The paper introduces a method for constructing L-Lipschitz deep residual networks (ResNets) using a Linear Matrix Inequality (LMI) framework. By reformulating the ResNet architecture as a pseudo-tridiagonal LMI and applying the Gershgorin circle theorem, the authors derive closed‑form constraints on network parameters that guarantee Lipschitz continuity. The work also presents a compositional framework for handling recursive systems in hierarchical architectures, while noting that the Gershgorin-based approximations can over‑constrain the system, reducing expressive capacity.
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arXiv:2510.17072v2 Announce Type: replace
Abstract: Regression with non-Euclidean responses---e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions---has b...
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