Abstract
We propose that correlations among neurons are generically strong enough to organize neural activity patterns into a discrete set of clusters, which can each be viewed as a population codeword. Our reasoning starts with the analysis of retinal ganglion cell data using maximum entropy models, showing that the population is robustly in a frustrated, marginally sub-critical, or glassy, state. This leads to an argument that neural populations in many other brain areas might share this structure. Next, we use latent variable models to show that this glassy state possesses well-defined clusters of neural activity. Clusters have three appealing properties: (i) clusters exhibit error correction, i.e., they are reproducibly elicited by the same stimulus despite variability at the level of constituent neurons; (ii) clusters encode qualitatively different visual features than their constituent neurons; and (iii) clusters can be learned by downstream neural circuits in an unsupervised fashion. We hypothesize that these properties give rise to a “learnable” neural code which the cortical hierarchy uses to extract increasingly complex features without supervision or reinforcement.
Highlights
Throughout the central brain, information about the external world, internal body states, and movement plans is represented by large populations of neurons
As we will see below, we propose that the large number of retinal ganglion cell types is needed to put the population code into the glassy state
Our analyses of neural populations with the maximum entropy model imply that the retinal population exists in a state that is similar to a spin glass (Figure 2)
Summary
Throughout the central brain, information about the external world, internal body states, and movement plans is represented by large populations of neurons. Having some form of implicit knowledge of receptive field functions of input neurons might be useful in this task, but it is not required With these ideas in mind, we have taken a different approach, that we denote the activity model. If we assume nearest neighbor correlation and a mosaic arrangement of spatial receptive fields, each cell type contributes 7 cells to the population coding unit; multiplying by 30+ cells types results in 200+ neurons What this means is that any location in visual space is encoded by roughly this many ganglion cells. We have used the maximum entropy principle to measure statistics of neural activity that can be well-sampled, such as the average firing rate and pairwise correlations of all neurons, and find the probability distribution with maximum entropy subject to these constraints.
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