In [1]:
from util import Video

What to simulate?

Inferring the right direction for mental rotation

Jessica B. Hamrick
Thomas L. Griffiths
Department of Psychology
University of California, Berkeley

Logic

Everyone who attends the CogSci conference is interested in cognitive science.

I am attending CogSci.

Therefore, I am interested in cognitive science.

Heuristics

The taller stimuli will fall further:

Battaglia, Hamrick, & Tenenbaum (2013)

Mental simulation

Schwartz & Black (1996); Hegarty (2004)

Mental simulation

Battaglia, Hamrick, & Tenenbaum (2013)

Mental simulation

Shepard & Metzler (1971)

Mental simulation is a tool...

...so how should it be used?

How do we decide what direction to rotate?

How do we decide when to stop rotating?

Previous approaches

Rotate through the minimum angle until images are aligned

(Shepard & Metzler, 1971)
  • How to compute the minimum angle?
  • What counts as "aligned", especially if the images are different?

Previous approaches

Compute the axis and direction of rotation prior to performing the rotation

(Funt, 1983; Just & Carpenter, 1985)
  • Why rotate if you already know the angle?
  • Will only work if the shapes can be aligned exactly.

A rational analysis

  • Problem: determine what spatial transformation(s) an object has undergone, given two images of that object
  • Assumption: we have a tool (mental simulation) that we can use to visualize transformations of an object
  • Goal: solve the problem using the fewest number of mental simulations

Our hypothesis

  • "Active sampling" (e.g. Gureckis & Markant, 2012)
  • Choose to run simulations that will give the most information about the answer
  • Implicitly minimizes the number of simulations

The task: same, or flipped?

Similar to Cooper (1975)

The task: same, or flipped?

200 participants $\times$ 200 trials on MTurk (w/ psiTurk)
720 stimuli (20 shapes $\times$ 18 rotations $\times$ 2 reflections)

Results similar to Cooper (1975) and Gardony et al. (2014)

Models of mental rotation

  • Oracle: Compute the minimum angle, then rotate to it.
  • Threshold: Rotate in the direction that makes the images look more similar, and keep rotating in that direction until the images look "similar enough".
  • Hill-climbing: Rotate in the direction that makes the images look more similar, and stop when they start to look less similar.
  • Active sampling: Rotate in the direction that gives the most information about whether the images are the same, and stop when there is enough information to make a decision.

Similarity

In [2]:
Video("videos/gold_standard1.mp4")
Out[2]:

Oracle model

Compute the minimum angle of rotation, then rotate to it.
In [3]:
Video("videos/oracle1.mp4")
Out[3]:

Threshold model

Rotate until the images look "similar enough".
In [4]:
Video("videos/threshold1.mp4")
Out[4]:

Hill-climbing (HC) model

Rotate until the images start to look less similar.
In [5]:
Video("videos/hill_climbing1.mp4")
Out[5]:

Active sampling (AS) model

Choose the most informative rotations.
  • Estimate the similarity function
  • Choose rotations that minimize the uncertainty of that estimate (Osborne et al., 2012)
  • Stop when enough evidence has been collected
  • What counts as "enough" can be biased using an unequal prior over the hypotheses of same vs. flipped

Active sampling (AS) model

Choose the most informative rotations.
In [6]:
Video("videos/bayesian_quadrature1.mp4")
Out[6]:

Results: response time

Results: response time

Results: individual stimuli

Results: accuracy

Summary

  • How should mental rotation be used?
  • Compared four models (oracle, threshold, hill climbing, active sampling) to human data
  • The active sampling model provides a more compelling explanation, and outperforms traditional models
  • Active sampling thus seems promising in it's ability to help answer the question of "what to simulate?"

If mental simulation is a tool...

  • When should we use it, as opposed to a different tool? (e.g. heuristics, logic, etc.)
  • What are the relevant things that need to be simulated?
  • How many simulations should be run?
  • How long should each simulation be run?

Thanks!

This research was supported by ONR MURI grant number N00014-13-1-0341, and a Berkeley Fellowship awarded to JBH.

Slides created using reveal.js and the IPython notebook.
Available from http://jhamrick.github.io/mental-rotation-slides-cogsci2014.