Looped Transformer tries to use one set of shared parameters, multiple rounds of iteration, to amplify model depth — but has always been blocked by an invisible problem: every revisit has this residual branch eating the same update, the forward-backward coupling differs from untied Transformer, and the empirical rule of DeepNorm taking α=β by layer count fails directly, with the loss curve jittering or even diverging when loop depth goes up. Princeton's Mengdi Wang and UCLA's Guanquan Cao team (arXiv 2607.13491, 2026-07-15) gives a first-principles answer. The paper translates the parameter being visited k times into a first-order perturbation bound, introducing the visit-alignment coefficient κ_R: in the decorrelated region κ_R degenerates, the bound recovers DeepNorm's 1/4 exponent; but in the conservative-alignment region — the more common state in engineering — the exponent must be lifted from 1/4 to 1/2, growing with loop count N. The core of DeepLoop: keep the Post-LN DeepNorm skeleton, just change the residual scaling coefficients to α=(2N)^{1/2} and β=(8N)^{-1/2}, with almost no extra compute, and loop depth can finally be stable. The experiments on GPT-2 small/medium are direct: when not looping, DeepLoop ties the baseline; once loop depth is turned on, validation loss and downstream tasks keep pulling apart, rather than the previous embarrassment of training loss going up while val loss ran away. The paper also emphasizes a key distinction — stable loop depth requires scaling by the number of parameter visits, not just the nominal layer count. The practical significance is that this rule is almost free engineering improvement: at the implementation layer, just bind DeepNorm's α, β to the unrolled depth N, and any team trying to scale loop depth into production inference or RL post-training can apply it directly without retraining a baseline. The Looped Transformer line, which uses few parameters for more depth, moves from "demonstrably trainable in theory" to "engineering-deployable".