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invertible residual networks

Invertible residual networks are deep neural network architectures based on standard residual connections that are mathematically constrained to define bijective, invertible transformations between input and output representations. Unlike conventional normalizing flow architectures that rely on rigid structural constraints such as dimension partitioning or autoregressive triangular Jacobians, invertible residual networks maintain standard residual block designs and ensure invertibility by restricting the Lipschitz constant of the residual mapping to be strictly less than one, often using spectral normalization. This contractive property guarantees a unique inverse computable through fixed-point iterations via the Banach fixed-point theorem. In generative modeling and probabilistic inference, invertible residual networks serve as flexible normalizing flows that enable tractable log-determinant Jacobian approximation, exact likelihood estimation, and efficient data generation without sacrificing the general representational power of residual networks.

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