  The model parameters of convolutional neural networks (CNNs) are determined
by backpropagation (BP). In this work, we propose an interpretable feedforward
(FF) design without any BP as a reference. The FF design adopts a data-centric
approach. It derives network parameters of the current layer based on data
statistics from the output of the previous layer in a one-pass manner. To
construct convolutional layers, we develop a new signal transform, called the
Saab (Subspace Approximation with Adjusted Bias) transform. It is a variant of
the principal component analysis (PCA) with an added bias vector to annihilate
activation's nonlinearity. Multiple Saab transforms in cascade yield multiple
convolutional layers. As to fully-connected (FC) layers, we construct them
using a cascade of multi-stage linear least squared regressors (LSRs). The
classification and robustness (against adversarial attacks) performances of BP-
and FF-designed CNNs applied to the MNIST and the CIFAR-10 datasets are
compared. Finally, we comment on the relationship between BP and FF designs.
