Neural Coding of Cognitive Control: The Representational Similarity Analysis Approach

Abstract

Cognitive control relies on distributed and potentially high-dimensional frontoparietal task representations. Yet, the classical cognitive neuroscience approach in this domain has focused on aggregating and contrasting neural measures - either via univariate or multivariate methods - along highly abstracted, 1D factors (e.g., Stroop congruency). Here, we present representational similarity analysis (RSA) as a complementary approach that can powerfully inform representational components of cognitive control theories. We review several exemplary uses of RSA in this regard. We further show that most classical paradigms, given their factorial structure, can be optimized for RSA with minimal modification. Our aim is to illustrate how RSA can be incorporated into cognitive control investigations to shed new light on old questions.

Keywords: anterior cingulate cortex (ACC); executive function; multivariate pattern analysis (MVPA); prefrontal cortex (PFC); representational similarity analysis (RSA).

Conflict of interest statement

Declaration of Interests We have no known conflict of interest to disclose.

Copyright © 2021 Elsevier Ltd. All rights reserved.

Figures

Figure 1, Key Figure.

Schematic of “classical” and RSA-style approaches in cognitive control research. Design, A color-word Stroop task with four colors and four words. The participant is instructed to name the stimulus hue rather than read the written word. Analysis, top, The classical approach begins by defining abstract factor levels (here, congruent and incongruent) to which conditions (e.g., stimuli) are assigned. Within these levels, the outcome variables of interest (e.g., response time) are summed (Σ) then contrasted. Measures, top, These unidimensional measures are typically interpreted in terms of control processes (e.g., slower reaction time on incongruent relative to congruent trials indicates heightened control demands). Analysis, bottom, The RSA approach keeps the task conditions disaggregated (↔↕) in order to examine the set of pairwise similarities among measures (e.g., brain activity patterns) from all conditions — that is, their full similarity structure (grey and black lines). This observed similarity structure is then compared to structures predicted from theory. For example, a model of target representations would predict greater similarity between patterns from trials in which the target response was identical (i.e., between stimuli of same hue: e.g., black line connecting blue-hued “BLUE” and “GREEN” stimuli) versus different (e.g., between stimuli of same word in different hues: black line connecting red-hued and blue-hued “BLUE”s). The RSA approach thus provides indices reflecting the strength which multiple different representational schemes were encoded (e.g., the space defined by the light blue basis vectors, which correspond to potentially encoded variables). Theory, Typically, classical measures support inference (large orange arrow linking Measure to Theory) regarding control processes (entire CONTROL component of model, orange). Conversely, RSA-based measures can map more directly (large blue arrow linking Measures to Theory) onto theorized control representations (blue nodes within CONTROL component).

Figure 2.

Diagrams of two reviewed RSA methods. A, Mapping internal representations of an artificial neural network (ANN) to brain activity with RSA [82]. An ANN was trained to perform a hierarchical action sequence task, in which the action at one point in the sequence depended on previously chosen actions (e.g., ingredients could only be added once; cream could only be added to coffee). After training, the ANN simulated each step of each sequence (depicted: the fourth step of two different sequences), and the resulting activation patterns (reddish nodes) within the context layer were extracted; the similarity structure of these patterns served as the Context Layer Model (right). A competing model (Sequence Model), which contained only information regarding position-in-sequence (i.e., not previous choices) was built by taking the distance (absolute difference) between each pair of steps (green arrow). B, RSA “fingerprinting” [114]. Individuals first performed a famous-face classification task, in which an exemplar face, linearly morphed between two famous faces (e.g., Brad Pitt and Mel Gibson), had to be classified (as either Brad or Mel). Each individual's categorizations were expressed in similarity matrix form (here, depicted as 2-dimensional perceptual geometries) then used as models to explain (green and purple arrows) neural similarity matrices (neural geometries) from each and every subject. Idiosyncratic brain–behavior relationships were identified in brain regions (i.e., rLPFC) for which the within-subject models (green arrows) were better fit on average than the between-subject models (purple arrows). Neural geometries were then used to predict the patterns of interference within a separate attentional search task that used the same stimulus set (grey arrow).

Box 1 Figure:

Illustration of prototypical classification and RSA approaches, using a toy example of a four-stimuli color-word Stroop experiment. Classification, Analysis and Conclusion, Trial-level activity patterns from a 2-voxel brain region (dACC) are depicted as points in 2-dimensional space. Classification corresponds to fitting a decision boundary (orange) that separates patterns along a single factor (e.g., congruency; hollow or filled points) and is typically assessed via cross-validation (training and test splits). Classification, Analytic Problem, Classification directly uses brain activity patterns to predict the task model (congruency). RSA, Analysis and Conclusion, Condition-average dACC activity patterns (observed geometry) are depicted as a spatial arrangement (or geometry) of four points (here, the color-word stimuli), with six inter-point distances (green lines). The smaller the distance between patterns, the more similar they are (green numbers). The observed geometry can also be represented as a similarity matrix, as can model geometries. RSA, Analytic Problem, In RSA, brain activity patterns are first transformed into geometries, which are then explained by task models (target, congruency).

Box 2 Figure:

A decomposition of color-word Stroop via full factorial RSA. A, The similarity structure evoked during a Stroop experiment is modeled as a weighted sum of three hypothesized coding schemes (for visibility, white-hued stimuli are displayed in grey). B, Predicted dissociations in coding schemes were found when applying this approach to fMRI data [58]. At the group level (left), target coding predominated in ventral somatomotor cortex (vM1/vS1), whereas distractor coding predominated in V1 (error bars indicate 95% CI of between-subject variance; asterisks indicate significant pairwise model comparison). Relative to DLPFC, coding of incongruency predominated in dorsomedial frontal cortex (DMFC, including dACC and pre-SMA). At the individual level (right), subjects with stronger target coding in DLPFC, but weaker congruency coding in DMFC had smaller Stroop effects. C, In full factorial RSA, the precision of models can be boosted by adding specific manipulations to better isolate representations relevant to cognitive control.