Learning recurrent dynamics in spiking networks

Abstract

Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that emerge after learning remains unknown. Here we show that modifying the recurrent connectivity with a recursive least squares algorithm provides sufficient flexibility for synaptic and spiking rate dynamics of spiking networks to produce a wide range of spatiotemporal activity. We apply the training method to learn arbitrary firing patterns, stabilize irregular spiking activity in a network of excitatory and inhibitory neurons respecting Dale’s law, and reproduce the heterogeneous spiking rate patterns of cortical neurons engaged in motor planning and movement. We identify sufficient conditions for successful learning, characterize two types of learning errors, and assess the network capacity. Our findings show that synaptically-coupled recurrent spiking networks possess a vast computational capability that can support the diverse activity patterns in the brain.

Training dynamically balanced excitatory-inhibitory networks

“…Whereas in some approaches the credit assignment problem is tackled by relying on coding assumptions variably linked to optimality criteria, target-based approaches, both in the context of feed-forward [20] and recurrent models, provide a straightforward solution. As shown above as well as in a recent work [27], it is not essential for the teacher network to be a rate model, as long as it effectively acts as a dynamic reservoir that expands task dimensionality via its recurrency, therefore proving rich targets.…”

“…Balanced networks can also be trained to produce prescribed chaotic dynamics (like the Lorenz attractor in Fig 6A) or multiple complex quasi-periodic trajectories. In another task, inspired by the work of Laje, and Buonomano [15] in rate networks, and similar to recent extensions to the QIF spiking case in [27], we trained a spiking network to reproduce a desired transient dynamics in response to an external stimulus. To do so, we recorded innate current trajectories generated by a randomly initialized LIF balanced network for a short period of time (2 sec) during its spontaneous activity.…”

“…In [33], the authors employed a clipping procedure on top of a FORCE training method, which entails rank-1 updates to the original randomly connected recurrent network, while in [18] the authors used an off-line two step Full-FORCE procedure to train a large network performing an oscillation task. In a slightly different setting, the authors of [27] used Full-FORCE to train networks of quadratic integrate and fire neurons to reproduce prescribed synaptic drive, as well as spiking rate patterns in response to a brief strong stimulus. They provide an example of an E/I network with parametrically tuned effective connectivity and no external currents that tracks its own innate trajectories, recorded over the course of spontaneous activity.…”

A solution to the learning dilemma for recurrent networks of spiking neurons

“…Instead, some of them were relying on control theory to train a chaotic reservoir of spiking neurons 32 – 34 . Others used the FORCE algorithm 35 , 36 or variants of it 35 , 37 – 39 . However, the FORCE algorithm was not argued to be biologically realistic, as the plasticity rule for each synaptic weight requires knowledge of the current values of all other synaptic weights.…”

Nonlinear stimulus representations in neural circuits with approximate excitatory-inhibitory balance

“…The relationship between connectivity and firing rates in recurrent spiking networks can be mathematically difficult to derive, which can make it difficult to derive gradient based methods for training recurrent spiking networks (though some studies have succeeded, see for example [48,49]). The piecewise linearity of firing rates in the semi-balanced state (see Eq (4)) could simplify the training of recurrent spiking networks because the gradient of the firing rate with respect to the weights can be easily computed.…”