Fig 1.
Stimulus representation and definition of perceptual separability in GRT.
The representation of a given identity changes randomly from trial to trial (dots at the bottom) according to some perceptual distribution (bell-shaped distributions at the top). Perceptual separability of identity from emotional expression (neutral vs. sad) holds if the perceptual distribution for identity does not change with emotional expression (left), and it fails if the perceptual distribution for identity does change with emotional expression (right).
Fig 2.
Schematic representation of multiple channels encoding a stimulus with a value of “3” in a target dimension.
If a stimulus with value “3” is presented, each channel gives an average response equivalent to the height of the tuning function at that stimulus value (i.e., the height at the dotted line). The vector of average responses is perturbed by random noise, producing the final channel output.
Fig 3.
Summary of the relation between encoding separability and decoding separability, according to our extension to GRT.
Arrows should be interpreted as conditional statements of the form “if X, then Y”. These relations mean that a failure of encoding separability is a valid inference from the observation of a failure of decoding separability. However, the presence of encoding separability cannot be validly inferred from an observation of decoding separability.
Fig 4.
Summary of the relation between decoding separability, classification accuracy invariance and classification accuracy generalization, according to our extension to GRT.
Arrows should be interpreted as conditional statements of the form “if X, then Y”.
Fig 5.
Summary of the theoretical relations found here.
Yellow rectangles represent tests that can be applied to neuroimaging data. Red rectangles represent properties of neural encoding. Green rectangles represent properties of perceptual representations. Solid directional arrows indicate that if the concept where the arrow starts is true, then the concept where the arrow ends must be true as well. Dotted directional arrows indicate that if the concept where the arrow starts is false, then the concept where the arrow ends must be false as well. Bidirectional arrows indicate that the two concepts are equivalent. Asterisks are displayed on relations or tests that depend on relatively strong assumptions (see main text for details).
Fig 6.
Results of the searchlight decoding separability test.
Yellow-red clusters represent regions in which violations of decoding separability of identity were stronger than violations of decoding separability of emotional expression. There were no regions in which violations of decoding separability of emotional expression were stronger than violations of decoding separability of identity. Green and red lines delimit face areas from the functional localizer. “L” and “R” represent left and right hemispheres, respectively.
Fig 7.
Results of the ROI-based decoding separability test.
The y-axis reports the standardized deviations from decoding separability (DDS) statistic. The points represent mean values and the error bars represent standard error of the mean. When decoding separability holds, this index should have a value around 0.5, which is represented with a horizontal dotted line. Mean statistics that were found to be significant (t-test, uncorrected) are marked with an asterisk.
Fig 8.
A schematic representation of a test of decoding separability for neuroimaging data, implemented as an extension to traditional linear decoding procedures.
The simplified example considers the representation of four stimuli in two voxels. Each point represents activity on a different trial, and each color represents a different stimulus that has been repeatedly presented during the experiment. The dotted line represents a classification bound that separates trials according to emotional expression. The line orthogonal to this bound represents the direction in voxel space that best discriminates one expression from the other. Decoding separability holds if the distributions along this dimension for a given value of the target dimension (emotional expression) are equivalent across changes in the irrelevant dimension (identity). Adapted from: http://figshare.com/articles/Test-of-separabilityof-neural-representations/1385406.