Transcranial Direct Current Stimulation over the Parietal Cortex Improves Approximate Numerical Averaging

Abstract

The parietal cortex has been implicated in a variety of numerosity and numerical cognition tasks and was proposed to encompass dedicated neural populations that are tuned for analogue magnitudes as well as for symbolic numerals. Nonetheless, it remains unknown whether the parietal cortex plays a role in approximate numerical averaging (rapid, yet coarse computation of numbers' mean)-a process that is fundamental to preference formation and decision-making. To causally investigate the role of the parietal cortex in numerical averaging, we have conducted a transcranial direct current stimulation (tDCS) study, in which participants were presented with rapid sequences of numbers and asked to convey their intuitive estimation of each sequence's average. During the task, the participants underwent anodal (excitatory) tDCS (or sham), applied either on a parietal or a frontal region. We found that, although participants exhibit above-chance accuracy in estimating the average of numerical sequences, they did so with higher precision under parietal stimulation. In a second experiment, we have replicated this finding and confirmed that the effect is number-specific rather than domain-general or attentional. We present a neurocomputational model postulating population-coding underlying rapid numerical averaging to account for our findings. According to this model, stimulation of the parietal cortex elevates neural activity in number-tuned dedicated detectors, leading to increase in the system's signal-to-noise level and thus resulting in more precise estimations.

The averaging of numerosities: A psychometric investigation of the mental line

“…While, analytically, averaging can be viewed as being equivalent to addition (followed by division by the number of terms), there are reasons to believe that this is not the way that participants estimate the average of rapid sequences of (symbolic) numbers (Brezis, Bronfman, & Usher, 2015Malmi & Samson, 1983;Mitrani-Rosenbaum, Glickman, & Usher, 2020), as they can provide accurate and rapid estimations of the average, even when they do not know the number of elements, or when elements in a specific range are to be discarded after the sequence presentation (Malmi & Samson, 1983). Rather, the evidence indicates that the estimation mechanism corresponds to a frequency-based estimation (the estimation of the center of mass of a noisy frequency distribution of the numbers), which is somewhat similar to the one suggested by the ANS representation system (see Brezis, Bronfman, Jacoby, Lavidor, & Usher, 2016;Brezis et al, 2015Brezis et al, , 2018. In particular, Brezis et al (2015Brezis et al ( , 2018 have proposed an ANS type of population code model, which accounts for a characteristic signature of the population code: Precision improves with the length of the sequence (see Fig.…”

Fast and effective: Intuitive processes in complex decisions

“…As our task involves some practice, the assumption that the decision mechanism includes learned weights (reflecting the attributes' importance) is not implausible. 2 Alternatively, the mechanism of weighted averaging could be mediated by a population code model (Brezis et al, 2016;Brezis et al, 2015;Brezis, Bronfman & Usher, 2017), which operates using numerosity detectors (Dehaene, Molko, Cohen & Wilson, 2004;Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2 This does not require to endorse all the assumptions of the PCS model, such as RT being based on convergence to asymptotic activation; an alternative assumption is an integration to boundary. The property of PCS that is important to our results is the parallel integration of values from all attributes.…”

“…Recent research has shown that an important precursor of WADDnumerical averagingcan be estimated in a relatively precise and yet automatic manner (Brezis, Bronfman, Jacoby, Lavidor, & Usher, 2016;Brezis, Bronfman, & Usher, 2015;Rusou, Zakay, & Usher, 2017). Here we set to test whether this ability extends to weighted averaging, by employing a job selection multi-attribute decision task.…”

Probing the architecture of visual number sense with parietal tRNS

“…We hypothesised that this may lead to two possible effectson behavioural performance. If a brain area implements a type of numerosity code, a tRNS-evoked response gain may result ina better discriminability between two stimuli (Carrasco, Ling & Read, 2004;Brezis,Bronfman, Jacoby, Lavidor, & Usher, 2016). Thiscan be measured as a steeper slope of a psychophysical function that fits the probability of choosing a test stimulus in reference to a standard ( Figure 1B).…”