Neuronal selectivity, population sparseness, and ergodicity in the inferior temporal visual cortex

Abstract

The sparseness of the encoding of stimuli by single neurons and by populations of neurons is fundamental to understanding the efficiency and capacity of representations in the brain, and was addressed as follows. The selectivity and sparseness of firing to visual stimuli of single neurons in the primate inferior temporal visual cortex were measured to a set of 20 visual stimuli including objects and faces in macaques performing a visual fixation task. Neurons were analysed with significantly different responses to the stimuli. The firing rate distribution of 36% of the neurons was exponential. Twenty-nine percent of the neurons had too few low rates to be fitted by an exponential distribution, and were fitted by a gamma distribution. Interestingly, the raw firing rate distribution taken across all neurons fitted an exponential distribution very closely. The sparseness a (s) or selectivity of the representation of the set of 20 stimuli provided by each of these neurons (which takes a maximal value of 1.0) had an average across all neurons of 0.77, indicating a rather distributed representation. The sparseness of the representation of a given stimulus by the whole population of neurons, the population sparseness a (p), also had an average value of 0.77. The similarity of the average single neuron selectivity a (s) and population sparseness for any one stimulus taken at any one time a (p) shows that the representation is weakly ergodic. For this to occur, the different neurons must have uncorrelated tuning profiles to the set of stimuli.

Cortical coding

“…The same value for the sparseness is obtained when one calculates it as the responses of a large set of neurons to a single stimulus, which is termed the population sparseness ap, and this indicates that the representation is weakly ergodic, that is that the response profiles of the different neurons are uncorrelated (Franco et al, 2007).…”

“…We showed that this is not the case, and that although a face-selective cell may respond only to faces, its firing rate is graded to a set of faces with some faces producing large responses, and more and more producing lower and lower responses, with each neuron having a different profile of responses to each of the different faces with an approximately exponential firing rate probability distribution (Baddeley et al, 1997;Baylis, Rolls, & Leonard, 1985;Franco, Rolls, Aggelopoulos, & Jerez, 2007;Treves, Panzeri, Rolls, Booth, & Wakeman, 1999) (see Fig. 1; and also Figs.…”

Neural and computational mechanisms of postponed decisions

“…Graded firing rate distributions are not usually examined in these attractor decision-making networks because the mean field analysis used to set the network parameters requires the same value for the weights within a pool. However, because neurons in the brain typically have graded firing rate distributions, frequently close to exponential (10,22), we have investigated the properties of decision-making networks with graded firing rate representations (16). Here, we investigate the activity of a similar network in a short-term memory period after a decision, and analyze whether the firing rate distribution in the delay period is similar to that found for MPC neurons in that some neurons encode little information in their firing rates, and others more information.…”

Invariant Representations of Objects in Natural Scenes in the Temporal Cortex Visual Areas

“…In a further study using 23 faces and 45 non-face natural images, a distributed representation was again found (Rolls and Tovee 1995a), with the average sparseness being 0.65. The sparseness of the representation provided by a neuron can be defi ned as where r s is the mean fi ring rate of the neuron to stimulus s in the set of S stimuli [see and Franco et al (2006)]. If the neurons are binary (either fi ring or not to a given stimulus), then a would be 0.5 if the neuron responded to 50% of the stimuli and 0.1 if a neuron responded to 10% of the stimuli.…”

“…If the spontaneous fi ring rate was subtracted from the fi ring rate of the neuron to each stimulus, so that the changes of fi ring rate, that is, the active responses of the neurons, were used in the sparseness calculation, then the "response sparseness" had a lower value, with a mean of 0.33 for the population of neurons. The distributed nature of the representation can be further understood by the fi nding that the fi ring rate distribution of single neurons when a wide range of natural visual stimuli are being viewed is approximately exponentially distributed, with rather few stimuli producing high fi ring rates, and increasingly large numbers of stimuli producing lower and lower fi ring rates (Baddeley et al 1997;Franco et al 2006;Rolls and Tovee 1995a;Treves et al 1999) (Fig. 2).…”