Abstract
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. In particular, this connectivity pattern appears to be constraining learning so that only neural activity patterns falling within the intrinsic manifold can be learned and elicited. Here, we use three different models of spiking neural networks (echo-state networks, the Neural Engineering Framework and Efficient Coding) to demonstrate how the intrinsic manifold can be made a direct consequence of the circuit connectivity. Using this relationship between the circuit connectivity and the intrinsic manifold, we show that learning of patterns outside the intrinsic manifold corresponds to much larger changes in synaptic weights than learning of patterns within the intrinsic manifold. Assuming larger changes to synaptic weights requires extensive learning, this observation provides an explanation of why learning is easier when it does not require the neural activity to leave its intrinsic manifold.
Highlights
The availability of novel experimental methods allows for simultaneous recording of 1000s of neurons and has made it possible to observe the fine structure of temporal evolution of taskrelated neuronal activity in vivo
This connectivity pattern appears to be constraining learning so that only neural activity patterns falling within the intrinsic manifold can be learned and elicited
Neural activity with D dimensions can by definition be decomposed into D time-independent components called principal components, factor loadings or neural modes (Fig 1A)
Summary
The availability of novel experimental methods allows for simultaneous recording of 1000s of neurons and has made it possible to observe the fine structure of temporal evolution of taskrelated neuronal activity in vivo. The activity at a particular time corresponds to a point in this space, and the temporal evolution of the neuronal activity constitutes a trajectory. Analysis of such trajectories has revealed that across different brain regions and in different behavioral conditions the neural activity remains low dimensional [1,2,3,4,5,6,7] (but see [8]) such that the dimensionality of the activity is much smaller than number of neurons. The trajectories corresponding to the task-related activity tend to be constrained to a linear subspace (the intrinsic manifold) of the state space rather than moving freely in all directions. Note that our goal is to build a conceptual understanding and not to faithfully model every aspect of the experiment
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