  Traditional deep learning models rely on methods such as softmax
cross-entropy and ArcFace loss for tasks like classification and face
recognition. These methods mainly explore angular features in a hyperspherical
space, often resulting in entangled inter-class features due to dense angular
data across many classes. In this paper, a new field of feature exploration is
proposed known as HyperSpaceX which enhances class discrimination by exploring
both angular and radial dimensions in multi-hyperspherical spaces, facilitated
by a novel DistArc loss. The proposed DistArc loss encompasses three feature
arrangement components: two angular and one radial, enforcing intra-class
binding and inter-class separation in multi-radial arrangement, improving
feature discriminability. Evaluation of HyperSpaceX framework for the novel
representation utilizes a proposed predictive measure that accounts for both
angular and radial elements, providing a more comprehensive assessment of model
accuracy beyond standard metrics. Experiments across seven object
classification and six face recognition datasets demonstrate state-of-the-art
(SoTA) results obtained from HyperSpaceX, achieving up to a 20% performance
improvement on large-scale object datasets in lower dimensions and up to 6%
gain in higher dimensions.
