  Standard deep learning models that employ the categorical cross-entropy loss
are known to perform well at image classification tasks. However, many standard
models thus obtained often exhibit issues like feature redundancy, low
interpretability, and poor calibration. A body of recent work has emerged that
has tried addressing some of these challenges by proposing the use of new
regularization functions in addition to the cross-entropy loss. In this paper,
we present some surprising findings that emerge from exploring the role of
simple orthogonality constraints as a means of imposing physics-motivated
constraints common in imaging. We propose an Orthogonal Sphere (OS) regularizer
that emerges from physics-based latent-representations under simplifying
assumptions. Under further simplifying assumptions, the OS constraint can be
written in closed-form as a simple orthonormality term and be used along with
the cross-entropy loss function. The findings indicate that orthonormality loss
function results in a) rich and diverse feature representations, b) robustness
to feature sub-selection, c) better semantic localization in the class
activation maps, and d) reduction in model calibration error. We demonstrate
the effectiveness of the proposed OS regularization by providing quantitative
and qualitative results on four benchmark datasets - CIFAR10, CIFAR100, SVHN
and tiny ImageNet.
