CDFlow: Building Invertible Layers with Circulant and Diagonal Matrices

תקציר מקורי באנגליתarXiv:2510.25323v4 Announce Type: replace Abstract: Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient computation of the Jacobian determinant and inverse. We introduce a novel invertible linear layer based on the product of circulant and diagonal matrices. This decomposition reduces parameter complexity from $\mathcal{O}(n^2)$ to $\mathcal{O}(mn)$ using $m$ diagonal matrices and $m-1$ circulant matrices while still approximating general linear transformations. By leveraging the Fast Fourier Transform, our approach reduces the time complexity of matrix inversion from $\mathcal{O}(n^3)$ to $\mathcal{O}(mn\lo