Title: Model Compression via Symmetries of the Parameter Space. Abstract: We provide a theoretical framework for neural networks in terms of the representation theory of quivers, thus revealing symmetries of the parameter space of neural networks. An exploitation of these symmetries leads to a model compression algorithm for radial neural networks based on an analogue of the QR decomposition. The algorithm is lossless; the compressed model has the same feedforward function as the original model. If applied before training, optimization of the compressed model by gradient descent is equivalent to a projected version of gradient descent on the original model. 