A stochastic world model on gravity for stability inference
- Department of Psychological and Cognitive Sciences & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, China
Figures
Figure 1 with 7 supplements
Gravity’s direction in the world model.
(a) The design of the behavioral experiment. Left: a rotating camera was used to rotate a stack 360° to display the three-dimensional appearance of the configuration. Middle: gravity’s direction was …
Figure 1—figure supplement 1
Construction of stacks with different configurations.
(a) Illustration of the block-stacking procedure to create stacks in different configurations. A configuration was constructed by placing multiple blocks within a designated area. If there was no …
Figure 1—figure supplement 2
Differentiating subjectivity from objectivity.
In both experiments 1 (a) and 2 (b), participants were instructed to determine which shape appeared most stable. Objectively, in the absence of external forces, all shapes possess equal stability. …
Figure 1—figure supplement 3
The stochastic world model on gravity of each participant.
Participants’ confidence level about normal trajectory in angles followed a Gaussian distribution, with the variance ranging from 11.1 to 37.1. No stochastic characteristic was observed in .
Figure 1—figure supplement 4
Wall experiment to test the impact of external forces on the measurement of stochastic gravity.
(a) Experimental setting. We replicated the original setup with the addition of a wall implemented on one side. Left: the overall experimental scene; right: the scene shown to participants. (b) …
Figure 1—figure supplement 5
The stochastic world model on gravity of each participant when gravity’s direction was inverted.
Participants’ confidence level about normal trajectory in angles also followed a Gaussian distribution, with the variance ranging from 9.1 to 28.4, and no stochastic characteristic was observed …
Figure 1—video 1
Collapse simulation under normal or abnormal gravity in an upright perspective.
Figure 1—video 2
Collapse simulation under normal or abnormal gravity in an upright perspective.
Figure 2 with 2 supplements
Stability inference by the world model on gravity.
(a) An experiment to rate the stability of stacks, half of which were stable and the other half unstable. (b) Top: the procedure of the natural gravity simulator (NGS) to estimate the actual …
Figure 2—figure supplement 1
Relation between the stability estimated by the mental gravity simulator (MGS) stability and that by participants when the world model was implemented with different Gaussian functions.
Only when the world model embodied Gaussian functions with intermediate variance (i.e., ) did the stability estimated by the MGS match participants’ stability inference. On the other hand, when …
Figure 2—figure supplement 2
Height illusion of stability inference when the world model was implemented with different Gaussian functions.
The illusion that tall objects are considered more unstable than short ones manifests at all levels of variances of Gaussian functions, with larger variance leading to a stronger illusion.
Figure 3 with 2 supplements
The origin of the stochastic feature of gravity’s direction.
(a) The reinforcement learning framework, which updated gravity’s direction of the world model by minimizing the difference between the expectation from the internal simulation (i.e., simulated …
Figure 3—figure supplement 1
The developmental trajectory of (top) and (bottom) angles.
Sampling probabilities of angles gradually decreased during reinforcement learning, with the probabilities from smaller angles having a lower decrement tendency. The probability of without …
Figure 3—figure supplement 2
The world models developed in the world containing stacks with different numbers of blocks.
The number of blocks ranged from 2 to 15, and in all the worlds gravity’s direction was in Gaussian distributions with the vertical direction as the maximum likelihood. Note that the world with …
Figure 4 with 2 supplements
The ecological advantage of the stochastic feature.
(a) Illustration that modeled humans’ decision-making behavior at different stages of the mental simulation using the natural gravity simulator (NGS) and mental gravity simulator (MGS). (b) The …
Figure 4—figure supplement 1
Ecological advantage of the world model embodied with different Gaussian functions.
(a) Prediction accuracy decreased when the variance of the Gaussian function increased, and reached an asymptote of 0.75. (b) Response time decreased as the variance increased and reached an …
Figure 4—figure supplement 2
The relation between the number of simulations and the variance of stability inference.
The simulation showed that the variance of stability inference decreased with the number of simulations. Note that the variance in the world model observed in participants best matched the variance …
Appendix 1—figure 1
An illustration of the procedure to estimate the possible number of configurations when blocks have an aspect ratio of .
(a) The cubic block with the length, width and height are . (b) Constructing a configuration by stacking two cubic blocks. The upper block could only be placed within a area to guarantee …
Appendix 1—figure 2
An illustration of the procedure to estimate the possible number of configurations when blocks have the aspect ratio of .
(a) Three types of rectangular blocks with an aspect ratio of . (b) There are nine possible two-block configurations when combining blocks with an aspect ratio of . (c) A three-block …
Author response image 1
Wall experiment to test the impact of external forces on the measurement of stochastic gravity.
(a) Experimental setting. We replicated the original setup with the addition of a wall implemented on one side. Left: the overall experimental scene; Right, the scene shown to participants. (b) …
Author response image 2
Trajectory experiment to test the stochastic nature of gravity represented in the mind.
(a) Experiment design. In this experiment, participants were required to use a mouse to determine the landing point of a parabolic trajectory (marked by the green dot), obscured by a grey rectangle. …
Author response image 3
RL learning curves as a function of θ angle with different sampling densities and learning rates.
Learning rates were adjusted to low (a), intermediate (b) and high (c) settings, while sampling densities were chosen at four levels: 5x5, 11x11, 31x31, and 61x61 shown from the left to the right. …
Author response image 4
Wall experiment to test the impact of external forces on the measurement of stochastic gravity.
(a) Experimental setting. We replicated the original setup with the addition of a wall implemented on one side. Left: the overall experimental scene; Right, the scene shown to participants. (b) …
Author response image 5
Differentiating Subjectivity from Objectivity.
In both Experiment 1 (a) and Experiment 2 (b), participants were instructed to determine which shape appeared most stable. Objectively, in the absence of external forces, all shapes possess equal …
Author response image 6
Wall experiment to test the impact of external forces on the measurement of stochastic gravity.
(a) Experimental setting. We replicated the original setup with the addition of a wall implemented on one side. Left: the overall experimental scene; Right, the scene shown to participants. (b) …
Author response image 7
Trajectory experiment to test the stochastic nature of gravity represented in the mind.
(a) Experiment design. In this experiment, participants were required to use a mouse to determine the landing point of a parabolic trajectory (marked by the green dot), obscured by a grey rectangle. …
Author response image 8
Perception Uncertainty in 3D stacks structures.
(a) Experimental design. A pair of two stacks with similar placements of blocks were presented sequentially to participants, who were instructed to judge whether the stacks were identical and to …
