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Deep learning has revolutionized human society, yet the black-box nature ofdeep neural networks hinders further application to reliability-demandedindustries. In the attempt to unpack them, many works observe or impactinternal variables to improve the comprehensibility and invertibility of theblack-box models. However, existing methods rely on intuitive assumptions andlack mathematical guarantees. To bridge this gap, we introduce Bort, anoptimizer for improving model explainability with boundedness and orthogonalityconstraints on model parameters, derived from the sufficient conditions ofmodel comprehensibility and invertibility. We perform reconstruction andbacktracking on the model representations optimized by Bort and observe a clearimprovement in model explainability. Based on Bort, we are able to synthesizeexplainable adversarial samples without additional parameters and training.Surprisingly, we find Bort constantly improves the classification accuracy ofvarious architectures including ResNet and DeiT on MNIST, CIFAR-10, andImageNet. Code: https://github.com/zbr17/Bort.

Bort: Towards Explainable Neural Networks with Bounded Orthogonal Constraint