Low Dimensional Activity in Spiking Neuronal Networks

Several recent studies have shown that neural activity in vivo tends to be constrained to a low-dimensional manifold. Such activity does not arise in simulated neural networks with homogeneous connectivity and it has been suggested that it is indicative of some other connectivity pattern in neuronal networks. Surprisingly, the structure of the intrinsic manifold of the network activity puts constraints on learning. For instance, animals find it difficult to perform tasks that may require a change in the intrinsic manifold. Here, we demonstrate that the Neural Engineering Framework (NEF) can be adapted to design a biologically plausible spiking neuronal network that exhibit low dimensional activity. Consistent with experimental observations, the resulting synaptic weight distribution is heavy-tailed (log-normal). In our model, a change in the intrinsic manifold of the network activity requires rewiring of the whole network, which may be either not possible or a very slow process. This observation provides an explanation of why learning is easier when it does not require the neural activity to leave its intrinsic manifold. Significance statement A network in the brain consists of thousands of neurons. A priori, we expect that the network will have as many degrees of freedom as its number of neurons. Surprisingly, experimental evidence suggests that local brain activity is confined to a space spanned by 10 variables. Here, we describe an approach to construct spiking neuronal networks that exhibit low-dimensional activity and address the question: how the intrinsic dimensionality of the network activity restricts the learning as suggested by recent experiments? Specifically, we show that tasks that requires animals to change the network activity outside the intrinsic space would entail large changes in the neuronal connectivity, and therefore, animals are either slow or not able to acquire such tasks.