Distinct representations of physical and perceived numerosity in convolutional neural networks
Poster No:
958
Submission Type:
Abstract Submission
Authors:
桂芬 苏1,2, Yuxuan Cai1,2, Delong Zhang1,2
Institutions:
1School of Psychology, South China Normal University, Guangzhou, Guangdong, China, 2Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive, Guangzhou, Guangdong, China
First Author:
桂芬 苏
School of Psychology, South China Normal University|Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive
Guangzhou, Guangdong, China|Guangzhou, Guangdong, China
School of Psychology, South China Normal University|Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive
Guangzhou, Guangdong, China|Guangzhou, Guangdong, China
Co-Author(s):
Yuxuan Cai, PhD
School of Psychology, South China Normal University|Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive
Guangzhou, Guangdong, China|Guangzhou, Guangdong, China
School of Psychology, South China Normal University|Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive
Guangzhou, Guangdong, China|Guangzhou, Guangdong, China
Delong Zhang
School of Psychology, South China Normal University|Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive
Guangzhou, Guangdong, China|Guangzhou, Guangdong, China
School of Psychology, South China Normal University|Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, South China Normal Unive
Guangzhou, Guangdong, China|Guangzhou, Guangdong, China
Introduction:
The "underestimation effect" on numerosity refers to the perceived phenomenon that a stimulus is subjectively perceived as less than its physical numerosity due to the configuration of the set, such as spatial adjacency, regular arrangement, and connectedness. However, it remains unclear whether the brain represents the physical and/or perceived numerosity. Recently, Kim et al. (2021) discovered spontaneous representation of numerosity in untrained convolutional neural networks (CNN) eliciting similar responses as numerosity-selective neurons in human brains. The CNN is believed to be analogous to the human brain, especially the ventral stream, given the hierarchical structure of information processing. Here, we employ CNN to explore the physical-perceived representations of numerosity and establish a link between the neural mechanism and behavior.
Methods:
Stimulus materials:
Two various types of stimuli, i.e., isolated dots (Fig. 1A) and connected dots (Fig. 1B), were employed in this study. To control the influence of different low-level features on the observed numerosity tuning in CNN, we categorized each lattice stimulus condition into three types: constant dot size, constant total area, constant convex hull but varying shapes in terms of stimuli. The numerosity included in each stimulus condition is as follows: 1, 2, 4...26, 28, 30 (with a gap of 2) (Fig. 1A). The stimuli are designed as images with the specific number of white dots distributed on a black background, with dimensions of 224*224 pixels or 227*227 pixels (depending on the properties of the neural network).
Analysis:
We input the isolated stimuli into the CNN, conducting a two-way ANOVA to identify neurons exhibiting numerosity-selective responses similar to the observations in the human brains, and analyze the preferred numerosity of these neurons. Then, we analyze whether these numerosity neurons exhibit similar response patterns to two different types of numerosity stimuli: isolated stimuli and connected stimuli. Specifically, we examine whether numerosity neurons demonstrate distinct response patterns to the two categories of numerosity stimuli that share the same physical quantity of dots (Fig2. A-B).
Next, we identified numerosity-selective neurons and their preferred numerosities under the two conditions, respectively. We compared the preferred numerosity of identical neurons between two stimulus conditions (Fig2. C-D). We calculated the proportion of numerosity-selective neurons under connected stimulus conditions that exhibited a bias toward larger numerosity, serving as a quantitative measurement of the underestimation effect in the CNN (Fig2. C-D).
Finally, we conducted validation analyses on multiple untrained and pretrained CNN (VGG16, VGG19, AlexNet).
Two various types of stimuli, i.e., isolated dots (Fig. 1A) and connected dots (Fig. 1B), were employed in this study. To control the influence of different low-level features on the observed numerosity tuning in CNN, we categorized each lattice stimulus condition into three types: constant dot size, constant total area, constant convex hull but varying shapes in terms of stimuli. The numerosity included in each stimulus condition is as follows: 1, 2, 4...26, 28, 30 (with a gap of 2) (Fig. 1A). The stimuli are designed as images with the specific number of white dots distributed on a black background, with dimensions of 224*224 pixels or 227*227 pixels (depending on the properties of the neural network).
Analysis:
We input the isolated stimuli into the CNN, conducting a two-way ANOVA to identify neurons exhibiting numerosity-selective responses similar to the observations in the human brains, and analyze the preferred numerosity of these neurons. Then, we analyze whether these numerosity neurons exhibit similar response patterns to two different types of numerosity stimuli: isolated stimuli and connected stimuli. Specifically, we examine whether numerosity neurons demonstrate distinct response patterns to the two categories of numerosity stimuli that share the same physical quantity of dots (Fig2. A-B).
Next, we identified numerosity-selective neurons and their preferred numerosities under the two conditions, respectively. We compared the preferred numerosity of identical neurons between two stimulus conditions (Fig2. C-D). We calculated the proportion of numerosity-selective neurons under connected stimulus conditions that exhibited a bias toward larger numerosity, serving as a quantitative measurement of the underestimation effect in the CNN (Fig2. C-D).
Finally, we conducted validation analyses on multiple untrained and pretrained CNN (VGG16, VGG19, AlexNet).
·Illustration of stimuli and experimental design
Results:
We found numerosity-selective neurons exhibit distinct response profiles between the isolated and connected stimuli (Fig2. A). More specifically, the preferred numerosity elicited by the connected stimuli appeared larger than those of the isolated stimuli (Fig2. C), indicating an underestimation effect on perceived numerosity compared to physical numerosity. Furthermore, we only observed these effects in the pretrained neural networks, but not in the untrained networks.
·Example responses of neurons preferring a numerosity (i.e., 8) to isolated or connected stimuli (A, B) and quantification of the underestimation effect (C, D) in pretrained and untrained networks
Conclusions:
Our findings indicate that CNN represent the perceived numerosity of stimuli, and this effect is observed exclusively in pretrained neural networks. In other words, unlike untrained neural networks that automatically represent numerosity, the representation of perceived numerosity in pretrained neural networks relies on specific training weights. Our results provide neural computational evidence for the postnatal nature representation of perceived numerosity in human, suggesting that humans may have an innate foundational representation of numerosity, while more advanced and nuanced representations may require the involvement of postnatal visual experience.
Brain Stimulation:
Non-Invasive Stimulation Methods Other
Higher Cognitive Functions:
Higher Cognitive Functions Other 1
Modeling and Analysis Methods:
Other Methods 2
Keywords:
Other - Convolutional Neural Network; Physical-Perceived Numerosity Representation; Underestimation Effect
1|2Indicates the priority used for review
Provide references using author date format
2. He L, Zhang J, Zhou T, Chen L. (2009), 'Connectedness affects dot numerosity judgment: Implications for configural processing', Psychonomic Bulletin & Review. 16(3). 509–517.
3. K. Nasr, P. Viswanathan, A. Nieder (2019), 'Number detectors spontaneously emerge in a deep neural network designed for visual object recognition'. Sci. Adv. 5, eaav7903.