Geometric sparsification in recurrent neural networks

A common technique for ameliorating the computational costs of running large neural models is sparsification, or the pruning of neural connections during training. Sparse models are capable of maintaining the high accuracy of state of the art models, while functioning at the cost of more parsimonious models. The structures which underlie sparse architectures are, however, poorly understood and not consistent between differently trained models and sparsification schemes. In this paper, we propose a new technique for sparsification of recurrent neural nets (RNNs), called moduli regularization, in combination with magnitude pruning. Moduli regularization leverages the dynamical system induced by the recurrent structure to induce a geometric relationship between neurons in the hidden state of the RNN. By making our regularizing term explicitly geometric, we provide the first, to our knowledge, a priori description of the desired sparse architecture of our neural net, as well as explicit end-to-end learning of RNN geometry. We verify the effectiveness of our scheme under diverse conditions, testing in navigation, natural language processing, and addition RNNs. Navigation is a structurally geometric task, for which there are known moduli spaces, and we show that regularization can be used to reach 90% sparsity while maintaining model performance only when coefficients are chosen in accordance with a suitable moduli space. Natural language processing and addition, however, have no known moduli space in which computations are performed. Nevertheless, we show that moduli regularization induces more stable recurrent neural nets, and achieves high fidelity models above 90% sparsity.