Jared Deighton

Jared Deighton, Wyatt Mackey, Ioannis Schizas et al.

Mammalian spatial navigation relies on specialized neurons, such as place and grid cells, which encode position based on self-motion and environmental cues. While extensive research has explored the computational role of grid cells, the principles underlying efficient place cell coding remain less understood. Existing spatial information rate measures primarily assess single-neuron encoding, limiting insights into population-level representations, while, the role of correlation in neural coding remains a subject of considerable debate. To address this, we introduce novel, correlation-aware information-theoretic measures that quantify the encoding efficiency of multiple neurons, including the joint stimulus information rate for neuron pairs and the spectral-stimulus information for arbitrary sized populations. The spectral-stimulus information, defined as the leading eigenvalue of the stimulus information matrix, is maximized when neurons exhibit localized, non-overlapping firing fields, mirroring place cell and head direction cell activity. We apply these measures to neural data recorded in mice and monkeys, elucidating differences in encoding efficiency across neuronal pairs and populations. Then, we demonstrate that these measures can be used to train recurrent neural networks (RNNs) via self-supervised learning, leading to the emergence of place cells and head direction cells. Our findings highlight how neural populations collectively encode stimuli, offering a more comprehensive framework for understanding stimulus encoding and optimizing artificial navigation systems in novel environments.

Wyatt Mackey, Ioannis Schizas, Jared Deighton et al.

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.