Certifying Residual Architectures from Their Primitives: A Sharp Stability Threshold
Whether a deep residual architecture trains stably is usually determined by training it, which is expensive and answers the question only for the architecture, depth, and floating-point format tested. In practice, stability is secured by heuristics for where to place normalization and which type to use, supported by experiments but lacking a common principle. We show that stability can instead be certified before training, directly from the architectural primitives of a residual block, as an explicit function of depth and floating-point format. The certificate has two elements: (a) a power-law growth bound, $|v(x)|\le c|x|^q+b$, whose exponent $q$ is computed from the block's primitives b...
| Authors | Hyemin Gu, Michael Tyrrell, Tuhin Sahai et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 July 2026 |
| Last updated at source | 29 September 2026 |
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