Abstract: Convolutional neural networks trained on raw image data must implicitly learn that an object is the same object regardless of its orientation, a burden that wastes model capacity and degrades sample efficiency. Group-equivariant convolutional networks (G-CNNs) address this by encoding geometric symmetries directly into the network architecture, guaranteeing that a transformation of the input produces a predictable, structured transformation of every intermediate feature map. In this work we study symmetry groups of increasing richness , C2, p4, p4m, and a steerable C8 backbone, and evaluate their effect on classification accuracy and parameter efficiency on the CIFAR-10 and CIFAR-100 benchmarks under a strictly controlled parameter budget. We implement the G-CNN framework of Cohen & Welling, a C8-steerable backbone via the e2cnn library, and a hyperbolic convolutional network that couples the best-performing equivariant backbone with a Poincaré ball classification head, motivated by the approximate tree-like structure of natural-image class hierarchies. Our central finding is that the value of a symmetry group is conditional on the dataset: the dihedral group p4m is the best equivariant model on CIFAR-10, where the data’s reflection symmetry aligns with the architectural constraint, while the rotation-only group p4 is best on CIFAR-100, where the additional dihedral constraint provides no benefit at a one-hundred-class budget. Equivariance consistently matches or exceeds the translation-only baseline at equal parameter count, and at matched training compute exceeds it by eight to nine percentage points on CIFAR-10. The hyperbolic classification head reaches parity with its Euclidean counterpart on CIFAR-10 but regresses by twelve points on CIFAR-100, contradicting parity reported in prior work at substantially larger backbone capacity and suggesting that the competitiveness of the hyperbolic head is capacity-dependent. Together, these results argue that geometric inductive biases must be matched to both the symmetry structure of the labels and the capacity of the backbone, rather than adopted as universal improvements.

Abstract: Cataract is among the leading causes of vision impairment worldwide, affecting approximately 94 million individuals who often lack access to timely diagnostic services. Early detection is critical to preventing irreversible vision loss. This paper presents Seg-Cat, a pupil segmentation pipeline designed to address a key limitation of current State-of-the-Art (SOTA) models: the tendency to focus on irrelevant visual features such as skin colour and eyebrow texture rather than the medically relevant pupil region. Seg-Cat employs classical image processing techniques alongside deep learning segmentation using a U-Net architecture, with novel shape-aware loss functions to enforce anatomically consistent pupil boundaries. Experimental results demonstrate that incorporating geometric regularisers (circular and elliptical loss) into the U-Net training objective yields significant improvements over the baseline, achieving a Test Dice score of 0.931 and IoU of 0.871 with the circular variant.