新闻 · arXiv cs.LG

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. Classical ODE theory gives a global forward flow on $[0, T]$ at $q \le 1$ and exhibits divergent velocity fields at any $q > 1$. The optimal-control analysis, via the…