Despite the strong performance in many computer vision tasks, Convolutional Neural Networks (CNNs) can sometimes struggle to efficiently capture longrange, complex non-linear dependencies in deeper layers of the network. We address this limitation by introducing Residual KAN, which incorporates the Kolmogorov-Arnold Network (KAN) within the CNN framework as a residual component. Our approach uses Chebyshev polynomials as the basis for KAN convolutions that enables more expressive and adaptive feature representations while maintaining computational efficiency. The proposed RKAN blocks, when integrated into established architectures such as ResNet and DenseNet, offer consistent improvements over the baseline models on various well-known benchmarks: CIFAR-100, Food-101, Tiny ImageNet, and the full ILSVRC-2012 (ImageNet) dataset. Our results demonstrate the potential of RKAN to enhance the capabilities of deep CNNs in visual data.

As Graph Neural Networks (GNNs) increase in popularity for scientific machine learning, their training and inference efficiency is becoming increasingly critical. Additionally, the deep learning field as a whole is trending towards wider and deeper networks, and ever increasing data sizes, to the point where hard hardware bottlenecks are often encountered. Emerging specialty hardware platforms provide an exciting solution to this problem. In this paper, we systematically profile and select low-level operations pertinent to GNNs for scientific computing implemented in the Pytorch Geometric software framework. These are then rigorously benchmarked on NVIDIA A100 GPUs for several various combinations of input values, including tensor sparsity. We then analyze these results for each operation. At a high level, we conclude that on NVIDIA systems: (1) confounding bottlenecks such as memory inefficiency often dominate runtime costs moreso than data sparsity alone, (2) native Pytorch operations are often as or more competitive than their Pytorch Geometric equivalents, especially at low to moderate levels of input data sparsity, and (3) many operations central to state-of-the-art GNN architectures have little to no optimization for sparsity. We hope that these results serve as a baseline for those developing these operations on specialized hardware and that our subsequent analysis helps to facilitate future software and hardware based optimizations of these operations and thus scalable GNN performance as a whole.