Directly training deep learning models for applications in large-scale cyber-physical systems can be intractable due to the large number of components and decision variables. Instead, we focus on exploiting spatial symmetries in systems by designing size-generalizable architectures. Once trained on small-scale examples, such architectures exhibit equivalent or comparable performance on large-scale systems. The first example we consider is a fully convolutional neural network, for which we prove a bound that guarantees generalization performance. We demonstrate generalizability empirically with applications to multi-target tracking and mobile infrastructure on demand. Next, we introduce a novel spatial transformer architecture, designed with two key properties in mind: shift-equivariance and locality. To provide these properties, the proposed architecture uses rotary positional encodings and spatially windowed attention. Our experiments in two distributed collaborative multi-robot tasks show that these design features are sufficient for size generalizability. Moreover, we demonstrate that the spatial transformer architecture is capable of decentralized execution, is robust to communication delays, can generalize to unseen tasks, and outperforms the previous state-of-the-art decentralized architecture in coverage control. Finally, we refocus on a particularly challenging optimization problem in power systems: optimal power flow. By appropriately formulating the Lagrangian dual problem, we can train graph attention networks with improved optimality and feasibility. Additionally, we show that after tuning the hyperparameters on one power system, the training performance can be reproduced on new power systems without further hyperparameter tuning.