities provide machine-checked per-matrix error bounds. The contraction profile thus gives a training-free instrument for two decisions: where to compress within layers, and which to remove.