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 limited 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. We found that 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.

Manifold attractors are a key framework for understanding how continuous variables, such as position or head direction, are encoded in the brain. In this framework, the variable is represented along a continuum of persistent neuronal states which forms a manifold attactor. Neural networks with symmetric synaptic connectivity that can implement manifold attractors have become the dominant model in this framework. In addition to a symmetric connectome, these networks imply homogeneity of individual-neuron tuning curves and symmetry of the representational space; these features are largely inconsistent with neurobiological data. Here, we developed a theory for computations based on manifold attractors in trained neural networks and show how these manifolds can cope with diverse neuronal responses, imperfections in the geometry of the manifold and a high level of synaptic heterogeneity. In such heterogeneous trained networks, a continuous representational space emerges from a small set of stimuli used for training. Furthermore, we find that the network response to external inputs depends on the geometry of the representation and on the level of synaptic heterogeneity in an analytically tractable and interpretable way. Finally, we show that a too complex geometry of the neuronal representation impairs the attractiveness of the manifold and may lead to its destabilization. Our framework reveals that continuous features can be represented in the recurrent dynamics of heterogeneous networks without assuming unrealistic symmetry. It suggests that the representational space of putative manifold attractors in the brain dictates the dynamics in their vicinity.