Conflicts are represented in a cognitive space to reconcile domain-general and domain-specific cognitive control

Reviewer #1 (Public Review):

People can perform a wide variety of different tasks, and a long-standing question in cognitive neuroscience is how the properties of different tasks are represented in the brain. The authors develop an interesting task that mixes two different sources of difficulty, and find that the brain appears to represent this mixture on a continuum, in the prefrontal areas involved in resolving task difficulty. While these results are interesting and in several ways compelling, they overlap with previous findings and rely on novel statistical analyses that may require further validation.

Strengths
1. The authors present an interesting and novel task for combining the contributions of stimulus-stimulus and stimulus-response conflict. While this mixture has been measured in the multi-source interference task (MSIT), this task provides a more graded mixture between these two sources of difficulty

2. The authors do a good job triangulating regions that encoding conflict similarity, looking for the conjunction across several different measures of conflict encoding

3. The authors quantify several salient alternative hypothesis and systematically distinguish their core results from these alternatives

4. The question that the authors tackle is of central theoretical importance to cognitive control, and they make an interesting an interesting contribution to this question

Concerns
1. It's not entirely clear what the current task can measure that is not known from the MSIT, such as the additive influence of conflict sources in Fu et al. (2022), Science. More could be done to distinguish the benefits of this task from MSIT.

2. The evidence from this previous work for mixtures between different conflict sources make the framing of 'infinite possible types of conflict' feel like a strawman. The authors cite classic work (e.g., Kornblum et al., 1990) that develops a typology for conflict which is far from infinite, and I think few people would argue that every possible source of difficulty will have to be learned separately. Such an issue is addressed in theories like 'Expected Value of Control', where optimization of control policies can address unique combinations of task demands.

3. Wouldn't a region that represented each conflict source separately still show the same pattern of results? The degree of Stroop vs Simon conflict is perfectly negatively correlated across conditions, so wouldn't a region that *just* tracks Stoop conflict show these RSA patterns? The authors show that overall congruency is not represented in DLPFC (which is surprising), but they don't break it down by whether this is due to Stroop or Simon congruency (I'm not sure their task allows for this).

4. The authors use a novel form of RSA that concatenates patterns across conditions, runs and subjects into a giant RSA matrix, which is then used for linear mixed effects analysis. This appears to be necessary because conflict type and visual orientation are perfectly confounded within the subject (although, if I understand, the conflict type x congruence interaction wouldn't have the same concern about visual confounds, which shouldn't depend on congruence). This is an interesting approach but should be better justified, preferably with simulations validating the sensitivity and specificity of this method and comparing it to more standard methods.

A chief concern is that the same pattern contributes to many entries in the DV, which has been addressed in previous work using row-wise and column-wise random effects (Chen et al., 2017, Neuroimage). It would also be informative to know whether the results hold up to removing within-run similarity, which can bias similarity measures (Walther et al., 2016, Neuroimage).

Another concern is the extent to which across-subject similarity will only capture consistent patterns across people, making this analysis very similar to a traditional univariate analysis (and unlike the traditional use of RSA to capture subject-specific patterns).

5. Finally, the authors should confirm all their results are robust to less liberal methods of multiplicity correction. For univariate analysis, they should report the effects from the standard p < .001 cluster forming threshold for univariate analysis (or TFCE). For multivariate analyses, FDR can be quite liberal. The authors should consider whether their mixed-effects analyses allow for group-level randomization, and consider (relatively powerful) Max-Stat randomization tests (Nichols & Holmes, 2002, Hum Brain Mapp).

Reviewer #2 (Public Review):

Summary, general appraisal

This study examines the construct of "cognitive spaces" as they relate to neural coding schemes present in response conflict tasks. The authors utilize a novel paradigm, in which subjects must map the direction of a vertically oriented arrow to either a left or right response. Different types of conflict (spatial Stroop, Simon) are parametrically manipulated by varying the spatial location of the arrow (a task-irrelevant feature). The vertical eccentricity of the arrow either agrees or conflicts with the arrow's direction (spatial Stroop), while the horizontal eccentricity of the arrow agrees or conflicts with the side of the response (Simon). A neural coding model is postulated in which the stimuli are embedded in a cognitive space, organized by distances that depend only on the similarity of congruency types (i.e., where conditions with similar relative proportions of spatial-Stroop versus Simon congruency are represented with similar activity patterns). The authors conduct a behavioral and fMRI study to provide evidence for such a representational coding scheme. The behavioral findings replicate the authors' prior work in demonstrating that conflict-related cognitive control adjustments (the congruency sequence effect) shows strong modulation as a function of the similarity between conflict types. With the fMRI neural activity data, the authors report univariate analyses that identified activation in left prefrontal and dorsomedial frontal cortex modulated by the amount of Stroop or Simon conflict present, and multivariate representational similarity analyses (RSA) that identified right lateral prefrontal activity encoding conflict similarity and correlated with the behavioral effects of conflict similarity.
This study tackles an important question regarding how distinct types of conflict, which have been previously shown to elicit independent forms of cognitive control adjustments, might be encoded in the brain within a computationally efficient representational format. The ideas postulated by the authors are interesting ones and the utilized methods are rigorous. However, the study has critical limitations that are due to a lack of clarity regarding theoretical hypotheses, serious confounds in the experimental design, and a highly non-standard (and problematic) approach to RSA. Without addressing these issues it is hard to evaluate the contribution of the authors findings to the computational cognitive neuroscience literature.

The primary theoretical question and its implications are unclear.

The paper would greatly benefit from more clearly specifying potential alternative hypotheses and discussing their implications. Consider, for example, the case of parallel conflict monitors. Say that these conflict monitors are separately tuned for Stroop and Simon conflict, and are located within adjacent patches of cortex that are both contained within a single cortical parcel (e.g., as defined by the Glasser atlas used by the authors for analyses). If RSA was conducted on the responses of such a parcel to this task, it seems highly likely that an activation similarity matrix would be observed that is quite similar (if not identical) to the hypothesized one displayed in Figure 1. Yet it would seem like the authors are arguing that the "cognitive space" representation is qualitatively and conceptually distinct from the "parallel monitor" coding scheme. Thus, it seems that the task and analytic approach is not sufficient to disambiguate these different types of coding schemes or neural architectures.

The authors also discuss a fully domain-general conflict monitor, in which different forms of conflict are encoded within a single dimension. Yet this alternative hypothesis is also not explicitly tested nor discussed in detail. It seems that the experiment was designed to orthogonalize the "domain-general" model from the "cognitive space" model, by attempting to keep the overall conflict uniform across the different stimuli (i.e., in the design, the level of Stroop congruency parametrically trades off with the level of Simon congruency). But in the behavioral results (Fig. S1), the interference effects were found to peak when both Stroop and Simon congruency are present (i.e., Conf 3 and 4), suggesting that the "domain-general" model may not be orthogonal to the "cognitive space" model. One of the key advantages of RSA is that it provides the ability to explicitly formulate, test and compare different coding models to determine which best accounts for the pattern of data. Thus, it would seem critical for the authors to set up the design and analyses so that an explicit model comparison analysis could be conducted, contrasting the domain-general, domain-specific, and cognitive space accounts.
Relatedly, the reasoning for the use of the term "cognitive space" is unclear. The mere presence of graded coding for two types of conflict seems to be a low bar for referring to neural activity patterns as encoding a "cognitive space". It is discussed that cognitive spaces/maps allow for flexibility through inference and generalization. But no links were made between these cognitive abilities and the observed representational structure. Additionally, no explicit tests of generality (e.g., via cross-condition generalization) were provided. Finally, although the design elicits strong CSE effects, it seems somewhat awkward to consider CSE behavioral patterns as a reflection of the kind of abilities supported by a cognitive map (if this is indeed the implication that was intended). In fact, CSE effects are well-modeled by simpler "model-free" associative learning processes, that do not require elaborate representations of abstract structures.

More generally, it seems problematic that Stroop and Simon conflict in the paradigm parametrically trade-off against each other. A more powerful design would have de-confounded Stroop and Simon conflict so that each could be separately estimation via (potentially orthogonal) conflict axes. Additionally, incorporating more varied stimulus sets, locations, or responses might have enabled various tests of generality, as implied by a cognitive space account.

Serious confounds in the design render the results difficult to interpret.

As much prior neuroimaging and behavioral work has established, "conflict" per se is perniciously correlated with many conceptually different variables. Consequently, it is very difficult to distinguish these confounding variables within aggregate measures of neural activity like fMRI. For example, conflict is confounded with increased time-on-task with longer RT, as well as conflict-driven increases in coding of other task variables (e.g., task-set related coding; e.g., Ebitz et al. 2020 bioRxiv). Even when using much higher resolution invasive measures than fMRI (i.e., eCoG), researchers have rightly been wary of making strong conclusions about explicit encoding of conflict (Tang et al, 2019; eLife). As such, the researchers would do well to be quite cautious and conservative in their analytic approach and interpretation of results.

This issue is most critical in the interpretation of the fMRI results as reflecting encoding of conflict types. A key limitation of the design, that is acknowledged by the authors is that conflict is fully confounded within-subject by spatial orientation. Indeed, the limited set of stimulus-response mappings also cast doubt on the underlying factors that give rise to the CSE modulations observed by the authors in their behavioral results. The CSE modulations are so strong - going from a complete absence of current x previous trial-type interaction in the cos(90) case all the way to a complete elimination of any current trial conflict when the prior trial was incongruent in the cos(0) case - that they cause suspicion that they are actually driven by conflict-related control adjustments rather than sequential dependencies in the stimulus-response mappings that can be associatively learned.

To their credit, the authors recognize this confound, and attempt to address it analytically through the use of a between-subject RSA approach. Yet the solution is itself problematic, because it doesn't actually deconfound conflict from orientation. In particular, the RSA model assumes that whatever components of neural activity encode orientation produce this encoding within the same voxel-level patterns of activity in each subject. If they are not (which is of course likely), then orthogonalization of these variables will be incomplete. Similar issues underlie the interpretation target/response and distractor coding. Given these issues, perhaps zooming out to a larger spatial scale for the between-subject RSA might be warranted. Perhaps whole-brain at the voxel level with a high degree of smoothing, or even whole-brain at the parcel level (averaging per parcel). For this purpose, Schaefer atlas parcels might be more useful than Glasser, as they more strongly reflect functional divisions (e.g., motor strip is split into mouth/hand divisions; visual cortex is split into central/peripheral visual field divisions). Similarly, given the lateralization of stimuli, if a within-parcel RSA is going to be used, it seems quite sensible to pool voxels across hemispheres (so effectively using 180 parcels instead of 360).

The strength of the results is difficult to interpret due to the non-standard analysis method.

The use of a mixed-level modeling approach to summarize the empirical similarity matrix is an interesting idea, but nevertheless is highly non-standard within RSA neuroimaging methods. More importantly, the way in which it was implemented makes it potentially vulnerable to a high degree of inaccuracy or bias. In this case, this bias is likely to be overly optimistic (high false positive rate).

A key source of potential bias comes from the fact that the off-diagonal cells are not independent (e.g., the correlation between subject A and B is strongly dependent on the correlation between subject A and C). For appropriate degrees of freedom calculation, the model must take this into account somehow. As fitted, the current models do not seem to handle this appropriately. That being said, it may be possible to devise an appropriate test via mixed-level models. In fact, Chen et al. have a series of three recent Neuroimage articles that extensively explore this question (all entitled "Untangling the relatedness among correlations") - adopting one of the methods described in the papers, seems much safer, if possible.

Another potential source of bias is in treating the subject-level random effect coefficients (as predicted by the mixed-level model) as independent samples from a random variable (in the t-tests). The more standard method for inference would be to use test statistics derived from the mixed-model fixed effects, as those have degrees of freedom calculations that are calibrated based on statistical theory.

No numerical or formal defense was provided for this mixed-level model approach. As a result, the use of this method seems quite problematic, as it renders the strength of the observed results difficult to interpret. Instead, the authors are encouraged using a previously published method of conducting inference with between-subject RSA, such as the bootstrapping methods illustrated in Kragel et al. (2018; Nat Neurosci), or in potentially adopting one of the Chen et al. methods mentioned above, that have been extensively explored in terms of statistical properties.

Reviewer #3 (Public Review):

Yang and colleagues investigated whether information on two task-irrelevant features that induce response conflict is represented in a common cognitive space. To test this, the authors used a task that combines the spatial Stroop conflict and the Simon effect. This task reliably produces a beautiful graded congruency sequence effect (CSE), where the cost of congruency is reduced after incongruent trials. The authors measured fMRI to identify brain regions that represent the graded similarity of conflict types, the congruency of responses, and the visual features that induce conflicts.

Using several theory-driven exclusion criteria, the authors identified the right dlPFC (right 8C), which shows 1) stronger encoding of graded similarity of conflicts in incongruent trials and 2) a positive correlation between the strength of conflict similarity type and the CSE on behavior. The dlPFC has been shown to be important for cognitive control tasks. As the dlPFC did not show a univariate parametric modulation based on the higher or lower component of one type of conflict (e.g., having more spatial Stroop conflict or less Simon conflict), it implies that dissimilarity of conflicts is represented by a linear increase or decrease of neural responses. Therefore, the similarity of conflict is represented in multivariate neural responses that combine two sources of conflict.

The strength of the current approach lies in the clear effect of parametric modulation of conflict similarity across different conflict types. The authors employed a clever cross-subject RSA that counterbalanced and isolated the targeted effect of conflict similarity, decorrelating orientation similarity of stimulus positions that would otherwise be correlated with conflict similarity. A pattern of neural response seems to exist that maps different types of conflict, where each type is defined by the parametric gradation of the yoked spatial Stroop conflict and the Simon conflict on a similarity scale. The similarity of patterns increases in incongruent trials and is correlated with CSE modulation of behavior. However, several potential caveats need to be considered.

One caveat to consider is that the main claim of recruitment of an organized "cognitive space" for conflict representation is solely supported by the exclusion criteria mentioned earlier. To further support the involvement of organized space in conflict representation, other pieces of evidence need to be considered. One approach could be to test the accuracy of out-of-sample predictions to examine the continuity of the space, as commonly done in studies on representational spaces of sensory information. Another possible approach could involve rigorously testing the geometric properties of space, rather than fitting RSM to all conflict types. For instance, in Fig 6, both the organized and domain-specific cognitive maps would similarly represent the similarity of conflict types expressed in Fig1c (as evident from the preserved order of conflict types). The RSM suggests a low-dimensional embedding of conflict similarity, but the underlying dimension remains unclear.

Another important factor to consider is how learning within the confined task space, which always negatively correlates the two types of conflicts within each subject, may have influenced the current results. Is statistical dependence of conflict information necessary to use the organized cognitive space to represent conflicts from multiple sources? Answering this question would require a paradigm that can adjust multiple sources of conflicts parametrically and independently. Investigating such dependencies is crucial in order to better understand the adaptive utility of the observed cognitive space of conflict similarity.

Taken together, this study presents an exciting possibility that information requiring high levels of cognitive control could be flexibly mapped into cognitive map-like representations that both benefit and bias our behavior. Further characterization of the representational geometry and generalization of the current results look promising ways to understand representations for cognitive control.