Effective cerebello–cerebral connectivity during implicit and explicit social belief sequence learning using dynamic causal modeling

Abstract To study social sequence learning, earlier functional magnetic resonance imaging (fMRI) studies investigated the neural correlates of a novel Belief Serial Reaction Time task in which participants learned sequences of beliefs held by protagonists. The results demonstrated the involvement of the mentalizing network in the posterior cerebellum and cerebral areas (e.g. temporoparietal junction, precuneus and temporal pole) during implicit and explicit social sequence learning. However, little is known about the neural functional interaction between these areas during this task. Dynamic causal modeling analyses for both implicit and explicit belief sequence learning revealed that the posterior cerebellar Crus I & II were effectively connected to cerebral mentalizing areas, especially the bilateral temporoparietal junction, via closed loops (i.e. bidirectional functional connections that initiate and terminate at the same cerebellar and cerebral areas). There were more closed loops during implicit than explicit learning, which may indicate that the posterior cerebellum may be more involved in implicitly learning sequential social information. Our analysis supports the general view that the posterior cerebellum receives incoming signals from critical mentalizing areas in the cerebrum to identify sequences of social actions and then sends signals back to the same cortical mentalizing areas to better prepare for others’ social actions and one’s responses to it.


Introduction
Although it has an established role in motor functioning and coordination, there is a growing interest in the role of the cerebellum in non-motor mental functions, such as social cognition (Van Overwalle et al., 2014). Recent research has shown that the posterior cerebellum is consistently activated during the process of understanding others' mental states (e.g. inferring their traits, beliefs and intentions), which is termed 'Mentalizing' or 'Theory of Mind' (Van Overwalle et al., 2014, 2020aGuell et al., 2018;Metoki et al., 2021). Also, research showed that posterior cerebellar activity increased with mentalizing complexity such as tracking multiple different mind states (Lewis et al., 2017). Several metaanalyses have reliably identified key areas in the cerebral cortex in the mentalizing processes, including the temporoparietal junction (TPJ), precuneus (PCun), temporal pole (TP) and medial prefrontal cortex (mPFC; Van Overwalle, 2009;Schilbach et al., 2012;Schurz et al., 2014;Molenberghs et al., 2016). However, less is known about how the posterior cerebellum interacts with the cerebral mentalizing network in social cognition.
How does the posterior cerebellum contribute to mentalizing? Inspired by the sequence detection hypothesis of the cerebellum (Leggio and Molinari, 2015), (Van Overwalle et al. 2019b) proposed that the posterior cerebellum encodes social sequences of people's actions, automatizes social sequences that occur frequently and hence immediately detects violations to these acquired sequences. This sequence detection function allows us to understand how social behaviors unfold over time and to react proactively to social actions of others. For example, when a person rummages in his or her pocket and then shows a candy to a child, this sequence of movements signals an invitation for the child to take the candy. It will come as an unwelcome surprise if that person starts eating the candy him-or herself instead. (Van Overwalle et al. 2019a) proposed that many social signals and interactions are based on this sort of social action sequences that become routines and so facilitate social understanding and behavior.
In line with this hypothesis, cerebellar patients showed significant difficulties in comprehending the correct sequence of social stories depicted in cartoon-like pictures (picture sequencing task), especially when a good understanding of the story is required to consider divergent beliefs held by other persons (Van Overwalle et al., 2019a). In one of the cartoons, for example, a boy was surprised to see that his chocolates were gone, because he did not know that they were eaten by a girl while he went away playing. To understand how this story unfolds, it is necessary to switch to the boy's perspective and initial belief that nothing happened in his absence. Using the same picture sequencing task, healthy participants showed stronger activation of the posterior cerebellar Crus I & II for stories involving social beliefs in comparison with nonsocial events (Heleven et al., 2019). The involvement of the posterior Crus I & II has been confirmed in many other tasks that compared generating or remembering sequences of social actions vs nonsequencing or nonsocial control conditions (Van Overwalle et al., 2021b), as well as in meta-analyses encompassing social cognition in general (Van Overwalle et al., 2014, 2020a. It is generally assumed that the sequencing function of the cerebellum is accomplished through multisynaptic communication with the cerebral cortex (Ito, 2008). Early evidence from anatomical studies on animals documented connections between the cerebellum and the cerebral cortex (Glickstein et al., 1985;Schmahmann, 1996;Kelly and Strick, 2003;Suzuki et al., 2012). Subsequent studies on humans using diffusion tensor imaging (DTI) to reconstruct cerebello-cerebral white matter pathways documented many cerebellar interconnections with the cerebral cortex (Sokolov et al., 2014;Karavasilis et al., 2019;Metoki et al., 2021). The specific cerebral areas where these connections make contact may determine the specificity of the cerebellar process (Diedrichsen et al., 2019). In particular, closed-loop circuits, which involve the same cerebellar and cerebral areas as the origin and target of reciprocal connectivity (Kelly and Strick, 2003), may provide the anatomical substrate for the domain-specific interaction. In the social domain, using DTI, Metoki et al. (2021) recently documented robust structural connections between cerebellar and cerebral mentalizing areas, including between Crus I and the TPJ, when participants were required to infer intentions of moving shapes. This finding provides initial support for the idea that incoming signals from key cerebral mentalizing areas responsible for intention understanding, such as the TPJ, are forwarded to the cerebellar Crus to identify the sequences of social events and are then fed back to cortical mentalizing areas, producing error signals in case of sequence violations. However, anatomical studies by themselves do not provide evidence for reciprocal functional closed-loop circuits in mentalizing.
The functional connectivity between the cerebellum and the cerebrum in social cognition has been demonstrated using several methodologies. Resting-state parcellation analyses showed that the cerebellum is organized in domain-specific networks and that the posterior cerebellum (especially Crus I & II) and some anterior parts (lobule IX) are topographically mapped to the mentalizing network in the cerebrum (Buckner et al., 2011;Guell et al., 2018). Task-related psychophysiological interaction connectivity analysis supported an intimate cerebello-cerebral mentalizing network by revealing strong functional connections from the posterior cerebellum to cerebral mentalizing areas . However, a limitation of these methods is that they are unable to identify the direction of connectivity between the cerebellum and the cerebrum, although this is essential to uncover bidirectional functional closed loops which are key to the sequencing hypothesis (Leggio and Molinari, 2015;Van Overwalle et al., 2019b). Dynamic causal modeling (DCM), in contrast, is a more powerful method that can identify the direction of functional connectivity and that avoids spurious (or indirect) correlations, because it rests on a comprehensive mechanistic model of the causal effects that generate the data. Therefore, this type of 'bidirectional functional' connectivity has also been referred to as 'effective' connectivity. Earlier DCM analyses have identified bidirectional effective closed loops between the bilateral posterior cerebellum and the bilateral TPJ when people were inferring others' traits (Van Overwalle et al., 2019c) and comprehending social stories involving other's beliefs in the picture sequencing task mentioned earlier (Van Overwalle et al., 2020b).

Implicit social sequence learning
An important feature of the cerebellum is that sequence detection and automatization occur largely implicitly, that is, beyond conscious awareness. This is immediately evident in motor learning such as learning to ride a bike, where verbal instructions aid little in keeping one's balance. The aim of the current study is to investigate the effective cerebello-cerebral connectivity of mentalizing areas during implicit social sequence learning and compare it with explicit social sequence learning.
To measure implicit sequence learning, the classic serial reaction time (SRT) paradigm (Nissen and Bullemer, 1987) was used. In this paradigm, participants rapidly respond to a sequence of stimuli, which are surreptitiously repeated (e.g. spatial locations on a screen). The results show that participants responded faster to the hidden repetition and slower to any sequence disturbances, demonstrating implicit sequence learning. Based on this SRT paradigm, Ma and colleagues (Ma et al., 2021) created a novel Belief SRT task that involves sequences of social beliefs ( Figure 1). Participants had to report how many flowers the two protagonists-Papa Smurf and Smurfette-believed they were offered. This task had two critical features. First, crucially for a social belief manipulation, the protagonists were either oriented toward the flowers so that they could see them or oriented away so that they could not see them. When oriented toward the flowers, the protagonist held 'true' beliefs about the flowers (i.e. trial 1 in Figure 1) and when oriented away, the protagonist held outdated or 'false' beliefs (i.e. trial 2 in Figure 1). Secondly, participants were not informed that there was a repeated sequence of true or false beliefs held by each protagonist (i.e. implicit learning; Ma et al., 2021). Learning this sequence could nonetheless make the task easier, because it allows participants to anticipate each protagonist's subsequent beliefs and participants could respond accordingly. To test how implicit vs explicit instructions contribute to this task, an explicit version of the Belief SRT task was also developed. The explicit task is identical to the implicit learning task except that participants were informed about the existence of a sequence, although the exact sequence was not given (i.e. explicit learning; Ma et al., 2022).
In the implicit and explicit Belief SRT tasks, there was an initial Training phase where the standard sequence was repeated, followed by a subsequent Test phase where the standard sequence was interrupted by random sequences. The initial Training phase Fig. 1. Schematic example showing the first six trials of the standard sequence in the Belief SRT task. In each trial, participants had to report the number of flowers as seen by the protagonists (Papa Smurf or Smurfette). Belief orientations followed a standard sequence. In the Belief SRT task, when the protagonist was oriented to the screen and could see the flowers (true trial), the number of target flowers had to be reported from the current trial; when the protagonist was oriented away from the screen and could not see the flowers (false trial), the number of target flowers had to be reported from the previous true trial from the same protagonist. The number of flowers was random (1 or 2), making the response unpredictable, and dissociating sequence learning from motor responses. Each trial was self-paced, with all stimuli remaining on screen for 3000 ms until a response was given and was followed by a response-stimulus interval of 400 ms before the next trial started (Trials 1 and 2). To illustrate the instructions for the Belief SRT task, in Trial 1, there is one flower that Papa Smurf can see because he is oriented toward the screen, meaning that the correct response is 1. In Trial 2, there are two flowers. Because Papa Smurf is oriented away from the screen, he cannot see the number of flowers on this trial; hence, he still thinks to have received one flower which he last saw on the previous (1st) trial. The correct response is thus again 1.
captures how the standard sequence is gradually learned during repeated practice, and the later Test phase captures how the learned standard sequence is applied while being occasionally disturbed by random sequences. Of main behavioral interest is the random sequence where a slowing down of responses compared to the standard sequence captures that the repeated sequence was learned and anticipated (Nissen and Bullemer, 1987). Although this behavioral effect was robustly replicated in the implicit and explicit Belief SRT tasks, the typical contrast of the repeated standard sequence against the random sequence (cf. meta-analysis by Janacsek et al., 2020) did not reveal activations of the cerebellum. Therefore, the current study focuses on the Training and Test phases of the standard belief sequence.
Regardless of the implicit or explicit instruction, the Belief SRT task showed that the posterior cerebellar Crus I and lobule VI, and cortical areas like the TPJ and PCun were activated during the initial Training phase. The cerebellar Crus II and (sub)cortical caudate and TP were additionally activated during the later Test phase (Table 1; Ma et al., 2021). Together, these results indicate that distinct areas are involved during different learning phases.
It is of interest to note that the posterior cerebellum was slightly more activated during implicit learning compared to explicit learning when participants tried to maintain the learned standard sequence in the later Test phase (Ma et al., 2021).

Effective connectivity
To analyze the cerebello-cortical effective connections during these implicit and explicit Belief SRT tasks, we applied DCM. As noted before, DCM is a well-established and biologically plausible method that allows us to estimate the strength of the connections from one area to the other and vice versa, that is, in two directions (Friston et al., 2003). This bidirectional connectivity allows us to test the existence of effectively closed loops. DCM estimates fixed and modulatory connections: Fixed (or 'endogenous' or 'intrinsic') connections reflect the connectivity between brain areas which are unmodulated by various experimental conditions and modulatory connections reflect modulation by conditions, that is, increase or decrease of connectivity depending on condition (Friston et al., 2003). By estimating all (bidirectional) connections at once in a single DCM model, false connectivity caused by indirect connections via other areas is controlled for (Van Overwalle et al., 2019c).
To test the effective cerebello-cerebral connectivity during social sequence learning, we applied DCM to our previous fMRI studies on implicit and explicit Belief SRT tasks (Ma et al., 2021). We hypothesized that there would be effective connectivity, mainly as closed loops, between the posterior cerebellum Crus I & II and the bilateral TPJ as suggested by previous DCM connectivity studies on social reasoning and belief understanding (Van Overwalle et al., 2019c, 2020b. Given the activation in additional brain areas (e.g. cerebellar lobule VI, caudate, PCun and TP) during the Belief SRT tasks mentioned earlier (Ma et al., 2021), we further expected that these brain areas might also be involved and connected. Based on earlier DCM analyses on social cognition where few modulatory connections were found depending on domain (social vs nonsocial) or consistency (consistent vs inconsistent contexts; Van Overwalle et al., 2019c, 2020b, we expect here also little modularity of the connections depending on the learning phase.

Method
We applied DCM to prior fMRI studies on implicit and explicit Belief SRT tasks (Ma et al., 2021). We briefly repeat here the main methodological features of these studies and refer to the original articles for more detailed information. After that, we describe the DCM analyses.

Participants
There were a total of 18 (14 female, mean age 21.2 ± 2.7) healthy, right-handed, Dutch-speaking participants in the implicit Belief SRT task and 22 (17 female, mean age 23.3 ± 4.1) in the explicit Belief SRT task. All of them had normal or corrected-to-normal vision and color perception. To avoid any carry-over effects (Geiger et al., 2018), participants completed the Belief SRT task with either implicit or explicit instruction. All participants gave written informed consent with the approval of the Medical Ethics Committee at the University Hospital of Ghent. Participants were paid 20 euros, and transportation costs were reimbursed in exchange for their participation.

Stimuli material
In the Belief SRT task ( Figure 1A), the target consisted of one or two flowers, appearing in one of four horizontal locations, marked by four little smurfs on the top of the screen. The target flower(s) were presented with clovers as distractors. The two protagonists, Papa Smurf and Smurfette, were each shown individually at the bottom of the screen with their faces oriented to or away from the screen. Participants were told: 'One of the four little smurfs will give the flowers while Papa Smurf or Smurfette is watching (facing the screen) or not watching (facing you). Papa Smurf and Smurfette count the flowers they receive. Throughout the task you have to track how many flowers Papa Smurf or Smurfette thinks he or she will get (1 or 2). If they are turned with their back to the four smurfs, you have to indicate how many flowers they (remember that they) received the last time' (Best translation from Dutch).
Participants only received the above information in the implicit task. In the explicit task (Ma et al., 2022), participants received additional information about a sequence they should search for: 'WATCH OUT! In this task, there is a fixed sequence of Papa Smurf and Smurfette and their orientations (toward or away from the screen). Try to find this sequence as that will make the task easier for you. After the task you will have to demonstrate that you have found this order' (Best translation from Dutch). Note that participants were explicitly informed about the kind of sequence they should search for (i.e. protagonists and their orientations), avoiding possible misunderstandings such as sequences tied to the flowers' location (which varied also throughout the experiment in an unrelated sequence). However, participants were not informed about the exact sequence itself so that the task tapped on sequence learning rather than memory processes (Deroost and Coomans, 2018).

Procedure
Here, we briefly summarize the essential aspects of the sequence learning procedure. For more details, we refer to prior fMRI studies on implicit and explicit Belief SRT tasks (Ma et al., 2021). The whole experimental task consisted of 30 blocks with 32 repeated trials each and was divided into a Training phase (blocks 1-5) and a Test phase (blocks 6 -30). Participants provided responses with their left middle or index finger (i.e. one or two flowers, respectively) via an MRI-compatible two-button response box.
In an initial Training phase, the standard sequence was repeated throughout five blocks. This standard sequence consisted of 16 trials of protagonists (smurfs) and orientations (beliefs) and was repeated two times per block. In a subsequent Test phase, there were eight standard blocks, identical to those in the Training phase, which were each followed by two types of random blocks: total random block, where protagonist and orientation were totally randomized with the limitation of at most two subsequent trials of the same orientation type, consistent with the standard blocks; random orientation blocks, where the orientation was changed into a different pseudo-random sequence, while the order of protagonists was identical as in the standard blocks (Supplementary Table S1). The last block at the end of the whole task was always a standard block.

Imaging procedure and preprocessing
Images were collected with a Siemens Magnetom Prisma fit 3T scanner system (Siemens Medical Systems, Erlangen, Germany) using a 64-channel radiofrequency head coil. Stimuli were projected onto a screen at the end of the magnet bore and viewed by way of a mirror mounted on the head coil. Stimulus presentation was controlled by E-Prime 2.0 (www.pstnet.com/eprime; Psychology Software Tools) running under Windows XP. Participants were placed head first and supine in the scanner bore and were instructed not to move their heads to avoid motion artifacts. Foam cushions were placed within the head coil to minimize head movements. First, high-resolution anatomical images were acquired using a T1-weighted 3D MPRAGE sequence (Repetition Time (TR) = 2250 ms, Echo Time (TE) = 4.18 ms, Inversion Time (TI) = 900 ms, Field of View (FOV) = 256 mm, flip angle = 9 ∘ , voxel size = 1 × 1 × 1 mm). Secondly, a fieldmap was calculated to correct for inhomogeneities in the magnetic field (Cusack and Papadakis, 2002). Thirdly, whole-brain functional images were collected in a single run using a T2*-weighted gradient multiband echo sequence, sensitive to Blood Oxygenation Level Dependent (BOLD) contrast (TR = 1000 ms, TE = 31.0 ms, FOV = 210 mm, flip angle = 52 ∘ , slice thickness = 2.5 mm, distance factor = 0%, voxel size = 2.5 × 2.5 × 2.5 mm, 56 axial slices, acceleration factor GRAPPA = 4).
SPM12 (Wellcome Department of Cognitive Neurology, London, UK) was used to process and analyze the fMRI data. To remove sources of noise and artifact, data were preprocessed. Inhomogeneities in the magnetic field were corrected using the fieldmap (Cusack and Papadakis, 2002). Functional data were corrected for differences in acquisition time between slices for each whole-brain volume, realigned to correct for head movement and co-registered with each participant's anatomical data. Then, the functional data were transformed into a standard anatomical space (2 mm isotropic voxels) based on the ICBM152 brain template (Montreal Neurological Institute). Normalized data were then spatially smoothed (6 mm full width at half maximum) using a Gaussian Kernel. Finally, using the Artifact Detection Tool (ART; http://web.mit.edu/swg/art/art.pdf; http://www.nitrc.org/projects/artifact_detect), the preprocessed data were examined for excessive motion artifacts and for correlations between motion and experimental design, and between global mean signal and experimental design. Outliers were identified in the temporal differences series by assessing betweenscan differences (Z-threshold: 3.0 mm, scan to scan movement threshold: 0.5 mm; rotation threshold: 0.02 radians). These outliers were omitted from the analysis by including a single regressor for each outlier. A default high-pass filter was used for 128 s, and serial correlations were accounted for by the default autoregressive (1) model.

Statistical analysis of neuroimaging data
The statistical analyses were performed using the general linear model of SPM12 (Wellcome Department of Cognitive Neurology, London, UK). At the first (single participant) level, an event-related design for measuring transient activity across trials was modeled by entering separate regressors for the trials of interest: two regressors for the trials in the standard blocks at the Training and Test phases (i.e. standard block at Training and standard block at Test), two regressors for the trials in the total random blocks and the trials in the random orientation blocks at the Test phase (i.e. total random at Test and random orientation at Test) and two additional regressors of no interest for pauses and error trials. This last regressor involved incorrect trials as well as one trial after each incorrect trial, because these latter trials may be affected by error processing on the prior trial.
At the second (group) level, we conducted a within-participant one-way analysis of variance and defined t-contrasts between regressors of interests. As mentioned earlier, the often-used fMRI contrast of the standard sequence at Test > Random sequence at Test (cf. meta-analysis by Janacsek et al., 2020) did not reveal any activation of the cerebellum in the original fMRI studies (Ma et al., 2021). Therefore, we focus the analysis here on two contrasts related to different phases in learning the standard belief sequence.
1. Initial training: brain activations during initial learning of the standard sequence are tested by the contrast: standard block at Training > standard block at Test. 2. Later test: brain activations during late learning in a context of sequence violations (in the Test phase) are tested by the contrast standard block at Test > standard block at Training. Note that this contrast does not show the mere late phase of sequence learning, as it also involves reinstating the learned standard sequence after random sequences.

Selection of regions of interest
Since we hypothesized that key mentalizing areas in the posterior cerebellar Crus I & II and in the cortical TPJ would be involved during SRT learning, we took a priori regions of interest (ROIs) of these areas from previous meta-analyses (Table 1; Van Overwalle and Baetens, 2009;Van Overwalle et al., 2020a), which were also used in previous DCM studies (Van Overwalle et al., 2019c, 2020b. There were additional activations of cerebellar (e.g. lobule VI) and cerebral areas (e.g. PCun and TP) related to sequence learning and mentalizing processes in the implicit and explicit Belief SRT tasks. However, instead of using the peak coordinates from these studies, we took a more generalized approach by taking a priori coordinates from meta-analyses (Hardwick et al., 2013;Schurz et al., 2014;Van Overwalle and Baetens, 2009; Table 1). To verify that these meta-analytic coordinates would also fit the activation data from the Belief SRT tasks, we constructed spheres around their centers with radius = 15 or 10 mm for the cerebrum and cerebellum/subcortical areas, respectively (given the smaller size of the cerebellum and subcortical areas). A small volume correction analysis revealed significant activations in the bilateral cerebellar lobule VI and PCun during the initial Training phase (i.e. standard block at Training > standard block at Test) and additional clusters in the bilateral TP and caudate during the later Test phase (i.e. standard block at Test > standard block at Training). Thresholds were similar as in the original Belief SRT studies, that is, cluster-forming threshold of P < 0.001 (uncorrected) with a minimum extent of 10 voxels and a cluster-wise significance level of P < 0.05 with family-wise error correction for multiple comparisons.
Individually tailored cerebral ROIs were created by extracting the time series using the eigenvariate within a sphere with a radius of 8 or 5 mm (for the cerebrum and cerebellum, respectively) around the nearest local maximum within the corresponding ROIs listed above, using a whole-brain threshold of the contrast at P < 0.05 (uncorrected). All voxels contributing to the ROI were conducted on an F-contrast involving the comparison of interest and adjusted using an F-contrast involving all experimental effects. If the individual ROI did not contain a peak surviving the P < 0.05 uncorrected threshold, the same procedure was repeated with reduced thresholds P < 0.10 and P < 1.00 (uncorrected) so that the time series of all ROIs were included for all participants (see Table 1 for details). In the latter case of P < 1.00, ROIs were centered around the group-based centers (Zhou et al., 2007). This procedure was used because pairwise exclusion is not possible in a DCM analysis as all time series from all ROIs are required. Setting a more tolerant threshold in some individual cases implies an optimal compromise between maximizing the effect of interest at the individual level while having all participants in the DCM analysis so that the results are not biased by excluding some participants (Zhou et al., 2007).

DCM specification.
We used exactly the same procedure as in the earlier DCM analysis by (Van Overwalle et al. 2020b) which followed the steps described in Friston et al. (2016) and Friston et al. (2015) and detailed in https://en.wikibooks.org/wiki/User:Peterz/sandbox. First, a full DCM was specified and estimated for each participant using SPM12 (cf. SPM procedure: spm_dcm_fit). A full model allows all connectivity parameters in all directions to be freely estimated. We specified a bilinear deterministic DCM without centering around the mean (Friston et al., 2003), which included (i) all forward and backward fixed connections between the ROIs, (ii) all the modulatory connections or parameters that reflect condition changes due to each experimental condition and (iii) direct input parameters that reflect the input driving the activity in the ROIs in all experimental and control conditions. Stated differently, the driving input in Matrix C consists of one vector with all the onsets of all experimental and control conditions combined as one input, and the modularity connections in Matrix B are specified only for the experimental conditions so that both matrix inputs are nonredundant to each other (Hillebrandt et al., 2014).
Secondly, we constructed a parametric empirical Bayes (PEB) model for the whole group of participants over all parameters (cf. SPM procedure: spm_dcm_peb). This makes it possible to estimate the effective connectivity averaged across all participants (cf. group average), considering the within-participants variability on the connectivity parameters, unlike a classical test (e.g. t-test) which ignores the estimated uncertainty (variance) about the connection strengths. Moreover, a group-level PEB allows us to control for differences between sets of studies by treating them as covariates, for example, any differences in the behavioral measures and procedures (Friston et al., 2016).
Thirdly, we automatically pruned away any connectivity parameter from the group-level PEB which did not contribute to the model evidence using Bayesian model reduction (cf. SPM procedure: spm_dcm_peb_bmc). This approach has the advantage that any reduced model at the group level can be estimated efficiently without having to re-estimate the reduced models at the lower level (single-participant levels) and is therefore recommended (Friston et al., 2015). Specifically, a greedy search iteratively prunes connection parameters from the full model until model evidence starts to decrease so that the most relevant nested models from the full PEB model are tested (a greedy search is recommended because the model space of all possible nested models is too large to be fully evaluated). Bayesian model averaging of the parameters of the best 256 pruned models is applied and used for group inferences (Zhou et al., 2018, p. 707, 2.7.4) and so determines the winning model empirically. We considered connectivity parameters as significant given a posterior probability of P > 0.95 (based on model comparisons with and without each parameter). This Bayesian approach both for first-level connectivity analysis (DCM) as well as group-level inference (PEB) on connectivity parameters eschews the multiple comparisons problem (Friston et al., 2003(Friston et al., , p. 1276. We applied these recent developments in DCM analysis to ensure that the connections revealed by the analyses are entirely data-based. Moreover, to rule out multicollinearity in the DCM estimates due to the relatively large number of ROIs within the smaller volume of the cerebellum, we ran two additional reduced models for the two Belief SRT tasks. One DCM model included only the hypothesized mentalizing cerebellar and cerebral areas (i.e. the left Crus I, the bilateral Crus II and the bilateral TPJ). Another DCM model included only robustly significant ROIs. These results did not change the main results appreciably and are therefore reported in Supplementary Tables S2-S5.

Results
The fixed and modulatory estimates of the connectivity between the cerebral and cerebellar ROIs of the reduced model (after pruning) in the implicit and explicit Belief SRT tasks are listed in Table 2 for the initial Training phase and in Table 3 for the later Test phase. We first report the fixed estimates which reflect the intrinsic connections between regions, and then we report the modulatory estimates which reflect the modulation of connections depending on the learning phases. We do not report the direct inputs, because none of the driving inputs reached significance.
Of most interest are the estimates in the off-diagonal cells of Tables 2 and 3. These values reflect how much activation in the source ROI (i.e. the top row) changes the activation in the target ROI (i.e. the left column), which is expressed in units per second or 1/s (Hz). Here, positive estimates indicate excitation, and negative estimates indicate inhibition between ROIs. Of less interest are the estimates in the diagonal cells of Tables 2 and 3 which correspond to self-connections, with positive estimates indicating greater self-inhibition, whereas negative estimates indicate less self-inhibition than the default (−0.5 Hz). Decreased selfinhibition suggests increased sensitivity to input from other brain areas (Zeidman et al., 2019).
As hypothesized, we found fixed bidirectional connectivity (i.e. closed loops) between the posterior cerebellar Crus I & II and the bilateral TPJ in both implicit and explicit Belief SRT tasks during both learning phases. Also, we found that the posterior cerebellum was linked to other hypothesized cerebral areas (i.e. PCun, TP and caudate). Additionally, we did not find many modulations. This is supported by the following detailed results. Table 2. Averaged connections in units of 1/s (Hz) for the contrast: standard block at Training > standard block at Test Notes: L = left, R = right, Lob. VI = cerebellar lobule VI. Cell entries refer to the connections from the top row ROIs to the left column ROIs with posterior probability. Empty cells denote connectivity = 0. Bold denotes the closed loops. Italic denotes the self-inhibitions in diagonal cells. Light gray denotes the cerebellar-cortical connectivity. **P > 0.95, *P > 0.50.

Connectivity in the initial training of the standard sequence
We first contrasted the standard blocks in the initial Training phase vs the standard blocks in the later Test phase to find out how the ROIs interact with each other during the initial learning of the belief sequence. For each task, we first discuss the 'fixed' connectivity between the cerebellum and the cerebrum, then within the cerebrum and then within the cerebellum. This is followed by a short discussion of modular connectivity.
For the implicit Belief SRT task (Table 2; Figure 2A), we found significantly closed loops between left Crus I, bilateral lobule VI and the right TPJ and a closed loop between left Crus I and the left TPJ, but only unidirectional links from the right Crus II to the bilateral TPJ. Closed loops were also found between the PCun and left Crus I and the right lobule VI. Within the cerebrum, the PCun was bidirectionally connected with the right TPJ, and the left TPJ was unidirectionally linked to its right counterpart. As shown in Figure 2B, within the cerebellum, most cerebellar ROIs were connected via closed loops to each other, except for a limited number of unidirectional links: on the left hemisphere from Crus II to Crus I, from the Crus II to lobule VI and from the lobule VI to the Crus I; on the right hemisphere, from lobule VI to Crus II, between hemispheres, from the left Crus I to the right lobule VI and from the left Crus II to the right Crus II. The modularity connections showed decreased self-inhibition in the bilateral Crus II, left lobule VI and bilateral TPJ during the initial Training phase. There were almost no modulations of the connections between ROIs, except for a weaker connection from the left to the right lobule VI during the initial Training phase.
We observed a largely similar pattern of connectivity for the explicit Belief SRT task (Table 2; Figure 2C, D) with again a few unidirectional exceptions which are, however, different than during the implicit task. As can be seen in Figure 2C, we found again significantly closed loops between the cerebral ROIs and the bilateral TPJ, except for unidirectional links from the left TPJ to the left Crus I and from the right TPJ to the left Crus II. Significant connections were also found between the PCun and cerebellar ROIs, and they were more numerous here: closed loops to all left cerebellar ROIs and unidirectional links to all the right ROIs. Within the cerebrum, we see again the same links between the left and Table 3. Averaged connections in units of 1/s (Hz) for the contrast: standard block at Test > standard block at Training Notes: L = left, R = right. Cell entries refer to the connections from the top row ROIs to the left column ROIs with posterior probability. Empty cells denote connectivity = 0. Bold denotes the closed loops. Italic denotes the self-inhibitions in diagonal cells. Light gray denotes the cerebellar-cortical connectivity. **P > 0.95, *P > 0.50. right TPJ and between the PCun and the right TPJ, but they were now all closed loops. As shown in Figure 2D, within the cerebellum, some cerebellar ROIs were connected via closed loops to each other: on the left hemisphere between the Crus I and Crus II, on the right hemisphere between lobule VI and Crus II and between hemispheres between left Crus I and right lobule VI. Unidirectional links were also observed on the left hemisphere from lobule VI to Crus II, between hemispheres from the left Crus I to the firth Crus II and from the right Crus II to the left Crus II.
The modularity connections showed significantly decreased self-inhibitions in the bilateral lobule VI, PCun and right TPJ during the initial Training phase. There were again almost no modulations of the connections, except for a weaker connection from the left TPJ to the PCun given the initial Training phase.

Connectivity in the later test of the standard sequence
We next used the reverse contrast of the later Test phase vs the initial Training phase to reveal the connectivity during maintaining the learned belief sequence in the later Test phase. We use the same order as before. For each task, we first discuss the 'fixed' connectivity between the cerebellum and the cerebrum, then within the cerebrum and then within the cerebellum, followed by a brief discussion of modular connectivity.
For the implicit Belief SRT task (Table 3; Figure 3A), we found again significantly closed loops between the cerebral ROIs and the bilateral TPJ. The left Crus I was connected via a closed loop to the left TP and received a link from the left caudate. There were significantly closed loops between the bilateral Crus II and additional (sub)cortical areas (i.e. bilateral TP and left caudate), except for a unidirectional link from the left Crus II to the right TP. Within the cerebrum (Figure 3B), most cerebral ROIs showed closed loops with each other, except for a limited number of unidirectional links: on the right hemisphere from the TPJ to TP, between hemispheres from the right TP to its left counterpart and from the right TPJ to the left TP and to the left caudate. Within the cerebellum, the left Crus I showed a closed loop with the right Crus II.
The modularity connections showed significantly decreased self-inhibitions in the left caudate and the bilateral TPJ but no change of self-inhibitions in the cerebellum. There was a decreased connection from the left TP to the left Crus I given the later Test phase.
For the explicit Belief SRT task, we see a similar pattern of connectivity as the implicit counterpart but now with more unidirectional than closed loops (Table 3; Figure 3C, D). As can be seen in Figure 3C, most closed loops between the cerebral ROIs and bilateral TPJ dropped, except for one closed loop between the left Crus I and the right TPJ. Instead, there were numerous unidirectional connections: from the left Crus II to the left TPJ, from the left TPJ to the left Crus I and from the bilateral TPJ to the contralateral Crus II. Again, the left Crus I showed a unidirectional link to the left TP and received a link from the right TP. We also found closed loops between the bilateral Crus II and the additional (sub)cortical areas (i.e. left caudate and bilateral TP), except for a unidirectional link from the right Crus II to the left TP. Within the cerebrum, some cerebral ROIs were connected via closed loops to each other: between the bilateral TPJ, between the left TPJ and the right TP. Unidirectional links were also observed on the left hemisphere from the TP to the TPJ and from the TPJ to the caudate; between hemispheres from the right TP to the left TPJ, from the right TPJ to the left TP and from the left caudate to the right TP. Within the cerebellum, most cerebellar ROIs were connected via closed loops to each other, except for a unidirectional link from the left Crus I to the right Crus II.
The modularity connections showed significantly decreased self-inhibitions in the left Crus II, right TP and left caudate. There were decreased connections from the right to the left Crus II and from the left TPJ to the right TP given the later Test phase.

Summary
To sum up, in line with our hypothesis, many connections revealed closed loops between the posterior cerebellum and the bilateral TPJ during both implicit and explicit Belief SRT tasks.
For both tasks, additional cerebellar ROIs were also linked to cerebral mentalizing areas. There were numerous (uni-and bidirectional) connections between the cerebellar lobule VI and the bilateral TPJ and the PCun during the initial Training phase (in comparison with the Test phase) and between the posterior cerebellum and the bilateral TP and left caudate during the later Test phase (in comparison with the Training phase). Additionally, there were numerous (uni-and bidirectional) connections within the cerebellum and the cerebrum. Another important observation is that the connectivity patterns were largely similar between the implicit and explicit tasks, although there were more closed loops in the implicit tasks. All connections showed positive as well as negative estimates without a clear downward vs upward pattern. Modulations of cerebellar and cerebral self-inhibitions were rare, and modulations of connections between ROIs were largely absent.

Discussion
In the current study, we used DCM to investigate dynamic cerebello-cerebral connectivity, particularly within the posterior cerebellum and the bilateral TPJ, during implicit and explicit Belief SRT tasks (Ma et al., 2021). After pruning away connections that did not significantly contribute to the model, the DCM analysis offered a model of effective connectivity that provided the best fit with the group-level data of the implicit and explicit tasks. Consistent with our hypothesis, we found that the posterior cerebellum Crus I & II and the bilateral TPJ were connected via closed loops. Moreover, we found that additional brain areas (the cerebellar lobule VI, PCun, TP and caudate) were bi-or unidirectionally linked to the posterior cerebellum and TPJ and so further contributed to belief sequence learning.
Overall, our current study supports the idea that the posterior cerebellum synchronizes neural activation with related mentalizing cerebral areas (i.e. TPJ, PCun and TP) during learning and maintaining a given belief sequence. It is important to emphasize that our ROIs for the DCM analysis were based on earlier metaanalyses and that we used a data-driven greedy search algorithm to reveal significant connections. In this way, a potential bias in favor of our hypothesis was strongly reduced.
The Belief SRT task is the first one to investigate implicit sequence learning in the social mentalizing domain and reveals distinct cerebellar processes and topography compared to nonsocial domains. This is attested by the observation that earlier research on visuomotor sequencing tasks revealed activation in more anterior cerebellar parts (Hardwick et al., 2013;Janacsek et al., 2020), whereas the Belief SRT task robustly activated the posterior cerebellum (Ma et al., 2021). Despite this distinct topography, the current DCM analysis demonstrates that cerebellar and cerebral mentalizing areas are functionally connected and continuously exchange neural signals.

Many cerebello-cerebral connections have closed-loop properties
In our DCM analysis, the so-called 'fixed' cerebello-cerebral connections reflected systematic links among brain areas independent of the initial Training and later Testing phases. In line with our hypothesis, for both implicit and explicit Belief SRT tasks, we found fixed connectivity, mainly as effectively closed loops, between the posterior cerebellum Crus I & II and the bilateral TPJ. The TPJ considered to be a key area for shifting to others' perspectives and inferring their transient mental states (Van Overwalle, 2009;Schurz et al., 2013). The current analysis confirms earlier DCM studies documenting closed-loop connectivity between the posterior cerebellum Crus II and the TPJ during social mentalizing (Van Overwalle et al., 2019c, 2020b, and our findings extend this functional synchronization to the left posterior cerebellum Crus I. The current analysis also revealed additional fixed cerebellocerebral effective closed loops between the posterior cerebellum and other neocortical mentalizing areas, including the PCun and TP. The PCun contributes to the mentalizing process by constructing mental images and social contexts related to different perspectives (Frith and Frith, 2006;Van Overwalle and Baetens, 2009;Schurz et al., 2013). The TP is believed to store social knowledge about others, such as social rules and etiquette (Schurz et al., 2013;Molenberghs et al., 2016). Understanding the different beliefs that protagonists maintain in a variety of situations is an indispensable process supported by these two areas so that their synchrony with cerebellar areas likely contributed to performance in the Belief SRT tasks. These findings extend earlier DCM studies on social mentalizing which found only unidirectional connections from the right cerebellar Crus II to the PCun (Van Overwalle et al., 2019c, 2020b. Overall, the closed loops identified in this analysis support the assumption put forward by (Van Overwalle et al. 2019b) that incoming social signals from mentalizing areas in the neocortex are sent further to the posterior cerebellum to identify and automatize their sequences and are then are fed back to cerebral mentalizing areas to affirm ongoing social behaviors or to warn and prepare for unexpected social violations.
The effectively closed loops observed here are supported by anatomical research documenting white matter connections that form closed loops between cerebellar and cerebral cortices. Using DTI on healthy adults, Karavasilis et al. (2019) found that the cerebellum is anatomically connected with the frontal and temporal cortices and to a lesser extent to the parietal cortex. A more recent DTI study by Metoki et al. (2021) provided evidence for white matter connections between mentalizing areas in the cerebellum (i.e. the posterior Crus I & II) and the cerebral cortex (i.e. mPFC, PCun, TP and TPJ). Interestingly, in that study, the right TPJ revealed strong contralateral pathways toward the cerebellum, while in the reverse direction, the cerebellum displayed weaker contralateral pathways to the TPJ and stronger ones to the mPFC, PCun and TP.

Other subcortical areas contribute to connectivity with the mentalizing neocortex
This analysis also found that the bilateral cerebellar lobule VI and the left caudate were linked to cerebral and cerebellar mentalizing areas via numerous closed loops. A recent study on social intentions inferred from moving geometrical shapes also revealed strong connectivity between the cerebellar lobule VI and mentalizing areas in the cerebral cortex . The cerebellar lobule VI and the caudate were consistently found in recent meta-analyses on visuomotor learning in classical SRT tasks (Hardwick et al., 2013;Janacsek et al., 2020). Recent DCM analyses on visuomotor sequence learning revealed connections between the cerebellum and putamen (including caudate (Tzvi et al., 2015;Liebrand et al., 2020). Because these subcortical areas have never been implicated in other DCM analyses related to social mentalizing as far as we are aware (Van Overwalle et al., 2019c, 2020b, this may suggest that the cerebellar lobule VI and the caudate subserve sequence learning not only in visuomotor contexts but also in some social settings. Alternatively, this may suggest that these areas are specific to some key aspects of the SRT paradigm (i.e. rapidly responding to sequential stimuli with minimal motor actions; Hardwick et al., 2013), rather than general visuomotor or social sequence learning processes.

Implicit sequence learning reveals more closed loops than explicit sequence learning
We observed similar patterns of connectivity between the implicit and explicit Belief SRT tasks. This implies that both types of belief sequence learning, in a social context, share the same effective connectivity within and between the cerebellar and cerebral mentalizing areas. However, interestingly, there were more withincerebellar and cerebello-cerebral closed loops in implicit belief sequence learning compared to explicit learning. This seems consistent with the general assumption that the cerebellum is specifically involved in implicit learning and automatization (Taylor et al., 2010;Morgan et al., 2021). For instance, cerebellar patients had impaired performance when implicitly learning a sequence of a shape's locations but had comparable performance when they were explicitly told to learn and reproduce a given letter sequence (Morgan et al., 2021). It will be of interest for future studies to test behavioral performance and effective cerebellocerebral connectivity for patients with cerebellar deficits during the completion of the implicit and explicit Belief SRT task. This will allow us to gain insight into how the cerebellum might go awry in social thinking and tailor diagnostic instruments for mentalizing sequencing to the specific needs of these clinical populations.

Little modulation of cerebello-cerebral connectivity
We did not find many modulations of cerebello-cerebral connectivity induced by the initial Training phase or the later Test phase. For both the implicit and explicit versions, the results revealed a few suppressive modulations within the cerebellum or within the cerebrum, and almost none between the cerebellum and cerebrum, when comparing the initial Training with the Test phase or vice versa. These limited modulations are consistent with earlier DCM research on explicit inferences of social beliefs and traits (Van Overwalle et al., 2019c, 2020b. Note, however, that the Belief SRT tasks measured implicit (and explicit) learning of belief-related sequences, but not of implicit mentalizing itself (i.e. participants were explicitly told to mentalize protagonists' beliefs). Overall, this seems to indicate that neural synchrony between the cerebello-cerebral mentalizing areas is rather robust and largely unaffected by task changes, such as learning phase, degree of implicitness or type of social inference (e.g. trait or belief). This observation needs to be followed up in future research.

No clear pattern of positive and negative connections
Although the present analysis largely confirms the hypothesized cerebello-cerebral connectivity between mentalizing areas, there was no clear pattern of positive and negative values for these connections. In earlier DCM analyses on social mentalizing, researchers found that all top-down connections from the TPJ to the posterior cerebellum were positive, and all bottom-up connections were negative (Van Overwalle et al., 2019c, 2020b. This pattern was absent in the current study, where downward and upward estimates between the bilateral TPJ and the posterior cerebellum showed mixed signs of estimates. We ran additional DCM analyses with reduced sets of ROIs to rule out that this was caused by the large number of ROIs within the smaller volume of the cerebellum, which may have led to a statistical problem of multicollinearity and hence a contradictory pattern of estimates. These reduced analyses, however, showed largely the same valence of connectivity as the original analyses. Another methodological explanation is that the earlier DCM analyses by Van Overwalle and colleagues used quite large samples (n = 91 and 49; Van Overwalle et al., 2019c, 2020b. Perhaps more participants than the current study (n = 18-22) are needed to discern a clear pattern of positive and negative connectivity. Alternatively, the tasks in the earlier analyses involved familiar social scenes (cf. chocolate scenario from the introduction), of which the correct sequence is well-known, while the Belief SRT task is set in a somewhat artificial context, with a new and unfamiliar sequence to be learned implicitly or explicitly. As the level of awareness and knowledge of the sequence might vary greatly between participants, this may have resulted in this mixed pattern.

Connectivity was not directly modulated by random sequences
As mentioned earlier, prior meta-analyses of SRT tasks (Hardwick et al., 2013;Janacsek et al., 2020) often compare the learned standard sequence against a random sequence or another baseline condition without a learned sequence. This reflects the assumption that a learned sequence rests on robust cerebellar involvement for encoding and automatizing, while novel or random sequences recruit a cerebellar process to a lesser extent. Surprisingly, this contrast did not reveal any activation of the cerebellum in the original Belief SRT studies (Ma et al., 2021). Therefore, we could not include it in the current DCM analysis. Some differences in SRT designs may account for this lack of a random sequence effect. Perhaps most importantly, many earlier SRT tasks in neuroimaging studies presented a combination of standard and random sequences from the beginning (Hardwick et al., 2013;Janacsek et al., 2020), while the present Belief SRT studies began with a long Training phase of a standard sequence without any random disruption, as is typically done in behavioral research (Ma et al., 2021). Although this set-up precluded an immediate examination of connectivity patterns in comparison with random sequences (in the Training phase), it showed significant contrasts against the later Test phase when random violations were introduced. It would be of theoretical interest for future studies to test how cerebello-cerebral connectivity is modulated by novel sequences against an already automatized sequence.

Connectivity within the cerebrum and the cerebellum
Within the cerebrum, we found connections between the right and left TPJ, and connections between the right TPJ and the PCun during the initial Training phase. During the later Test phase, almost all cerebral ROIs (bilateral TPJ, bilateral TP and the caudate) were connected to each other, and most of these connections formed effectively closed loops during implicit learning. Although specific mentalizing areas are responsible for specific functions, our results suggest that these cerebral mentalizing areas exchange signals with each other in integrative functional synchrony, especially when participants were learning and automatizing a social sequence. The effective connections between the bilateral TPJ and the bilateral TP support previous studies, showing that these cerebral areas are co-activated during mentalizing (see meta-analyses by Van Overwalle and Baetens, 2009;Schurz et al., 2014;Molenberghs et al., 2016;Wang et al., 2021). Also, while earlier studies on mentalizing showed effectively closed loops between the bilateral TPJ using DCM (Van Overwalle et al., 2019c, 2020b, our DCM results further revealed effective connections between the TPJ and TP which are consistent with anatomical connections between the TPJ and TP via fiber tracts . Within the cerebellum, we found that most cerebellar ROIs were connected to each other within one hemisphere or across the two hemispheres, suggesting intra-and interhemispheric connectivity in the cerebellum. Our DCM findings are supported by DTI analyses of the human cerebellum which revealed short intracerebellar fibers representing a local intracerebellar circuitry (Catani et al., 2008) as well as transverse white matter fibers crossing the two hemispheres at the level of the cerebellar vermis (Salamon et al., 2007). It is likely that these paths are also used for exchanging social information.

Implications
Studying the dynamic changes in activation of brain areas via connectivity is important to understand the functionality of the brain. In the current study, we showed robust effective cerebellocerebral connectivity during the learning of belief sequences. However, functional and structural connectivity is not always a simple one-to-one mapping (Suárez et al., 2020;Wang et al., 2021). Therefore, it will be of interest to use structural techniques like DTI to test in more depth how the cerebello-cerebral relationships are organized via anatomical connections during implicit and explicit social sequence learning. This would provide even stronger evidence for the role of the posterior cerebellum in mentalizing with the sequential organization (Van Overwalle et al., 2019b).
Also, for clinical populations with social deficits, it will be of interest for future studies to investigate whether there is a deficit within-cerebellar and cerebral mentalizing areas, or whether there is distorted connectivity between these mentalizing areas (Van Overwalle et al., 2021a). For example, researchers showed that during the resting state, people with autism revealed no differences in TPJ organization and components compared to neurotypical participants, but they had a significant decrease in connectivity between the right TPJ and the left posterior cerebellar Crus II (Igelströ m et al., 2017). As DCM can reveal the effective direction of connectivity, future studies can further reveal whether autistic patients have weak connections from the posterior cerebellum to the cerebral mentalizing areas or vice versa, resulting in their failure to flexibly learn and automatize sequential information during social cognition.
As the posterior cerebellum is close to the skull (Grimaldi et al., 2016), our connectivity study suggests the posterior cerebellum as a possible new target for noninvasive brain stimulation (Cattaneo et al., 2021;Van Overwalle et al., 2021a). Previous studies showed that transcranial magnetic stimulation of the posterior cerebellum reduced response times for generating the correct order of mentalizing stories  and that transcranial direct current stimulation (tDCS) improved emotion discrimination (Ferrucci et al., 2012). Together with our results of functional connectivity, future studies stimulating the posterior cerebellar Crus I/II and cortical areas, such as the TPJ, could shed light on the causal roles of cerebello-cerebral areas involved in social processes. Stimulating the cerebellum may also be possible indirectly. A study combining tDCS and fMRI showed that stimulating the prefrontal cortex not only induced stronger activation in this area but also resulted in increased cerebellar activation during implicit emotion regulation (Abend et al., 2019). Future studies combining stimulation and fMRI are needed to test how functional connectivity is changed after stimulation. For example, during social sequence learning, it is of critical importance to see whether stimulating the posterior cerebellar Crus I/II can result in stronger TPJ activation and stronger connectivity with the cerebrum and so improves mentalizing capacities. Also vice versa, how stimulating cortical mentalizing areas might impact the posterior cerebellum and mentalizing functionality. Perhaps the combined stimulation of both cerebellar and cerebral areas might result in an additive effect, which might be advantageous for clinical purposes.

Conclusion
Using DCM, we found closed loops between the posterior cerebellum (e.g. Crus I & II) and cerebral areas sensitive to mentalizing (i.e. TPJ, PCun and TP). The analysis suggests that a specific cerebello-cerebral mentalizing network is engaged while learning social belief sequences. The closed loops in this network confirm the hypothesis by (Van Overwalle et al. 2019a) that the posterior cerebellum receives signals from cerebral mentalizing areas about incoming social information and sends back confirmatory or corrective signals about the social sequences identified in this information to the same cerebral areas. Many unresolved questions remain and need to be answered in future studies: To what extent is awareness of a social sequence important in connectivity? Are there other sources that may lead to potential modulations which were quite rare in the present studies? How robust are patterns of positive downward and negative upward connectivity in social sequence learning revealed in prior DCM analyses? Although many questions remain and research on social sequence learning is still young, one fact is obvious: social belief understanding relies heavily on the connectivity of key mentalizing cerebral areas, such as the bilateral TPJ with the posterior cerebellum, and is therefore unlikely to function properly without the latter.