Experimental design.

(A) The left panel shows the orthogonal stimulus-response mappings of the two participant groups. In each group the stimuli were only displayed at two quadrants of the circular locations. One group were asked to respond with the left button to the upward arrow and with the right button to the downward arrow presented in the to-left and bottom-right quadrants, and the other group vice versa. The right panel shows the time course of one example trial. The stimuli were displayed for 600 ms, preceded and followed by fixation crosses that lasted for 1400 ms in total. (B) Examples of the five types of conflict, each containing congruent and incongruent conditions. The arrows were presented at locations along five orientations with isometric polar angles, in which the vertical location introduces the spatial Stroop conflict, and the horizontal location introduces the Simon conflict. Dashed lines are shown only to indicate the location of arrows and were not shown in the experiments. (C) The definition of the angular difference between two conflict types and the conflict similarity. The angle θ is determined by the acute angle between two lines that cross the stimuli and the central fixation. Therefore, stimuli of the same conflict type form the smallest angle of 0, and stimuli between Conflict 1 and Conflict 5 form the largest angle of 90°, and others are in between. Conflict similarity is defined by the cosine value of θ.

The conflict similarity modulation on the behavioral CSE in Experiment 1.

(A) RT and (B) ER are plotted as a function of congruency types on trial n−1 and trial n. Each column shows one similarity level, as indicated by the defined angular difference between two conflict types. Error bars are standard errors. C = congruent; I = incongruent; RT = reaction time; ER = error rate.

The congruency effect and parametric modulation effect detected by uni-voxel analyses.

Results displayed are thresholded with voxel-wise one-tailed p < .005 and cluster-size > 20 voxels. The congruency effect denotes the higher activation in incongruent than congruent condition. The positive parametric modulation effect (I_pm – C_pm) denotes the higher activation when the conflict type contained a higher ratio of Simon conflict component (bottom left panel). The negative parametric modulation effect [converted to positive with – (I_pm – C_pm)] denotes the higher activation when the conflict type contained a higher ratio of spatial Stroop conflict component (bottom right panel). I = incongruent; C = congruent; pm = parametric modulator.

Summary statistics of regions showing larger encoding strength in incongruent than congruent conditions for the conflict type and orientation effects.

The conflict type effect.

(A) Brain regions surviving the FDR-correction (pFDR < 0.05 and p < 0.001) across the 360 regions (criterion 1). Labeled regions are those meeting the criterion 2. (B) The regions showing stronger encoding of conflict type in the incongruent than congruent conditions (criterion 2). ** pFDR < .01, *** pFDR < .001. (C) The brain-behavior correlation of the right 8C (criterion 3). (D) Illustration of the different encoding strength of conflict type similarity in incongruent versus congruent conditions of right 8C. l = left; r = right.

The axial orientation effect.

(A) Brain regions surviving the FDR-correction (pFDR < 0.05 and p < 0.001) across the 360 regions (criterion 1). Labeled regions are those meeting the criterion 2. (B) The regions showing stronger encoding of orientation in the incongruent than congruent conditions (criterion 2). * pFDR < .05, ** pFDR < .01, *** pFDR < .001.

Illustration of the hypothesized dimensionalities of different representations.

The shade of the red color indicates the degree of dimensionality (i.e., how many dimensions are needed to represent different states). The dimensionality of domain-general representation is extremely low, with all representations compressed to one dot. The dimensionality of domain-specific representation is extremely high, with each control state encoded in a unique and orthogonal dimension. The dimensionality of the organized representation is modest, enabling distant states to be separated but also allowing close states to share representations. The solid arrows show the axes of different dimensions. The dashed arrows indicate how the representational dimensionality can be reduced by projecting the independent dimensions to a common dimension.

The congruency effects of Experiment 1 (A and B) and Experiment 2 (C and D). Error bars denote the standard errors of mean. Conf 1 to 5 denotes the five conflict types. Small insets on top of panel A denote an example of stimuli positions for each conflict type. RT = reaction time; ER = error rate.

The conflict similarity modulation on performance of Experiment 1 (A, B, D and E) and Experiment 2 (C and F), respectively. A and D are scatter plots of CSE [i.e., (CI−CC) − (II−IC)] for RT and ER as a function of the cosine similarity, respectively. In B, C, E and F, the cosine similarity and RT / ER are normalized across conflict similarity levels within each of the four CSE conditions (i.e., CC, II, CI and IC). Conflict similarity for CC and II conditions are reversed (multiplied by −1), such that for all the four CSE conditions, higher conflict similarity is expected to be associated with worse performance (see Behavioral analysis in Methods). Each dot represents a subject. The thin colored lines in B, C, E and F are the fitted lines for each of the four CSE conditions, and the thick black lines are the fitted lines collapsing across all CSE conditions. For panel C and F some similarity levels are missing because of the limited trial numbers in the experimental design in Experiment 2. CSE = congruency sequence effect; RT = reaction time; ER = error rate; CI = congruent (trial n−1)-incongruent (trial n); IC = incongruent-congruent; CC = congruent-congruent; II = incongruent-incongruent.

Neural congruency effect (I−C) by GLM2 [see the Estimation of fMRI activity with univariate general linear model (GLM) of Methods in the main text], plotted as a function of conflict type in different cortical ROIs. The ROIs were selected because they show a statistically significant congruency effects or parametric modulation effects when analyzed using the univariate GLM1.The pre-SMA and ACC showed overall congruency effects regardless of the conflict type (upper panel); the right IPS and right dmPFC were positively modulated by the conflict type and the left MFG was negatively modulated by the conflict type (lower panel). Conf 1 to 5 denotes the five conflict types, from the spatial Stroop to the Simon. Pre-SMA = pre-supplementary motor area; ACC = anterior cingulate cortex; IPS = inferior parietal sulcus; dmPFC = dorsomedial prefrontal cortex; MFG = middle frontal gyrus.

The cross-subject RSA model and the rationale. The RSM is calculated as the Pearson’s correlation between each pair of conditions and the 35 subjects. For 17 subjects, the stimuli were displayed on the top-left and bottom-right quadrants, and they were asked to respond with left hand to the upward arrow and right hand to the downward arrow. For the other 18 subjects, the stimuli were displayed on the top-right and bottom-left quadrants, and they were asked to respond with left hand to the downward arrow and right hand to the upward arrow. Within each subject, the conflict type and orientation regressors were perfectly covaried. For instance, the same conflict type will always be on the same orientation. To de-correlate conflict type and orientation effects, we conducted the RSA across subjects from different groups. For example, the dashed ellipses highlight the conditions that are orthogonal to each other on the orientation representation, response, and Simon distractor, when their conflict type, target and spatial Stroop distractor are the same. The dashed boxes show the possible target locations for different conditions. RSM = representational similarity matrix.

The cortical regions showing different effects in the main RSA. (A) The target effect reflects the above chance encoding of upward and downward arrow directions, and is most strongly encoded in the visual, memory and semantic regions, possibly because producing a goal-direct response to the stimulus require processing in all these regions. (B) the response effect reflects the above chance encoding of left and right responses, and is most strongly encoded in motor regions. (C) the spatial Stroop distractor effect reflects the above chance encoding of vertical location of the stimulus, and is most strongly encoded in left visual regions. (D) the Simon distractor effect reflects the above chance encoding of horizontal locations of the stimulus, and is most strongly encoded at the right visual regions, among others. All p-values are FDR-corrected (pFDR < 0.05 and raw p < 0.001) across the 360 cortical ROIs. Brighter colors denote stronger effects as indicated by the opposite of log-transformed p values.

The representational connectivity between the right 8C area and the cortical regions showing significant encoding of orientation. The black bars represent regions showing both the overall orientation effect and higher encoding of orientation in incongruent than congruent conditions; the grey bars are regions showing only the overall orientation effect but not higher encoding of orientation in incongruent than congruent conditions; and the white bars are regions not showing any of the effects of interest (i.e., qFDR > 0.05 for all the conflict type, orientation, congruency, target, response, spatial Stroop distractor and Simon distractor effects). The grey and white bars show controlled regions. Error bars are the standard error of the mean. The dashed line indicates the 95% confidence interval of the highest connectivity of controlled regions (i.e., left V3). l = left, r = right.

Brain activations for the uni-voxel parametric analysis in GLM1 (voxel-wise one-tailed p < .005, cluster > 20)