  Deep learning has revolutionized human society, yet the black-box nature of
deep neural networks hinders further application to reliability-demanded
industries. In the attempt to unpack them, many works observe or impact
internal variables to improve the comprehensibility and invertibility of the
black-box models. However, existing methods rely on intuitive assumptions and
lack mathematical guarantees. To bridge this gap, we introduce Bort, an
optimizer for improving model explainability with boundedness and orthogonality
constraints on model parameters, derived from the sufficient conditions of
model comprehensibility and invertibility. We perform reconstruction and
backtracking on the model representations optimized by Bort and observe a clear
improvement in model explainability. Based on Bort, we are able to synthesize
explainable adversarial samples without additional parameters and training.
Surprisingly, we find Bort constantly improves the classification accuracy of
various architectures including ResNet and DeiT on MNIST, CIFAR-10, and
ImageNet. Code: https://github.com/zbr17/Bort.
