Training spiking recurrent neural networks on neuronal recordings or behavioral tasks has become a prominent tool to study computations in the brain. With an increasing size and complexity of neural recordings, there is a need for fast algorithms that can scale to large datasets. We present optimized CPU and GPU implementations of the recursive least-squares algorithm in spiking neural networks. The GPU implementation allows training networks to reproduce neural activity of an order of millions neurons at order of magnitude times faster than the CPU implementation. We demonstrate this by applying our algorithm to reproduce the activity of > 66, 000 recorded neurons of a mouse performing a decision-making task. The fast implementation enables efficient training of large-scale spiking models, thus allowing for in-silico study of the dynamics and connectivity underlying multi-area computations.

Neural representations of information are shaped by local network interactions. Previous studies linking neural coding and cortical connectivity focused on stimulus selectivity in the sensory cortex 1–4. Here we study neural activity in the motor cortex during naturalistic behavior in which mice gathered rewards with multidirectional tongue reaching. This behavior does not require training and thus allowed us to probe neural coding and connectivity in motor cortex before its activity is shaped by learning a specific task. Neurons typically responded during and after reaching movements and exhibited conjunctive tuning to target location and reward outcome. We used an all-optical 5,4,6,7 method for large-scale causal functional connectivity mapping in vivo. Mapping connectivity between > 20,000,000 excitatory neuronal pairs revealed fine-scale columnar architecture in layer 2/3 of the motor cortex. Neurons displayed local (< 100 µm) like-to-like connectivity according to target-location tuning, and inhibition over longer spatial scales. Connectivity patterns comprised a continuum, with abundant weakly connected neurons and sparse strongly connected neurons that function as network hubs. Hub neurons were weakly tuned to target-location and reward-outcome but strongly influenced neighboring neurons. This network of neurons, encoding location and outcome of movements to different motor goals, may be a general substrate for rapid learning of complex, goal-directed behaviors.

Task-related neural activity is widespread across populations of neurons during goal-directed behaviors. However, little is known about the synaptic reorganization and circuit mechanisms that lead to broad activity changes. Here we trained a subset of neurons in a spiking network with strong synaptic interactions to reproduce the activity of neurons in the motor cortex during a decision-making task. Task-related activity, resembling the neural data, emerged across the network, even in the untrained neurons. Analysis of trained networks showed that strong untrained synapses, which were independent of the task and determined the dynamical state of the network, mediated the spread of task-related activity. Optogenetic perturbations suggest that the motor cortex is strongly-coupled, supporting the applicability of the mechanism to cortical networks. Our results reveal a cortical mechanism that facilitates distributed representations of task-variables by spreading the activity from a subset of plastic neurons to the entire network through task-independent strong synapses.

Foraging animals must use decision-making strategies that dynamically adapt to the changing availability of rewards in the environment. A wide diversity of animals do this by distributing their choices in proportion to the rewards received from each option, Herrnstein’s operant matching law. Theoretical work suggests an elegant mechanistic explanation for this ubiquitous behavior, as operant matching follows automatically from simple synaptic plasticity rules acting within behaviorally relevant neural circuits. However, no past work has mapped operant matching onto plasticity mechanisms in the brain, leaving the biological relevance of the theory unclear. Here we discovered operant matching in Drosophila and showed that it requires synaptic plasticity that acts in the mushroom body and incorporates the expectation of reward. We began by developing a novel behavioral paradigm to measure choices from individual flies as they learn to associate odor cues with probabilistic rewards. We then built a model of the fly mushroom body to explain each fly’s sequential choice behavior using a family of biologically-realistic synaptic plasticity rules. As predicted by past theoretical work, we found that synaptic plasticity rules could explain fly matching behavior by incorporating stimulus expectations, reward expectations, or both. However, by optogenetically bypassing the representation of reward expectation, we abolished matching behavior and showed that the plasticity rule must specifically incorporate reward expectations. Altogether, these results reveal the first synaptic level mechanisms of operant matching and provide compelling evidence for the role of reward expectation signals in the fly brain.