Adaptive Spontaneous Transitions between Two Mechanisms of Numerical Averaging

Brezis, Noam; Bronfman, Zohar Z.; Usher, Marius

doi:10.1038/srep10415

Cited by 45 publications

(101 citation statements)

References 40 publications

(48 reference statements)

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“…Although the mechanism underlying rapid numerical averaging remains largely unknown, it has been recently hypothesized that approximate averaging relies on lowerlevel processes of summary statistics extraction (Brezis et al, 2015;Dotan, Friedmann, & Dehaene, 2014;Van Opstal, de Lange, & Dehaene, 2011;Verguts & Fias, 2004;Dehaene, 2001), whereby upon exposure to a multitude of continuous features (e.g., spatial-orientation, circle-diameter) observers exhibit high sensitivity to the average of the ensemble (Alvarez & Oliva, 2008; Chong & Treisman, Figure 6. Accuracy in sham, frontal, and parietal stimulation (within-participant results; n = 12).…”

Section: Neurocomputational Model and Fitting Resultsmentioning

confidence: 99%

“…Each trial began with a central fixation cross (300 msec) after which a sequence of two-digit numbers was presented (white Arabic numerals on black background; each number was displayed for 500 msec). The numbers ranged between 10 and 90 and were sampled from four predefined triangular distributions (see also Brezis et al, 2015). The sequence set size (i.e., the quantity of presented numbers) was 4, 8, or 16 and was randomized between trials.…”

Section: Stimulus Materialsmentioning

confidence: 99%

“…In a previous work (Brezis, Bronfman, & Usher, 2015), we have built on the exact/approximate numerical processing distinction and proposed that it plays a critical role in numerical averaging and implicit preference formation. In particular, we suggested that approximate numerical averaging relies on a different mechanism than exact (analytic) averaging (e.g., calculation of the sum of the numbers and division by the number of elements), with the former relying on a population code, as in perceptual averaging (see also Modeling section below).…”

Section: Introductionmentioning

confidence: 99%

“…To investigate whether the parietal cortex is causally involved in approximate averaging, we have conducted two within-participant tDCS studies, in which observers were stimulated while being presented with rapid sequences (500 msec per number) of two-digit numbers after which they were requested to convey (using an analog scale) an estimation of the numbers' average ( Figure 1A; see also Brezis et al, 2015). In both experiments, each participant attended two experimental sessions: one in which the anodal stimulation was delivered over the right parietal cortex 1 (Piazza et al, 2004;Dehaene, Piazza, Pinel, & Cohen, 2003;Dehaene et al, 1999) and another in which the anodal stimulation was delivered over the right frontal cortex (order of sessions was counterbalanced; in both sessions, the cathode was placed over the contralateral supraorbital area; see Figure 1B).…”

Section: Introductionmentioning

confidence: 99%

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

Brezis

Bronfman

Jacoby

et al. 2016

Journal of Cognitive Neuroscience

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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.

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Section: Neurocomputational Model and Fitting Resultsmentioning

confidence: 99%

Section: Stimulus Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Brezis

Bronfman

Jacoby

et al. 2016

Journal of Cognitive Neuroscience

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“…Humans can efficiently extract the average gender or emotion from a set of faces (26)(27)(28). Crucial for our proposal, ensemble averaging is also possible with symbolic stimuli: Humans can efficiently extract the mean value of a set of number stimuli (29,30).…”

Section: Discussionmentioning

confidence: 99%

Continuous track paths reveal additive evidence integration in multistep decision making

Calderon

Dewulf

Gevers

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Multistep decision making pervades daily life, but its underlying mechanisms remain obscure. We distinguish four prominent models of multistep decision making, namely serial stage, hierarchical evidence integration, hierarchical leaky competing accumulation (HLCA), and probabilistic evidence integration (PEI). To empirically disentangle these models, we design a two-step reward-based decision paradigm and implement it in a reaching task experiment. In a first step, participants choose between two potential upcoming choices, each associated with two rewards. In a second step, participants choose between the two rewards selected in the first step. Strikingly, as predicted by the HLCA and PEI models, the first-step decision dynamics were initially biased toward the choice representing the highest sum/mean before being redirected toward the choice representing the maximal reward (i.e., initial dip). Only HLCA and PEI predicted this initial dip, suggesting that first-step decision dynamics depend on additive integration of competing second-step choices. Our data suggest that potential future outcomes are progressively unraveled during multistep decision making.multistep decision making | computational modeling | reaching task I magine leaving your house in search of food in the neighborhood. Outside, you must first decide to go left or right. Going left subsequently affords a second left-right choice between Thai and Italian food, whereas going right affords another left-right choice between Mexican and Lebanese food. This illustrates a typical twostep tree path decision-making scenario (i.e., four potential tree paths; see Fig. 1A). Such two-step decisions have been conceptualized within the framework of model-based reinforcement learning (1, 2), and recent work has focused on which brain areas underpin reward representation in multistep decision making (3-5). However, the computations underlying multistep decision making are still debated. To address this issue, we distinguish four computational models. We derive and contrast empirical predictions from the four models and test them. In the following paragraph we explain the common ideas and distinguishing features of the four models.In each model, each tree path is associated with an evidence (E) accumulator (e.g., in Fig. 1A, there are four tree paths; we will use Fig. 1A and Supporting Information, Appendix A: Computational Models, Fig. S1, to illustrate the four models). The two leftmost E accumulators (i.e., leading to 3 and 9 in Fig. 1A) are taken as inputs to a left motor evidence (ME) accumulator. The two rightmost E accumulators project to a right ME accumulator. All models reach decisions by gradually updating their E and/or ME accumulator values at each iteration depending on the rewards associated with each tree path. Models can be conceptually distinguished based on three features. The first featuremapping-defines how E accumulators map to ME accumulators; in particular, this feature distinguishes models where only the maximally active E accumulator pro...

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Valuation and estimation from experience

Olschewski

Newell

Oberholzer

et al. 2021

Behavioral Decision Making

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The processing of sequentially presented numerical information is a prerequisite for decisions from experience, where people learn about potential outcomes and their associated probabilities and then make choices between gambles. Little is known, however, about how people's preference for choosing a gamble is affected by how they perceive and process numerical information. To address this, we conducted a series of experiments wherein participants repeatedly sampled numbers from continuous outcome distributions. They were incentivized either to estimate the means of the numbers or to state their minimum selling prices to forgo a consequential draw from the distributions (i.e., the certainty equivalents or valuations). We found that participants valued distributions below their means, valued high-variance sequences lower than low-variance sequences, and valued left-skewed sequences lower than right-skewed sequences. Though less pronounced, similar patterns occurred in the mean estimation task where preferences should not play a role. These results are not consistent with prior findings in decision from experience such as the overweighting of high numbers and the underweighting of rare events. Rather, the qualitative effects, as well as the similarity of effects in valuation and estimation, are consistent with the assumption that people process numbers on a compressed mental number line in valuations from experience.

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Adaptive Spontaneous Transitions between Two Mechanisms of Numerical Averaging

Cited by 45 publications

References 40 publications

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

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

Continuous track paths reveal additive evidence integration in multistep decision making

Valuation and estimation from experience

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