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What is: Invertible 1x1 Convolution?

SourceGlow: Generative Flow with Invertible 1x1 Convolutions
Year2000
Data SourceCC BY-SA - https://paperswithcode.com

The Invertible 1x1 Convolution is a type of convolution used in flow-based generative models that reverses the ordering of channels. The weight matrix is initialized as a random rotation matrix. The log-determinant of an invertible 1 × 1 convolution of a h×w×ch \times w \times c tensor hh with c×cc \times c weight matrix W\mathbf{W} is straightforward to compute:

logdet(dconv2D(h;W)dh)=hwlogdet(W)\log | \text{det}\left(\frac{d\text{conv2D}\left(\mathbf{h};\mathbf{W}\right)}{d\mathbf{h}}\right) | = h \cdot w \cdot \log | \text{det}\left(\mathbf{W}\right) |