In three experiments, patients with CA and neurotypical (NT) healthy participants solved symbolic arithmetic, alphabet transformation, and grammar sequential problems. These sequential problems required a series of discrete steps to be completed in a specific order to reach a solution. In Experiment 1, the CA group demonstrated impairment in a subtraction task, providing novel evidence of the cerebellum’s contribution to symbolic arithmetic reasoning. In addition, we found a selective impairment of the CA group compared to the NT group. The CA group exhibited a disproportionate expectancy effect only (no difference in the complexity effect). Consistent with Experiment 1, in Experiment 2, using the alphabet transformation task, we found a distinct disproportionate expectancy effect (no difference in the complexity effect). Transforming alphabetic letters by an arithmetic operator is a less commonly used cognitive operation than subtracting digits. This allowed us to reduce the potential effects of top-down processes and show that CA’s impairment also appears when there are fewer top-down effects. Rather, this probably increased the need to develop algorithmic procedures during the task.

In Experiments 1 and 2, participants identified if a given problem was correct or not based on their previous knowledge; however, in Experiment 3, we probed novel cognitive VE under uncertainty. We formed a new scenario where prior lifetime knowledge is absent, and participants are required to learn a new grammatical rule within the task. The participants’ expectations were novel and were not based on previous top-down processes. Utilizing an AGL task Pothos, 2007, participants needed to learn a new Markovian grammar, regarding how to organize a sequence of letters in a specific order. To assess the effect of the participant’s uncertainty, we manipulated the level of similarity between grammatical and nongrammatical problems. We found that the CA group showed selective impairment only in the low similarity condition (higher sensitivity), probably where expectations are higher. Although it was not a causal finding and no behavioral evidence was found, an fMRI study (Lesage et al., 2017Lesage et al., 2017) revealed that activity in the right posterolateral cerebellum correlated with the predictability of the upcoming target word. Together with our current findings and others (Fiez et al., 1992; Moberget et al., 2014), this pattern of results might indicate that the cerebellum is necessary for higher cognition through a VE mechanism.

Across the three experiments, we examined the effect of VE in both established and newly learned cognitive procedures, considering varying levels of potential top-down effects. The CA group showed a disproportionate expectancy effect compared to the NT group. We found that the between-group differences in the expectancy effect are consistent across tasks. Notably, the results indicate that CA patients had both intact processing of the problems’ complexity (i.e. number of steps) and intact ability to discriminate between correct and incorrect problems when certainty decreased (i.e. sensitivity was lower). Thus, the results indicate a distinct role of the cerebellum in processing VE across these sequential cognitive tasks.

Several theories are in line with the principle of neural reuse and our hypothesis that the cerebellum contributes to many domains using the same core cognitive mechanism (Saban and Gabay, 2023). Rozin, 1976 proposed that computations that initially evolved to solve specific problems become accessible to other systems through evolution, as well as within the individual lifetime of an organism. Change or expansion of a function, because it is more generally available or accessible, ‘would have adaptive value when an area of behavioral function could profit from programs initially developed for another purpose.’ This idea has been reframed and elaborated upon in Gallese’s ‘neural exploitation’ hypothesis (Gallese and Cuccio, 2018) and Anderson’s ‘massive redeployment’ hypothesis (Anderson, 2010; Anderson, 2007). The core idea is that neural networks can acquire new uses after establishing an initial function. Decades of empirical research from human and animal experiments, including our own, support this framework (Hull, 2020; Saban and Gabay, 2023; Saban et al., 2021b; Balsters et al., 2013). The broad involvement of the cerebellum in motor and nonmotor functions supports the idea of neural reuse, indicating this specific structure’s potential ability to reuse its core function.

A few hypotheses have been proposed based on the idea that cerebellar contributions to motor control may extend to the cognitive domain (Ito, 2008; Fiez et al., 1992; McDougle et al., 2022). For example, in one recent paper (McDougle et al., 2022) it was hypothesized that the cerebellum supports dynamic continuous transformations of mental representations. However, the concrete implementation of ‘continuity’ in terms of higher mental representations remains an open question (Dietrich and Markman, 2003). Currently, there is no established direct evidence supporting the existence of such ‘continuous’ and ‘dynamic’ higher cognitive processes. Indeed, a recent later study by the same authors found no support for this hypothesis within the language domain (i.e. semantic processing task) (King et al., 2024). It is unclear whether the utilized problems, such as simple addition or mental rotation, are entirely solved using ‘continuous transformation’ or through previously learned procedural knowledge of the required mental steps. The constraints on the cerebellum’s role remain an open question, particularly whether its role is limited solely to tasks requiring ‘continuous mental transformation,’ as previously suggested (McDougle et al., 2022). Therefore, more consistent and well-established cerebellar parsimonious theories are still needed.

One might be concerned that if the cerebellum is involved in sequential operations, its involvement in mental letter rotation, which can be assumed as ‘continuous transformation,’ may appear contradictory. We note that the boundary between continuous and stepwise, procedural operations is not always clear-cut and may vary depending on the participant’s strategy and previous knowledge, which is not always fully known to the researchers. But this is a debatable consideration. More importantly, a careful reading of our paper suggests that our experiments were designed to examine VE within tasks that involve sequential processing. Notably, we are not claiming that the cerebellum is involved in sequential processing per se. Rather, our findings point to a more specific role for the cerebellum in processing VE that arises during the construction of multi-step procedural tasks. In fact, the results indicate that while the cerebellum may not be directly involved in the procedural process itself, it is critical when expectations are violated within such a context. This distinction is made possible in our study by the inclusion of a control condition (the complexity effect), which allows for a unique dissociation in our experimental design—one that, to our knowledge, has not been sufficiently addressed in previous studies (McDougle et al., 2022).

Additionally, in the case of arithmetic problem solving—such as the tasks used in prior studies (McDougle et al., 2022)—there is substantial evidence that these problems are typically solved through stepwise, procedural operations. Arithmetic reasoning, used in our Experiments 1 and 2, has been robustly associated with procedural, multi-step strategies, which may be more clearly aligned with traditional views of cerebellar involvement in sequential operations. Thus, we propose that the role of the cerebellum in continuous transformations should be further examined.

We suggest a more parsimonious theory – the cerebellum contributes to VE, a field that was highly examined before. Yet, to reconcile these findings, we propose that the cerebellum’s contribution may not be limited to either continuous or stepwise, procedural operations per se, but rather to a domain-general process: the processing of VE. This theoretical framework can explain performance patterns across mental rotation tasks, grammar learning, and procedural arithmetic.

Another concern is related to oculomotor deficits (e.g. downbeat nystagmus), which are common in CA and could have influenced participants’ performance. While the SARA scale does not assess oculomotor function, our experimental design – in all three experiments – has control conditions that help account for general processing differences, including those that could arise from oculomotor deficits. These conditions, such as the correct trials and the complexity effects, allow us to isolate effects specifically related to VE while minimizing the influence of broader performance factors, such as eye movement abnormalities. We also note that, while some patients can experience oculomotor symptoms such as downbeat nystagmus, none of our tasks required precise visual tracking or gaze shifts. In our experimental tasks, stimuli were centrally presented, and no visual tracking or saccadic responses were required.

Our study is subject to two main limitations. First, information about anatomical-behavioral relationships can provide valuable data and will certainly be important in the long run for understanding how the cerebellum contributes to cognition. For example, one can ask if performance is related to gross measures such as total cerebellar volume or finer measures such as whether the observed deficits are associated with atrophy in particular regions. These analyses typically require large sample sizes, especially when dealing with atrophic processes (where the pathology tends to be relatively diffuse). Relatedly, we could not perform brain connectivity analysis, which limits our ability to examine the interactions between the cerebellum and other brain regions, such as the basal ganglia (BG) and the frontal lobe. This lack of brain connectivity data also restricts our ability to compare the cerebellum’s functional contributions to those of other regions. For example, in a recently published paper (2024), we found that the BG plays a distinct role in mathematical complexity processes (Saban et al., 2024). Unfortunately, we do not have imaging data for many of the patients.

Yet, there is added value in studies that include behavioral results from neurological groups defined based on clinical diagnosis. This is common in the literature, as seen in other recently published studies (Saban et al., 2024; McDougle et al., 2022) in high-impact journals (PNAS, Journal of Neuroscience, Brain). In addition, the current experimental design is already complex, with two groups and three experiments, including control conditions. However, future work should use lesion analysis or connectivity methods to identify the specific anatomical-behavioral relationships critical for arithmetic and language operations.

A few important questions remain open in the literature concerning the cerebellum’s role in expectation-related processes. The first is whether the cerebellum contributes to the formation of expectations or the processing of their violations. In Experiments 1 and 2, the CA group did not show impairments in the complexity manipulation. Solving these problems requires the formation of expectations during the reasoning process. Given the intact performance of the CA group, these results suggest that they are not impaired in forming expectations. However, in both Experiments 1 and 2, patients exhibited selective impairments in solving incorrect problems compared to correct problems. Since expectation formation is required in both conditions, but only incorrect problems involve a VE, we hypothesize that the cerebellum is involved in VE processes. We suggest that the CA group can form expectations in familiar tasks, but are impaired in processing unexpected compared to expected outcomes. This supports the notion that the cerebellum contributes to VE, rather than to forming expectations.

In Experiment 3, during training, participants learn a novel rule (grammar), forming new expectations on how strings of letters should be. Afterwards, during testing, the participants are requested to identify if a novel string following the rule or not. We examined sensitivity to distinguish between grammatical and non‐grammatical strings of letters, thus taking into account a baseline ability to identify expected strings. Additionally, both in the low‐similarity and high‐similarity conditions, there are expectations regarding whether the strings following the rule or not. However, in the high‐similarity condition, there is more uncertainty regarding which strings are following the grammatical rule, as demonstrated in a lower sensitivity (d prime). Given the group differences only in the low similarity condition, these results suggest the CA group is impaired only when the rules are more certain. Given these results, we suggest that forming cognitive expectations is not necessarily dependent on the cerebellum. Rather, we propose that the cerebellum is critical for processing VE (detection or processing of detected errors) under conditions of more certainty. One remaining question for future studies is whether the cerebellum contributes to detection of a mismatch between the expectation and sensory evidence, or the processing of a detected VE.

We suggest that these key questions are relevant to both motor and non-motor domains and were not fully addressed even in the previous, well-studied motor domain. Importantly, while previous experimental manipulations Taylor et al., 2014; Moberget et al., 2014; Riva, 1998; Butcher et al., 2017 have provided valuable insights regarding the cerebellar role in these processes, some may have confounded these two internal constructs due to task design limitations (e.g. lack of baseline conditions). Notably, some of these previous studies did not include control conditions, such as correct trials, where there was no VE. In addition, other studies did not include a control measure (e.g. complexity effect), which limits their ability to infer the specific cerebellar role in expectation manipulation.

Thus, the current experimental design used in three different experiments provides a valuable novel experimental perspective, allowing us to distinguish between some, but not all, of the processes involved in the formation of expectations and their violations. For instance, to our knowledge, this is the first study to demonstrate a selective impairment in rule-based VE processing in cerebellar patients across both numerical reasoning and artificial grammar tasks. If feasible, we propose that future studies should disentangle different forms of VE by operationalizing them in experimental tasks in an orthogonal manner. This will allow us to achieve a more detailed and well-defined cerebellar motor and non-motor mechanistic account.

Conclusion

Our findings support neural reuse hypotheses (Rozin, 1976; Anderson, 2007) in that the cerebellum contributes to both motor and non-motor functions using a similar mechanism (Hull, 2020; Moberget et al., 2014; Flaumenhaft et al., 2025). The cerebellum not only contributes to motor control but also to cognitive procedures necessary for processing sequential arithmetic reasoning, alphabet transformation, and grammar problems using a similar mechanism – processing VE.

To conclude, theories of universal cerebellar transform propose that the cerebellum plays an essential role in modulating not only motor functions but also cognitive and affective processes (Guell et al., 2018; Schmahmann, 2004). The dysmetria of thought theory posits that cognitive and affective symptoms observed in cerebellar patients arise from the same dysfunction that affects motor control. This concept highlights the interconnectedness of motor, emotional, and cognitive domains, suggesting that impairments in one domain can reflect core problems in others. Our study provides convergent empirical evidence for the potential core role of the cerebellum and aligns with these previous theoretical frameworks.