On the Residual Scaling of Looped Transformers: Stability and Transferability
Looped (weight-tied) Transformers apply a shared residual block $N$ times ($h \leftarrow h + \varepsilon\,f(h)$, same $f$ at each step), increasing effective depth without adding parameters. Prior depth-scaling analyses prescribe $\varepsilon = 1/\!\sqrt{L}$ for depth-$L$ residual networks. We show that this is insufficient for looped architectures: weight sharing makes residual updates correlated across iterations, requiring the stronger scaling $\varepsilon = 1/N$. For multi-layer blocks ($L$ unique layers looped $N$ times), we derive a factored parameterization $\varepsilon = λ/(N\!\sqrt{L})$ that separates the two sources of growth: $1/N$ controls the within-layer loop correlation, an...
| Authors | Shaowen Wang, Bingrui Li, Ge Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 June 2026 |
| Last updated at source | 11 September 2026 |
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