Title: PRANC: Pseudo RAndom Networks for Compacting deep models. Abstract: Compacting deep models has various applications where the communication and/or storage is expensive including multi-agent learning. We introduce a simple yet effective framework for compacting neural networks. In short, we train our network to be a linear combination of many pseudo-randomly generated frozen models. Then, one can reconstruct the model by communicating or storing the single `seed' scalar used to generate the pseudo-random `basis' networks along with the learned linear mixture coefficients. Our method, denoted as PRANC, learns almost $100\times$ fewer parameters than a deep model and still performs reasonably well on several datasets and architectures. PRANC enables 1) efficient communication of models between agents, 2) efficient model storage, and 3) memory-efficient inference by generating layer-wise weights on the fly. We test PRANC on CIFAR-10, CIFAR-100, tinyImageNet, and ImageNet-100 with various architectures like AlexNet, LeNet, ResNet18, ResNet20, and ResNet56 and demonstrate a massive reduction in the number of parameters while providing satisfactory performance on these benchmark datasets.