The material-weight illusion is a Bayes-optimal percept under competing density priors

Abstract

The material-weight illusion (MWI) is one example in a class of weight perception illusions that seem to defy principled explanation. In this illusion, when an observer lifts two objects of the same size and mass, but that appear to be made of different materials, the denserlooking (e.g., metal-look) object is perceived as lighter than the less-dense-looking (e.g., polystyrene-look) object. Like the size-weight illusion (SWI), this perceptual illusion occurs in the opposite direction of predictions from an optimal Bayesian inference process, which predicts that the denser-looking object should be perceived as heavier, not lighter. The presence of this class of illusions challenges the often-tacit assumption that Bayesian inference holds universal explanatory power to describe human perception across (nearly) all domains: If an entire class of perceptual illusions cannot be captured by the Bayesian framework, how could it be argued that human perception truly follows optimal inference? However, we recently showed that the SWI can be explained by an optimal hierarchical Bayesian causal inference process (Peters, Ma & Shams, 2016) in which the observer uses haptic information to arbitrate among competing hypotheses about objects' possible density relationship. Here we extend the model to demonstrate that it can readily explain the MWI as well. That hierarchical Bayesian inference can explain both illusions strongly suggests that even puzzling percepts arise from optimal inference processes. AbstractThe materialweight illusion (MWI) is one example in a class of weight perception illusions that seem to defy principled explanation. In this illusion, when an observer lifts two objects of the same size and mass, but that appear to be made of different materials, the denserlooking (e.g., metallook) object is perceived as lighter than the lessdenselooking (e.g., polystyrenelook) object. Like the sizeweight illusion (SWI), this perceptual illusion occurs in the opposite direction of predictions from an optimal Bayesian inference process, which predicts that the denserlooking object should be perceived as heavier , not lighter. The presence of this class of illusions challenges the oftentacit assumption that Bayesian inference holds universal explanatory power to describe human perception across (nearly) all domains: If an entire class of perceptual illusions cannot be captured by the Bayesian framework, how could it be argued that human perception truly follows optimal inference? However, we recently showed that the SWI can be explained by an optimal hierarchical Bayesian causal inference process (Peters, Ma & Shams, 2016) in which the observer uses haptic information to arbitrate among competing hypotheses about objects' possible density relationship. Here we extend the model to demonstrate that it can readily explain the MWI as well. That hierarchical Bayesian inference can explain both illusions strongly suggests that even puzzling percepts arise from optimal inference processes.

The material-weight illusion disappears or inverts in objects made of two materials

“… Peters et al (2016) proposed a model that predicts the illusion as the result of Bayesian integration in a framework of multiple competing density priors (as proposed by Yuille and Bülthoff 1996 ) and the likelihood of incoming haptic information. These same authors recently proposed a similar mechanism underlying the classic MWI ( Peters et al 2018 ). Within this framework, the classic and inverted MWI may reflect two different estimates resulting from the same basic mechanism.…”

“…However, because this model is only a post hoc explanation of our results, future studies should test it systematically. If the Bayesian account proposed by Peters et al (2016) can explain the SWI ( Peters et al 2016 ), the classic MWI ( experiment 2 and Peters at al. 2018 ), the inverted MWI ( experiment 1 ), the absence of an illusion ( experiment 3 ), and weight perception in objects with a nonuniform weight distribution ( experiment 4 ), one might also expect to find an inverted SWI in bipartite objects with unequally sized halves but equal weight distribution.…”

Variance misperception under skewed empirical noise statistics explains overconfidence in the visual periphery

“…To this simple Type 1 system we add an additional hierarchical or metacognitive (Type 2) inference layer to explore several hypotheses about how the noise in the system (both internal noise and external noise (Lu and Dosher, 2008) ) governs the Type 1 decision space. Drawing inspiration from (1) Bayesian ideal observer analysis demonstrating that natural scene statistics govern Type 1 perception (Adams et al, 2004;Girshick et al, 2011;Peters et al, 2015;Stocker and Simoncelli, 2006) , and (2) hierarchical models in which a Bayesian ideal observer's inference about latent variables also governs the ultimate percept (Knill and Richards, 1996;Knill and Saunders, 2003;Körding et al, 2007;Körding and Tenenbaum, 2007a;Odegaard et al, 2015;Peters et al, 2018Peters et al, , 2016Samad et al, 2015;Yuille and Bülthoff, 1996) , we developed and compared a series of 'flat' and 'hierarchical' inference models with varying 'knowledge' or reliance of natural scene statistics of noise in central versus peripheral vision to evaluate their predictions for peripheral inflation.…”

“…A Bayesian observer that is sensitive to environmental statistics about a given variable will represent expectations about such variables as prior distributions --for example, about light source location, motion speed, or contour orientation (Adams et al, 2004;Girshick et al, 2011;Stocker and Simoncelli, 2006) , as mentioned above. Here, we hypothesized that central and peripheral environmental distributions of noise experienced by the visual system also lead the visual system to form prior expectations about variability as a latent variable, following previous convention in hierarchical Bayesian inference in vision and multisensory integration (Beierholm et al, 2009;Knill and Richards, 1996;Knill and Saunders, 2003;Körding et al, 2007;Körding and Tenenbaum, 2007a;Landy et al, 2011;Odegaard et al, 2015;Peters et al, 2018Peters et al, , 2016Peters et al, , 2015Samad et al, 2015;Shams et al, 2000;Wozny et al, 2008;Yuille and Bülthoff, 1996) . That is, the visual system learns to expect that central vision typically involves less noisy signals, while peripheral vision typically involves noisier signals.…”

“…However, while such empirical priors are based in fact, they can sometimes lead to inaccurate perceptual estimates when the system is required to use them in Bayes-optimal computations. For example, empirical priors about man-made versus natural objects' densities are used by the system in judging visuo-haptic weight estimates (Peters et al, 2015) , but in ways that lead to illusory percepts of heaviness due to simplification of complex, continuous priors over density into mixtures of Gaussians (Peters et al, 2018(Peters et al, , 2016 --perhaps due to biological restrictions on information coding (Heng et al, 2020) . It has also been shown that highly asymmetric (skewed) priors over stimulus location which are initially learned correctly can be relied upon as if they were Gaussian when the observer is required to use them in a cue combination task (Acerbi et al, n.d.) , and that incorrect priors in general can lead to illusions across many areas of visual perception in both healthy and atypical perception (Flanagan et al, 2008;Geisler and Kersten, 2002;Teufel et al, 2013;Valton et al, 2019;Weiss et al, 2002) .…”