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We demonstrate that a deep model can be reparametrized as a linearcombination of several randomly initialized and frozen deep models in theweight space. During training, we seek local minima that reside within thesubspace spanned by these random models (i.e., `basis' networks). Ourframework, PRANC, enables significant compaction of a deep model. The model canbe reconstructed using a single scalar `seed,' employed to generate thepseudo-random `basis' networks, together with the learned linear mixturecoefficients.  In practical applications, PRANC addresses the challenge of efficientlystoring and communicating deep models, a common bottleneck in severalscenarios, including multi-agent learning, continual learners, federatedsystems, and edge devices, among others. In this study, we employ PRANC tocondense image classification models and compress images by compacting theirassociated implicit neural networks. PRANC outperforms baselines with a largemargin on image classification when compressing a deep model almost $100$times. Moreover, we show that PRANC enables memory-efficient inference bygenerating layer-wise weights on the fly. The source code of PRANC is here:\url{https://github.com/UCDvision/PRANC}

PRANC: Pseudo RAndom Networks for Compacting deep models