A Bayesian Perspective on Accumulation in the Magnitude System

Abstract

Several theoretical and empirical work posit the existence of a common magnitude system in the brain. Such a proposal implies that manipulating stimuli in one magnitude dimension (e.g. duration in time) should interfere with the subjective estimation of another magnitude dimension (e.g. size in space). Here, we asked whether a generalized Bayesian magnitude estimation system would sample sensory evidence using a common, amodal prior. Two psychophysical experiments separately tested participants on their perception of duration, surface, and numerosity when the non-target magnitude dimensions and the rate of sensory evidence accumulation were manipulated. First, we found that duration estimation was resilient to changes in surface and numerosity, whereas lengthening (shortening) the duration yielded under- (over-) estimations of surface and numerosity. Second, the perception of surface and numerosity were affected by changes in the rate of sensory evidence accumulation, whereas duration was not. Our results suggest that a generalized magnitude system based on Bayesian computations would minimally necessitate multiple priors.

Multiplexing of EEG signatures for temporal and spatial distance estimates

“…Consistent with this finding, we also observed a significantly lower average value of the feedback constant k for the temporal reproduction task [t(15) = 3.635, p = 0.002, d = 0.91], indicating that the adaptive feedback window was wider for temporal than spatial estimates. However, no significant difference was detected between the slope of reproduced intervals for temporal and spatial reproduction tasks [Paired t-test: t(15) = -0.651, p = 0.525], suggesting that despite the difference in veridicality, the degree of central tendency was the same; further, no correlation between slope values was observed [Pearson r = -0.239, p = 0.374], suggesting that a common mechanism did not underlie central tendency effects observed across both tasks (Martin et al, 2017). Additionally, when analyzing CV values, a repeated measures ANOVA with task and interval as factors detected a main effect of task [F(1,15)=14.425, p = 0.002, η 2 p = 0.49] but not interval [F(1,15)=1.079, p = 0.381] or interaction [F(1,15)=0.552, p = 0.768]; when collapsing across duration, this effect was shown to be due to a higher CV for the temporal reproduction task [t(15) = -3.798, p = 0.002, Cohen's d = 0.95],…”

“…However, one question that continues to be controversial is whether temporal and spatial dimensions are processed independently (Marcos & Genovesio, 2017;Cai & Connell, 2016;Robinson, et al 2019). Previous studies have used a variety of methodologies and behavioral paradigms to provide evidence of a symmetrical or asymmetrical relationship between the perception of space and time (Bueti & Walsh, 2009;Martin, et al 2017). Among these studies, self-motion reproduction, imagined temporal estimates, virtual navigation and temporal and spatial production have resulted in conflicting findings.…”

Distinct temporal mechanisms modulate numerosity perception

“…Such an interpretation could mean that there are less specialized duration mechanisms interacting with different magnitudes, such as numerosity and space, as the ATOM theory suggests (Bueti & Walsh, 2009;Walsh, 2003), and other, more specialized duration mechanisms dedicated for duration processing only. This distinction could also explain the contradicting findings from (behavioral) studies examining the interaction of time and numerosity (Chun et al, 2018;Javadi & Aichelburg, 2012;Javadi et al, 2014;Lambrechts et al, 2013;Martin et al, 2017;Tsouli et al, 2019).…”

“…Based on this model, number and duration discrimination rely on a single magnitude system which operates in either the counting or the timing mode (Fetterman, 1993). From an experimental perspective, a number of behavioral (Alards-Tomalin, Walker, Kravetz, & Leboe-McGowan, 2016;Cappelletti, Freeman, & Butterworth, 2011;Cappelletti et al, 2009;Chun, Lee, Lee, & Cho, 2018;Dormal, Seron, & Pesenti, 2006;Gilaie-Dotan, Rees, Butterworth, & Cappelletti, 2014;Javadi & Aichelburg, 2012;Lambrechts, Walsh, & Van Wassenhove, 2013;Martin, Wiener, & Van Wassenhove, 2017;Tokita & Ishiguchi, 2011;Tsouli, Dumoulin, te Pas, & van der Smagt, 2019) and neuroimaging (Bueti & Walsh, 2009;Cappelletti et al, 2014;Castelli, Glaser, & Butterworth, 2006;Hayashi et al, 2013;Javadi, Brunec, Walsh, Penny, & Spiers, 2014) studies provide support for a partly shared processing system for numerosity and time, whereas other studies suggest that numerosity and time are independent and are processed by distinct mechanisms (Agrillo, Piffer, & Adriano, 2013;Agrillo, Ranpura, & Butterworth, 2010).…”

Eliciting contextual temporal calibration: The effect of bottom-up and top-down information in reproduction tasks

“…In fact, this has been proposed to serve as a way to optimize behavior, because the prior information can dampen the consequences of noise during the perception of a single event (Faisal, Selen, & Wolpert, 2008), a phenomenon especially relevant in noisy, real-world settings (Van Rijn, 2018). Evidence for the integration of sensory evidence and prior knowledge can be observed in many perceptual and cognitive tasks (e.g., for any magnitude estimation task, Martin, Wiener, & van Wassenhove, 2017), and modeled with Bayesian observer models (e.g., Petzschner, Glasauer, & Stephan, 2015). Bayesian models of perception also have a significant impact on the field of time perception (for an overview, see Shi, Church, & Meck, 2013;Van Rijn, 2016), for example to explain the central tendency observed in multi-duration tasks, or temporal context effect.…”