DipDNN: Decomposed Invertible Pathway Deep Neural Networks
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: Inverse consistency, analytical invertibility, physics embedding, inverse stability, deep narrow networks
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Abstract: Deep neural networks (DNNs) enable highly accurate one-way inferences from inputs to outputs. However, there is an elevated need for consistency in bi-directional inferences, such as state estimation, signal recovery, privacy preservation, and reasoning. Since standard DNNs are not inherently invertible, previous works use multiple DNNs in a nested manner to obtain consistent and analytical forms of inverse solutions. However, such a design is not only computationally expensive due to DNN compositions, but also forces splitting the input/output equally, which is inapplicable in many applications. To reduce the restriction, other works use fixed-point iterations to enable approximation of one-to-one mapping, but the numerical approximation leads to reconstruction errors compared with the analytical inverse. To preserve the analytical form with minimum computational redundancy, we proposed decomposed-invertible-pathway DNNs (DipDNN) that decompose the nested design. We enforce one-to-one mapping in each layer by minimally adjusting the weights and activation functions of standard dense DNNs. We prove that such an adjustment guarantees strict invertibility without hurting the universal approximation. As our design relaxes the alternative stacking of nested DNNs, the proposed method does not need a fixed splitting of inputs/outputs, making it applicable for general inverse problems. To further boost the two-way learning accuracy, we show that the proposed DipDNN is easily integrated into a parallel structure. With the analytical invertibility, bi-Lipschitz stability regularization naturally fits into the scheme to avoid numerical issues. Numerical results show that DipDNN can recover the input exactly and quickly in diverse systems.
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Submission Number: 3006
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