The field of deep learning is moving towards a greater understanding of the underlying geometry and topology of neural networks. Researchers are exploring new frameworks and models that leverage geometric and topological insights to improve the robustness and generalization of deep learning models. This includes the development of geometry-aware deep learning frameworks, discrete functional geometry models, and topological deep learning approaches. These innovative approaches are showing promise in improving the performance of deep learning models, particularly in tasks that require understanding complex structural patterns. Noteworthy papers include: A Class of Random-Kernel Network Models, which establishes a depth separation theorem in sample complexity. Geometric origin of adversarial vulnerability in deep learning, which introduces a geometry-aware deep learning framework that promotes intra-class compactness and inter-class separation. Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs, which provides a unified framework for analyzing ReLU networks through the lens of discrete functional geometry. Topotein: Topological Deep Learning for Protein Representation Learning, which applies topological deep learning to protein representation learning. WIPUNet: A Physics-inspired Network with Weighted Inductive Biases for Image Denoising, which investigates how physics-inspired priors can inform image denoising.