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.

本文提出了一种解释性前馈 (FF) 设计，通过数据统计推导出当前层的网络参数，构建了基于 Saab 变换和 LRS 级联的卷积与全连接层的 CNN， 并在 MNIST 和 CIFAR-10 数据集上比较了 BP 和 FF 设计的分类准确性和鲁棒性，并探讨了 BP 和 FF 设计之间的关系。