Distinguishing Conjoint and Independent Neural Tuning for Stimulus Features With fMRI Adaptation. Drucker, Kerr, Aguirre. Innovative Methodology 2009.

  1. “We describe an application of functional magnetic resonance imaging (fMRI) adaptation to distinguish between independent and conjoint neural representations of dimensions by examining the neural signal evoked by changes in one versus two stimulus dimensions and considering the metric of two-dimension additivity.”
  2. “Do different neurons represent individual stimulus dimensions or could one neuron be tuned to represent multiple dimensions?”
  3. “This study describes an application of functional magnetic resonance imaging (fMRI) to distinguish conjoint from independent representation of two stimulus dimensions within a spatially restricted population of neurons.”
  4. “If the recovery for a combined change is simply the additive combination of the recovery for each dimension in isolation, we take this as evidence for independent neural populations. When the neural recovery for a combined change is subadditive, this may reflect populations consisting of neurons that conjointly represent the two stimulus dimensions.”
  5. “These two possibilities could be distinguished directly by measuring the tuning of individual neurons. However, the signal obtained with BOLD fMRI averages the population neural response from a voxel, making this measurement unavailable.”
  6. “To distinguish conjoint and independent tuning in this case, we must measure the properties of the neural population using adaptation methods.”
  7. “In summary, we may distinguish between conjoint and independent tuning of neurons in a population by comparing the recovery from adaptation for combined transitions to that seen for isolated transitions along each stimulus dimension.”
  8. “In theory, one could conduct the test described earlier by measuring the BOLD fMRI response to three stimulus pairs: a pair that differs only in color, a pair that differs only in shape, and a pair that differs in both color and shape.”
    1. To make this robust though, more thorough sampling is needed
  9. Looking at the difference between Manhattan and Euclidian distance helps figure out how neurons respond to stimuli with multiple dimensions (additive/independent or not)
  10. Another issue that needs to be addressed before interpreting how neurons respond requires figuring out how linear changes in stimuli lead to changes in neural response — assumed to be nonlinear <I figure they measure this as they vary only 1 dimension?>
  11. They have a model to estimate the nonlinearity, <trying to deal with varying forms of nonlinearities seems complex the way they do it maybe there is a better way>
  12. “A different violation of the model assumptions occurs when the underlying neural representation is independent for the stimulus dimensions, but its neural instantiation is not aligned with the assumed dimensional axes of the study. For example, consider an experiment designed to examine the neural representation of rectangles. The stimulus space used in the experiment consists of rectangles that vary in height and width, and the experimenter models these two parameters. It may be the case, however, that a population of neurons actually has independent tuning for the sum and difference of height and width (roughly corresponding to area and aspect ratio)—a 45° rotation of the axes as modeled by the experimenter.”
  13. “In summary, when significant loading on the Euclidean contraction covariate is obtained in an experiment, an additional test is necessary to reject the possibility of independent,but misaligned, neural populations. Post hoc testing of the performance of the model under assumed rotations of the stimulus axes can distinguish between the independent, but rotated, and the conjointly tuned cases.”
  14. “Earlier, we considered how these concepts are related to receptive fields that are either linear or radially symmetric within a stimulus space. Intermediate receptive fields are possible, however, with oval shapes of varying elongation. In such cases the population would not be wholly independent, but instead represent one dimension to a greater extent than the other. These intermediate cases are considered readily within the framework of the Minkowski exponent that defines the representational space.”
  15. fmris introduce other problems related to things they are bad at measuring
  16. “The test for a conjointly tuned neural population amounts to the measurement of variance attributable to the Euclidean contraction covariate. We consider here optimizations of the approach to maximize power for this test.”
  17. Instead of sampling stimuli from a grid of parameter space, they sample from nested octagons
    1. Helps keep points at a diagonal more evenly spaced than those that are up/down which is an issue in rectangular sampling. “the dioctagonal space increases the range of the Euclidean contraction covariate, thus improving power.”
  18. “Our selection of stimuli was motivated by the psychological study of integral and separable perceptual spaces. Some visual properties of objects are apprehended separately (e.g., color and shape), whereas other dimensions are perceived as a composite (e.g., saturation and brightness); these have been termed separable and integral dimensions (Shepard 1964). We hypothesized that integral perceptual dimensions are represented by populations of neurons that represent the dimensions conjointly, whereas separable dimensions are represented by independent neural populations; similar ideas have been proposed recently”
  19. First set of experiments are on “popcorn” and “moons”
  20. Screen Shot 2015-08-05 at 12.10.34 PM
  21. There is evidence that the two dimensions used for both stimuli sets are perceptually independent
  22. <Maybe they dont actually do an experiment on the stars that vary orange to red with differing number of points and only use them as an example?  that would be a bummer>
  23. “During separate fMRI scanning sessions … Subjects were required to monitor and report the position of a bisecting line, which was randomly tilted and shifted within preset limits … to maintain attention.”
  24. “For each subject, we identified within ventral occipitotemporal cortex voxels that showed recovery from adaptation to both stimulus axes for both stimulus spaces …Most voxels were concentrated around the right posterior fusiform sulcus, corresponding to ventral LOC…”
  25. In popcorn they find the neural representation is not independent based on dimension, but for the crescents they may indeed be independent
  26. “Although a particular study may find independent tuning for a pair of stimulus dimensions, it does not automatically follow that neurons are therefore tuned “for” those axes. It remains possible that the dimensions selected for study are manifestations of some further, as yet unstudied, organizational scheme.”
  27. In discussion, mentions other features that are thought to be represented independently on a neural level
  28. “Our method amounts to using a linear model to test the metric of a space—an approach that has been considered problematic…we have argued by simulation for the validity of our model for two dimensions with 16 regularly spaced samples.”
    1. “Herein we have considered several types of nonlinearities and distortions that can exist in neural representation or recovery from adaptation. Although we find that the method is generally robust to these deviations, there naturally exists the possibility of further violations of the assumptions of the model that we have not evaluated.”
  29. “We envision the use of the metric estimation test to study the representation of stimulus properties across sensory cortical areas. By revealing the presence of independently tuned neural populations, the fundamental axes of perceptual representation might be identified. Interestingly, a given stimulus space may be represented conjointly in one region of cortex, but independently in another.”
    1. This is true of the visual system

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