Supplementary Material: " Compressing Neural Networks: Towards Determining the Optimal Layer-wise Decomposition "

The input tensor shape is 6 3 3. The corresponding weight matrix has f = 20 rows (one row per filter) and 24 columns (c κ1 κ2), as for the corresponding feature matrix, it has 24 rows and 4 columns, the 4 here is the number of convolution windows (i.e., number of pixels/entries in each of the output feature maps). After multiplying those matrices, we reshape them to the desired shape to obtain the desired output feature maps. In this section, we provide more details pertaining to our method. A.1 Method Preliminaries Our layer-wise compression technique hinges upon the insight that any linear layer may be cast as a matrix multiplication, which enables us to rely on SVD as compression subroutine. Focusing on convolutions we show how such a layer can be recast as matrix multiplication. Similar approaches have been used by Denton et al. (2014); Idelbayev and Carreira-Perpinán (2020); Wen et al. (2017) among others. The equivalence of Y and Y can be easily established via an appropriate reshaping operation since p= p1p2. Equipped with the notion of correspondence between convolution and matrix multiplication our goal is to decompose the layer via its matrix operator W Rf cκ1κ2. To this end, we compute the j-rank approximation of W using SVD and factor it into a pair of smaller matrices U Rf j and V Rj cκ1κ2.