Extracting Number-Selective Responses from Coherent Oscillations in a Computer Model

Abstract

Cortical neurons selective for numerosity may underlie an innate number sense in both animals and humans. We hypothesize that the number- selective responses of cortical neurons may in part be extracted from coherent, object-specific oscillations . Here, indirect evidence for this hypothesis is obtained by analyzing the numerosity information encoded by coherent oscillations in artificially generated spikes trains. Several experiments report that gamma-band oscillations evoked by the same object remain coherent, whereas oscillations evoked by separate objects are uncorrelated. Because the oscillations arising from separate objects would add in random phase to the total power summed across all stimulated neurons, we postulated that the total gamma activity, normalized by the number of spikes, should fall roughly as the square root of the number of objects in the scene, thereby implicitly encoding numerosity. To test the hypothesis, we examined the normalized gamma activity in multiunit spike trains, 50 to 1000 msec in duration, produced by a model feedback circuit previously shown to generate realistic coherent oscillations. In response to images containing different numbers of objects, regardless of their shape, size, or shading, the normalized gamma activity followed a square-root-of-n rule as long as the separation between objects was sufficiently large and their relative size and contrast differences were not too great. Arrays of winner-take-all numerosity detectors, each responding to normalized gamma activity within a particular band, exhibited tuning curves consistent with behavioral data. We conclude that coherent oscillations in principle could contribute to the number-selective responses of cortical neurons, although many critical issues await experimental resolution.

Connecting neural coding to number cognition: a computational account

“…Theories of how number sensitive neural activity develops have been supported by computational models (e.g. Ahmad et al ., 2002; Dehaene, 2007; Dehaene & Changeux, 1993; Miller & Kenyon, 2007; Pearson, Roitman, Brannon, Platt & Raghavachari, 2010; Verguts & Fias, 2004). These studies demonstrate the development of number selective activity from other inputs, such as perceptual object tracking, or accumulator‐like summation coding (Miller & Kenyon, 2007; Verguts & Fias, 2004).…”

“…Ahmad et al ., 2002; Dehaene, 2007; Dehaene & Changeux, 1993; Miller & Kenyon, 2007; Pearson, Roitman, Brannon, Platt & Raghavachari, 2010; Verguts & Fias, 2004). These studies demonstrate the development of number selective activity from other inputs, such as perceptual object tracking, or accumulator‐like summation coding (Miller & Kenyon, 2007; Verguts & Fias, 2004). Computational results show number selective activity coded with tuning functions that are proportional to the number magnitude, skewed on the linear scale and symmetric on the log scale, similar to the neural data (Dehaene, 2007).…”

Possible dendritic contribution to unimodal numerosity tuning and Weber-Fechner law-dependent numerical cognition

“…In contrast, if only the network-based mechanism (Dehaene and Changeux, 1993; Verguts and Fias, 2004) operates, strengthening inhibition would reduce overall activity of the number-selective neurons but would not shift the peak position of the tuning curve (c.f., Figure 1A). Another existing model for unimodal numerosity tuning based on oscillations (Miller and Kenyon, 2007) assumes winner-take-all competition at the final stage, which could be implemented by lateral inhibition similar to what is considered in the network-based models (Dehaene and Changeux, 1993; Verguts and Fias, 2004), so that strengthening inhibition is expected not to shift the tuning curve; thus this is also expected to be distinguishable from the proposed model. In order to test the contribution of the proposed model, it would also be interesting to examine whether and how single neuronal properties such as the dendritic morphology or the spike width correlates with the numerosity preference in vivo .…”