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Preprint Jul 2026

Certifying Residual Architectures from Their Primitives: A Sharp Stability Threshold

The results provide a way to assess the trade-off between stability and representational flexibility directly from block primitives, before training, and improve out-of-distribution generalization in operator learning and accuracy in time-series forecasting.

Hyemin Gu, M. Tyrrell, T. Sahai et al. · 0 citations
#data science Jul 2026

Sharp Stability Threshold and Certification for Designing Stable Residual Architectures

We propose \emph{the sublinear-growth principle} for deep residual architectures -- a sharp stability threshold on the input-magnitude exponent of every residual block's velocity field: $$\|v(x, t)\| \leq c\,\|x\|^q + b, \qquad q \in [0, 1].$$ The threshold $q = 1$ is established via two independent arguments. Classica...

Hyemin Gu, Michael Tyrrell, T. Sahai et al. · 0 citations

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