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The authors propose a novel strongly monotone and Lipschitz residual layer, F(x) = μx + H(x), where the nonlinear block H is a "feed-through network" (FTN) architecture. This allows them to establish tight bounds on the layer's monotonicity and Lipschitzness using the integral quadratic constraint (IQC) framework.
By composing these monotone and Lipschitz layers with orthogonal layers, the authors construct bi-Lipschitz networks (BiLipNets) that have much tighter Lipschitz bounds compared to models based on spectral normalization.
The authors formulate the model inversion F^-1 as a three-operator splitting problem, which can be efficiently solved using the Davis-Yin splitting algorithm.
The authors introduce a new scalar-output network, the Polyak-Lojasiewicz network (PLNet), which satisfies the Polyak-Lojasiewicz condition. PLNets can be used to learn non-convex surrogate losses with favorable properties, such as a unique and efficiently-computable global minimum.
Experiments demonstrate the effectiveness of the proposed BiLipNet and PLNet models for tasks like uncertainty quantification and surrogate loss learning, especially in high-dimensional settings.
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by Ruigang Wang... at arxiv.org 05-03-2024
https://arxiv.org/pdf/2402.01344.pdfDeeper Inquiries