Individual neurons in the brain have complex intrinsic dynamics that are highly diverse. We hypothesize that the complex dynamics produced by networks of complex and heterogeneous neurons may contribute to the brain's ability to process and respond to temporally complex data. To study the role of complex and heterogeneous neuronal dynamics in network computation, we develop a rate-based neuronal model, the generalized-leaky-integrate-and-fire-rate (GLIFR) model, which is a rate equivalent of the generalized-leaky-integrate-and-fire model. The GLIFR model has multiple dynamical mechanisms, which add to the complexity of its activity while maintaining differentiability. We focus on the role of after-spike currents, currents induced or modulated by neuronal spikes, in producing rich temporal dynamics. We use machine learning techniques to learn both synaptic weights and parameters underlying intrinsic dynamics to solve temporal tasks. The GLIFR model allows the use of standard gradient descent techniques rather than surrogate gradient descent, which has been used in spiking neural networks. After establishing the ability to optimize parameters using gradient descent in single neurons, we ask how networks of GLIFR neurons learn and perform on temporally challenging tasks, such as sequential MNIST. We find that these networks learn diverse parameters, which gives rise to diversity in neuronal dynamics, as demonstrated by clustering of neuronal parameters. GLIFR networks have mixed performance when compared to vanilla recurrent neural networks, with higher performance in pixel-by-pixel MNIST but lower in line-by-line MNIST. However, they appear to be more robust to random silencing. We find that the ability to learn heterogeneity and the presence of after-spike currents contribute to these gains in performance. Our work demonstrates both the computational robustness of neuronal complexity and diversity in networks and a feasible method of training such models using exact gradients.

Brain-computer interfaces (BCIs) decode recorded neural signals from the brain and/or stimulate the brain with encoded neural signals. BCIs span both hardware and software and have a wide range of applications in restorative medicine, from restoring movement through prostheses and robotic limbs to restoring sensation and communication through spellers. BCIs also have applications in diagnostic medicine, e.g., providing clinicians with data for detecting seizures, sleep patterns, or emotions.