The Dimensionality of Neural Coding for Cognitive Control Is Gradually Transformed within the Lateral Prefrontal Cortex

Participants

Twenty-five volunteers gave informed consent before the scanning session began. The sample consisted of 15 females and 10 males, with an average age of 28 years and SD = 6. All volunteers speak English as their native language and are right-handed. All participants completed a screening questionnaire about magnetic resonance imaging safety before the functional MRI experiment started. None of them reported having any previous brain injury or neurological or psychiatric condition. This study was reviewed and approved by the Northwest Research Ethics Committee.

Design and stimuli

After the structural scan, volunteers completed 11 runs of echo-planar imaging in a single session. Run 1 was the localizer experiment, and its associated results have been previously published (Chiou et al., 2023). This localizer was designed to probe cognitive control for semantic and perceptual processes, and its individual-level contrast results were used to localize control-related ROIs for each participant. Runs 2–11 were the RSA decoding experiment. As the primary goal of our study was to compare the similarities and differences among prefrontal subareas, decoding analysis on the data of Runs 2–11 was primarily focused on the individual-specific prefrontal ROIs defined by the localizer contrasts.

Details about the localizer task are comprehensively described in a previous study (Chiou et al., 2023). Below we report the key information: We used a two-by-two factorial design in which different types of processing (semantic processing on lexical stimuli vs visuospatial processing on pictorial stimuli) and the extent of difficulty required to achieve a correct response (easy vs hard) were orthogonally manipulated. There were four items displayed in each trial (either four English words or four geometric patterns), and one of the four items served as an “oddball,” either semantically incongruous with other words (belonging to a separate semantic category from the rest) or perceptually incongruous with the others (having a distinct visual configuration). Difficulty level was manipulated by varying the closeness of semantic categories or the similarity of visual patterns. Participants had to indicate the oddball with a button response. The localizer experiment had a block design, with each of the four conditions having 12 blocks; each block consisted of three trials; each trial started with a fixation cross (0.1 s), followed by a quadruplet of stimuli (3.9 s). Together with interblock intervals, the localizer task had a total duration of 647.5 s. The experiment was programmed using E-Prime 2.0 (2013, Psychology Software Tools). When performing the task, participants responded by pressing one of the four designated buttons on an MR-compatible response pad using their right fingers. All text stimuli were in white color and displayed on a black background; the text was in Arial typeface, with 24 points of font size. Stimuli were displayed using an MRI-specialized LCD screen (1,920 × 1,080; NordicNeuroLab) and projected onto a coil-mounted device for viewing stimuli.

The RSA decoding experiment contained 10 runs of scanning (Runs 2–11). We employed a five-by-two factorial design that fully crossed different types of task processing (five tasks: semantic association, synonym decision, color knowledge, numerical comparison, and shape matching) with the difficulty with which to attain a correct answer (easy vs hard). The overall structure of the experiment is illustrated in Figure 1A. As the figure shows, in each trial, there was a reference item on the top (a word, a number, or a shape) and three options beneath. In different tasks, participants were asked to engage in different types of cognitive operations and choose an answer in relation to the reference. The specifics of task requirements were as follows: (1) For the semantic association task, participants evaluated the relationship between the reference noun word and three options and chose the option (target) semantically most associated with the reference. We manipulated the strength of association between the easy and hard conditions of this task such that the semantic relationship was obvious and straightforward in the easy condition (e.g., “salt” and “pepper”), but ambiguous and indirect in the hard condition (e.g., “salt” and “grain”). To ensure the adequacy of stimuli, eight additional volunteers (none took part in the MRI study) were recruited to rate semantic association between the reference and options on a five-point scale, and the data showed that, as intended, the targets were significantly more strongly associated with the references in the easy context (mean ± SD, 4.56 ± 0.27) than in the hard condition (3.39 ± 0.65); the difference was found at the individual level (by-item analysis: p < 10⁻⁹ for all raters) and the group level (by-subject analysis, p < 0.001), and the nontarget options (foils) were significantly less associated with the references than targets (ps < 0.001). We also controlled for word length (by letter count) and lexical frequency (using the corpus of Van Heuven et al. (2014) for all words used in the task so that “easy versus hard” did not differ on these linguistic variables. (2) For the synonym decision task, participants compared the conceptual similarity between the reference noun and the three options and chose the most synonymous option with the reference. We manipulated the ease with which to access lexicosemantics by using concrete nouns (tangible/perceptible concepts, such as “box” or “kettle”) in the easy condition and abstract nouns (e.g., “onus” or “deceit”) in the hard condition, based on the well-documented findings that lexical access to abstract words is cognitively more taxing than to concrete words (Hoffman et al., 2015). We adopted the concreteness ratings from Brysbaert et al. (2014) to ensure that the concrete words used in the easy condition were rated as more concrete than the abstract words in the hard condition (p < 10⁻²⁵) while there was no difference in word length and lexical frequency (both ps > 0.45); we recruited eight additional participants to rate the synonymy of words and ensured that the targets and references were judged as more synonymous with each other compared with foils (ps < 0.001 for both concrete and abstract words). (3) For the color knowledge task, participants needed to retrieve knowledge about the canonical color of objects; the references were nouns associated with a typical color attribute (e.g., “banana” is typically yellow), and the task was to choose the option that shared a similar color to the reference. The difficulty manipulation here concerned the relationship between the references and foils—in the hard condition, the foils were semantically highly related to the references, which made them highly distracting as participants must actively suppress a tendency to respond to those semantically related (yet task-irrelevant) foils and concentrate on identifying the semantically unrelated targets using the arbitrary task rule (i.e., pairing words using color similarity; for the precedent of this task design, see Badre et al., 2005). In the easy condition, in contrast, the targets and foils were all semantically unrelated to the references (despite the targets and references sharing similar colors), hence reducing the interference of foils. We collected rating data from eight additional volunteers to ascertain that the foils were significantly more related to the references in the hard than easy condition (ps < 0.0001) while the targets and references were minimally related despite sharing similar colors. Word length and lexical frequency were controlled to ensure these factors did not confound the key manipulation (both ps > 0.27). (4) For the numerical comparison task, volunteers compared the numerical distance between the reference number and three options and identified the option numerically nearest to the reference. The numbers were three-digit numerals, ranging from 200 to 999. In the easy condition, the target had an obviously closer distance to the reference compared with foils, whereas in the hard condition, the distance was not obvious, which necessitated careful comparison to identify the target. (5) For the shape matching task, volunteers viewed geometric shapes and were asked to compare their perceptual sizes. In the easy condition, it was easy to identify the target because the sizes of the foils obviously differed from the reference and target, whereas in the hard condition, careful visual inspection was necessary to select the target because all options’ sizes were perceptually comparable to the reference. For the three conditions in which lexical stimuli were used (i.e., semantic association, synonym decision, and color knowledge), we carefully cherry-picked 1,200 words as the references, targets, and foils to ensure that (1) each word only appeared once in the entire experiment and (2) none of the words was repeatedly used to avoid the effect of residual memory from previous trials interfering between conditions/tasks. In all tasks, the targets were equally likely to appear in each of the three locations and thus equally likely to be reacted to using any of the three buttons.

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Figure 1.

A, The design of the RSA decoding experiment contained 10 task conditions. Specifically, there were five tasks (1, semantic association; 2, synonym decision; 3, color knowledge; 4, numerical comparison; 5, shape matching), and for each task, we manipulated the level of difficulty to achieve a correct response (easy vs hard), yielding 10 conditions in total. B, Selection of voxels for defining individual-specific ROIs was based on the following procedure: First, functionally defined group-level clusters from Fedorenko et al. (2013) and Jackson (2021) were used to constrain the scope of selection and ensure consistency with prior literature. Second, based on the functional clusters’ alignment with gyri and sulci structures, the clusters were divided into four sections: frontal eye field (FEF; cyan), middle frontal gyrus (MFG; blue), inferior frontal sulcus (IFS; magenta), and inferior frontal gyrus (IFG; red). Third, using the results of the localizer experiment, for each individual participant, we selected the top 200 voxels, which were mostly contiguous and maximally responsive to the ROI-defining contrast within each of the four PFC divisions. Examples of results from one participant are illustrated as the orange patches in the inset boxes.

Each run of scanning consisted of 20 blocks of trials; prior to the onset of each block, an instruction was presented for 3 s to inform the upcoming task (i.e., semantic association, synonym decision, color knowledge, numerical comparison, and shape matching). Each block consisted of five trials; each trial began with a fixation dot (0.4 s), followed by a quadruplet of stimuli (one reference and three options) displayed for 3.5 s, yielding 19.5 s duration for each block of trials, and each block was succeeded by a 2 s interval before the onset of next instruction. We counterbalanced the order in which the 10 conditions appeared across runs and participants so that each condition was equally probable to appear in any slot of the sequences and equally probable to be preceded and succeeded by any other conditions, with each condition having 20 blocks of trials in total and each run lasting 489 s. The order of stimuli within each condition was randomized. Participants were instructed to respond as quickly and accurately as possible within a trial's time limit. All stimuli (words, numbers, and shapes) were presented in white color against a black background. Identical devices and parameters for stimuli display and response collection to the localizer experiment were used in the present RSA decoding experiment. It is worth noting that, using a fully counterbalanced factorial structure in our experimental design, we ensured that all conditions were equally likely to appear in each run of scans, with each condition having the same number of blocks, and evenly distributed across the timeslots across the 10 runs, which prevented some confounding biases in RSA that an unbalanced design might have (for discussion, see Freund et al., 2021b).

Regions of interest

A common practice of multivoxel pattern analysis (MVPA) is to investigate distributed patterns of activity within an ROI using anatomical templates (Woolgar et al., 2011) or atlas parcellations (Freund et al., 2021b). Although this method offers high consistency across individuals (i.e., exactly the same voxels are selected for all participants), it omits the heterogeneity of brain activities between individuals. As demonstrated in recent reports (Shashidhara et al., 2020; Fedorenko, 2021), the loci of functional responses are somewhat idiosyncratic for each person; the conventional method of atlas parcel provides a ballpark estimate but is not sensitive enough to capture subtle idiosyncrasy, which has been suggested to be particularly problematic for decoding prefrontal representations (Bhandari et al., 2018). To tackle this issue, in the present study, when defining the ROIs, we employed the “group-constrained yet individual-specific” method advocated by Fedorenko (2021), which has been demonstrated to successfully capture individual variation while ensuring all individual loci are situated within a predefined target realm (Fedorenko et al., 2013; Blank and Fedorenko, 2017; Mineroff et al., 2018). The steps for defining ROIs were as follows: (1) First, we specified the scope for selecting voxels using the functional masks from Fedorenko et al. (2013) and Jackson (2021). Fedorenko et al. (2013) focused on “domain-general” executive control and identified a group of prefrontal regions, mostly in the dorsolateral prefrontal cortex (DLPFC) that encompasses the frontal eye field (FEF) and middle frontal gyrus (MFG). Jackson (2021) conducted a meta-analysis surveying the literature on “domain-specific” semantic control (executive operations specifically on semantic representations) and identified several regions in the ventrolateral prefrontal cortex (VLPFC) that encompassed the entirety of the inferior frontal gyrus (IFG) and inferior frontal sulcus (IFS, a fissure just superior to the IFG). It is worth noting that the two studies that we used here to define the boundaries of voxel selection are highly representative of the literature in that they used a wide variety of paradigms (i.e., seven tasks probing domain-general control in 197 subjects and 87 fMRI studies on diverse ways of semantic control). The masks are openly downloadable from the original studies. (2) Next, using the macroanatomy of AAL atlas (Tzourio-Mazoyer et al., 2002), the clusters of domain-general control (Fedorenko et al., 2013) and domain-specific control (Jackson, 2021) were parcellated into four divisions based on the alignment with gyrus/sulcus structures (for illustration, see Fig. 1B): (1) The FEF parcel contains exclusively domain-general voxels and is most dorsocaudal; (2) the MFG parcel contains exclusively domain-general voxels and is ventral/rostral to the FEF; (3) the IFS is the conjunction zone between the domain-general and domain-specific clusters and is located ventral/rostral to the MFG; (4) the IFG contains exclusively domain-specific voxels and is most ventrorostral. Note that the FEF parcel covered the conventionally agreed-upon location of the FEF and a nearby patch that corresponded to Area i6-8 of the Connectome Atlas, but for simplicity, we call this whole region FEF. (3) Finally, for each of the four prefrontal parcels and for every participant, individual localizer result was used to identify the top 200 voxels showing the biggest contrast parameters (see Fig. 1B inset boxes for examples). Specifically, we used to localizer's main effect contrast of “hard > easy” (aggregating across levels of the semantic condition and visuospatial condition) to identify 200 voxels showing the largest response to the overall effect of difficulty. The selected voxels from each parcel were used to construct individual-specific ROIs for subsequent analysis. Note that the localizer data for ROI construction was entirely separate from the main experiment's data for multivoxel decoding. In Extended Data Figure 1-1, we report the individual results of ROI creation, using the selection of IFG voxels as an example, to explain why the “group-constrained/individual-specific” approach is able to maintain consistency at the group level while accommodating individual variation. It is worth stressing that the number of voxels was predefined before we conducted any analysis; the number (200 voxels) was based on prior studies showing that increasing the size of an ROI up to 200 voxels robustly improved decoding before it reached a plateau as more voxels were added (Shashidhara et al., 2020). With this protocol to define ROIs, we were able to adapt to the heterogeneous distribution between individual results while considering prefrontal anatomy and ensuring consistency with prior literature. Moreover, given that an unequal number of voxels is known to be a confounding factor to multivariate decoding (Todd et al., 2013), our approach prevents this problem by ensuring an equivalent number of voxels in every ROI and thus creating a level playing field for comparing between ROIs. With this procedure, we ensured consistency at multiple levels: First, task-based clusters and macroanatomical templates were used as constraints to ensure the loci/extent of “search spaces” were aligned across participants (“spatial consistency”). Second, localizer contrasts were used to cherry-pick only those voxels tuned to cognitive control (“functional consistency”). Third, using the clusters of previous large-scale studies to define the bounds of search spaces ensured “literature consistency” with prior research. In Figure 2, we report the heatmaps showing the proportion of convergence among the selected voxels across participants for each of the four prefrontal zones.

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Figure 2.

In the figure, the proportion of overlap between each participant's selected voxels is color-coded with the XYZ-coordinate of highest inter-individual consistency pinpointed, and the scope for voxel selection (the blue cluster) is rendered on a volumetric MNI template. The figure also shows the coordinate at which the highest proportion of overlap is located, as well as the range of min/max overlap (proportion ranging from 0 to 1) in each of the four zones. These maps of overlap reveal two important messages: (1) While there is individual variation in the precise locations of functional brain responses, there is still sufficient consistency (∼40%) in the approximate locations where reliable responses are observed across participants. (2) Outside the highly overlapped regions, there is a great deal of individual variation. This echoes the suggestions by Fedorenko (2021) that an individual-tailored and group-constrained approach (the method we adopt for the present study) is crucial for ensuring that the definition of an ROI is sensitive to individual variation while the scope of voxel selection is constrained by anatomical division and previous results in the literature.

For each individual, we additionally defined two ROIs in the posterior/superior parietal cortex (PPC) and the posterior middle temporal gyrus (pMTG) for the “representational alignment” analysis to investigate how the four prefrontal ROIs share representational structures with remote areas and whether there is any systematic change along the dorsocaudal–ventrorostral axis. Whereas the PPC is part of the dorsal attention network and heavily involved in visuospatial tasks (Yeo et al., 2011; Mengotti et al., 2020), the pMTG is part of the semantic control system and frequently involved when semantic operations become more difficult (Davey et al., 2016; Jackson, 2021; Chiou et al., 2023). Our previous report of the localizer data (Chiou et al., 2023) also showed that the PPC and pMTG are, respectively, the regional peaks for visuospatial control (MNI: −28, −58, 52) and semantic control (−62, −42, −8). Given that the PPC and pMTG have distinct functional profiles, we used different localizer contrasts to define the ROIs: (1) For the PPC, confined within the cortical mask of the superior parietal lobule (Harvard Oxford Atlas: Desikan et al., 2006), we selected the top 200 voxels showing largest responses to the localizer contrast of “visuospatial-hard > visuospatial-easy” for each participant to construct individually tailored ROIs. (2) For the pMTG, confined in the posterior/temporo-occipital divisions of the middle temporal gyrus, we individually selected 200 voxels showing the largest responses to the localizer contrast of “semantic-hard > semantic-easy.” Akin to the way we defined prefrontal ROIs, our approach accommodated individual variation while ensuring the equivalent number of voxels in each ROI, and all chosen voxels were near the group-level average and situated in a predefined target territory.

In Extended Data Figure 1-2, we report a univariate analysis of the localizer results, comparing the four prefrontal ROIs’ preferences for semantic versus visuospatial processing. Results corroborate the previous literature on prefrontal functions (Nee and D'Esposito, 2016)—the dorsolateral PFC preferentially responds to visuospatial processing, while the ventrolateral PFC preferentially responds to semantic processing. This justified our labeling (in subsequent figures of our study) of the FEF (most dorsocaudal) as “visual-sensitive,” the IFG (most ventrorostral) as “semantic-sensitive,” and the MFG and IFS (situated in the intermediate territory) as “domain-general” (owing to these two regions responding equally strongly to visuospatial and semantic processing).

fMRI acquisition and preprocessing

The MRI protocol and preprocessing parameters are identical to those reported in Chiou et al. (2023). A Siemens 3 Tesla PRISMA system was used to acquire all of the MRI data. Anatomical images were attained with a T₁-weighted magnetization-prepared rapid gradient echo (MPRAGE) sequence [repetition time (TR), 2,250 ms; echo time (TE), 3.02 ms; inversion time, 900 ms; 230 Hz per pixel; flip angle, 9°; field of view (FOV), 256 × 256 × 192 mm; GRAPPA acceleration factor, 2]. Task-related data were obtained with a multiecho multiband (MEMB) blood oxygenation level-dependent (BOLD)-weighted echo-planar imaging (EPI) pulse sequence. This MEMB sequence has the strengths that it acquired four functional volumes for each TR (multiecho, enabling capturing signals that peaked at early and late echo times that are often overlooked by conventional protocols) and simultaneously recorded two slices during the acquisition of each volume (multiband, expediting the acquisition rate). The parameters included the following: TR, 1,792 ms; TE₁, 13 ms; TE₂, 23.89 ms; TE₃, 34.78 ms; TE₄, 45.67 ms; flip angle, 75°; FOV, 192 × 192 mm; MB factor, 2; in-plane acceleration, 3. Each EPI volume consisted of 46 axial slices, acquired from the top and middle slice in descending order, with a voxel size of 3 × 3 × 3 mm and FOV of 240 × 240 × 138 mm. A series of 362 and 273 functional volumes per run, respectively, were acquired for the localizer experiment and the RSA decoding experiment.

All raw DICOM data were converted to NIfTI format using dcm2niix. The T1 structural images were processed using the standard processing pipeline of the FSL package's “fsl_anat” function (Version 5.0.11; https://fsl.fmrib.ox.ac.uk/). This procedure involves the following six steps: (1) Reorient images to standard MNI space (“fslreorient2std”), (2) automatically crop image to remove the neck (“robustfov”), (3) bias-field correction to fix field inhomogeneity (“fast”), (4) registration into the MNI space (“flirt” and “fnirt”), (5) brain extraction (using “fnirt” nonlinear method), and (6) tissue-type segmentation to separate white/gray matter and other structures (“fast”). Each T₁ image was individually inspected for accuracy after being normalized into the MNI space. The functional EPI data were preprocessed using a combination of tools in FSL, AFNI (Version 18.3.03; https://afni.nimh.nih.gov/), and a specialized Python package to perform TE-dependent analysis (Kundu et al., 2012, 2013, 2017). Despiked (“3dDespike”), slice-time corrected (“3dTshift,” matched to the middle slice), and realigned (“3dvolreg”) images were submitted to the “tedana” toolbox, which took the time series data from all of the four TEs and decomposed the data into BOLD signals and noises (non-BOLD). Specifically, decomposition was based on whether a signal series depended on the four echo times—with the strength of multiple echo times, the algorithm was able to tell apart noises that fluctuated randomly and independently of the timing of four TEs (e.g., scanner's drift, cardiac/respiratory noises, and head motion) from signals that systematically varied with the timing of TEs (e.g., real functional data of BOLD). Data from the four echo times were optimally integrated, weighted based on the intensity of the T2* signal in each voxel, and separated from the TE-independent/non-BLOD noises (Kundu et al., 2017). Finally, the optimally combined images were coregistered into the individual's T₁ structural scan (using FSL's “flirt”), normalized to the MNI space (using FSL's “fnirt” warps and “flirt” transform), and smoothed with a 6 mm FHWM Gaussian kernel.

Multivoxel pattern analysis (RSA and classification)

Prior to multivariate decoding, we used SPM12 to construct general linear models (GLM) to fit the data of the localizer experiment and the RSA experiment, convolving each participant's design matrix with a canonical hemodynamic response function. For the localizer experiment, four task regressors were created in the GLM (semantic-easy, semantic-hard, visuospatial-easy, visuospatial-hard), which enabled the relevant contrasts for defining ROIs. For the RSA experiment, 10 task regressors were created to enable constructing a 10 × 10 representational distance matrix in RSA (association-easy, association-hard, synonym-easy, synonym-hard, color-easy, color-hard, number-easy, number-hard, shape-easy, shape-hard). Based on the established methods (Kriegeskorte et al., 2008; Nili et al., 2014), for the off-diagonal elements of the matrix, we calculated the neural similarity between each pair of experimental conditions as the Pearson’s correlation of the two conditions’ vectorized patterns of neural activities; the similarity results were converted into a distance measure (1 – Pearson's r) to represent how distant the neural patterns are from one another. In addition to constructing matrices using the neural data, we also constructed various theoretical matrices based on different assumptions about the relationship between task conditions and used them to account for the neural results. Details of the theoretical models are presented later in the Results section. Based on the standard practice of RSA (Nili et al., 2014), we used a rank-based correlation index Kendall's τ (τ-a) to measure the similarity between different matrices. We also computed Spearman's ρ and found that it yielded entirely consistent results with τ-a; however, we chose to report τ-a as Nili et al. (2014) recommend that, compared with Spearman's ρ, τ-a offers a more conservative and detailed prediction.

While simple correlation approaches (e.g., τ-a or Spearman's ρ) have been widely used to evaluate how well a hypothesis explains a neural representation, more statistical control is needed to assess the unique variance explained by a hypothesis under consideration while the explanatory influences from all other sources are removed. This concern is especially crucial in one of our analyses in which we sought to compare the prefrontal subregions to investigate whether their neural coding was loaded with certain information. In this analysis, the neural matrices served as the candidates for adjudication, and the theoretical matrices were the targets of prediction—e.g., among the four regions, which carried the most information about reaction times, and which least? In this regard, an important consideration was that we needed to control for the confounding influences from all other subregions when gauging the unique variance that each brain region could explain. Given that our four ROIs are spatially contiguous, it is critical to statistically rule out the contamination from other regions to get a clean estimate for each region. To this end, we used two approaches that have been widely adopted to verify the relationship between a target matrix with multiple candidate matrices—partial correlation (Fernandino et al., 2022) and multiple regression (Freund et al., 2021b). While both methods are commonly used to assess the unique relationship between two matrices while controlling for the effects of other variables, they differ in mathematical definitions and the degree of strictness (i.e., partial correlation is a “purer” index in which covariance with confounding variables are removed from both of the matrices under assessment; in contrast, multiple regression removes covariance from only one of the two matrices, typically the predictor/candidate matrix). By verifying both approaches, we also aimed to check whether they produced consistent conclusions. Specifically, (1) we computed partial correlation (Spearman's ρ), which focused on the unique relationship between the neural and theoretical matrices (e.g., the similarity between IFG and a hypothesis matrix) while excluding the covariance they shared with all other prefrontal areas (i.e., the FEF, MFG, and IFS). (2) We computed multiple regression, following the example of Freund et al. (2021a). In this analysis, the off-diagonal elements of the four candidate matrices (i.e., the neural matrices of four prefrontal ROIs) simultaneously entered the regression as the predictors. The neural data were warped into vectors, rank-transformed, and normalized into z-scores, while one of the theoretical matrices served as the dependent/predicted variable. With this approach, the regression coefficient β of each regressor represented the explanatory power unique to each regressor while the effects from all other regressors were excluded. It is worth noting that RSA was performed at the individual level to ascertain that fine-grained, voxel-wise representations were preserved for every person, and group-level statistics (e.g., comparing the sizes of partial correlations or regression coefficients) were performed only after representational distance matrices were computed for each participant and for each ROI.

Finally, in addition to relating neural matrices to theoretically constructed matrices (which is a more common practice in RSA), we also performed “representational alignment” analyses, which quantified the extent to which brain regions’ representational structures aligned with one another (cf. Ito and Murray, 2023). When computing representational alignment between two brain regions, we extracted the off-diagonal elements of the neural matrices and calculated the rank-based correlation between regions. A high correlation means the two regions were representationally similar, which has been suggested to be driven by intensified informational exchange and tighter coupling of time series between the two regions (see Anzellotti and Coutanche, 2018, for discussion about “representational connectivity”). As a complementary analysis of representational alignment, we also extracted each region's fluctuation of BOLD time series and computed the correlation between brain regions as per the conventional measure of covariation-based functional connectivity.

Following the approach of Ito and Murray (2023), we computed the representational dimensionality for each participant and each brain region. It was calculated as the “participation ratio” that quantified the degree to which all of the dimensions contributed evenly to a region's neural code. If a region has low dimensionality, the first few dimensions can explain a large proportion of the variance while the remaining dimensions only have a negligible contribution. That is, the first few dimensions are enough to capture this region's overall representation, thus a low participation ratio (only a small proportion of the dimensions have explanatory power). In contrast, if a region has high dimensionality, most of the dimensions are dispensable, and each of them contributes to defining different aspects of the representation. Using the method of Ito and Murray (2023), the participation ratio was calculated as follows:dimx=(∑i=1mλi)2∑i=1mλi2. Here, dim_x corresponds to the participation ratio of region X, and λ_i corresponds to the eigenvalues of the region's representational distance matrix. As per Ito and Murray (2023), each region's matrix was decomposed into several eigenvectors/dimensions (the total number of eigenvectors of a matrix is the number of task conditions, m), with eigenvalues (λ_i) quantifying the importance/contribution of a given dimension. The computation was performed individually on each region to quantify whether eigenvalues were disproportionately (low-dimensional) or evenly distributed (high-dimensional) in the whole eigenspace (eigenspectrum). Specifically, the more even the eigenspectrum of this region's matrix, the higher its dimensionality— namely, relying on the initial few eigenvectors is insufficient to explain the full breadth of variance, and additional eigenvectors are necessary to explain the full volume of variance, hence driving up the participation ratio. Note, here the feature dimensions were constrained by the number of conditions in our experimental design, rather than by the number of voxels in each region, as the goal was to examine how well the neural representations differentiated task conditions and to identify the dimensions involved.

We also performed classification analyses on the multivoxel patterns as a complementary approach to RSA. Prior to the classification analyses, we remodeled the data of the RSA experiments in which each block of a task condition was modeled as an individual regressor so as to increase the number of samples for training the classifier in the k-fold validation procedure. We performed classification with The Decoding Toolbox (TDT; Hebart et al., 2015), which used a linear support vector machine (SVM) for classification with a “C = 1” cost parameter (Chang and Lin, 2011). For each classification, a leave-one-run-out 10-fold splitter was used whereby the algorithm learned to distinguish between relevant categories using the data from nine of the ten runs; its ability to correctly predict was tested using the unseen data from the remaining “held-out” run. This procedure was iterated over all possible combinations of runs used for training and testing. By partitioning the datasets based on different runs of scanning, there was no contamination of information leaking from the training sets to the testing sets. The accuracy scores were then averaged across folds to produce a mean accuracy score for further statistical analysis. This was done separately for each participant and for each region. Particularly, we used classification to evaluate whether the multivoxel pattern of brain regions has the ability to cross-classify between two disparate domains (e.g., training on the lexicosemantic domain, and then testing on the visual–perceptual or a numerical domain, and vice versa).