The brain is a learning machine that continually adapts to varying and uncertain environments worldwide. Through learning, the developing brain gradually becomes able to comprehend and produce structured information, such as music. Predictive coding, currently a predominant theory on sensory perception (Friston, 2010; Heilbron and Chait, 2018), provides a neurophysiological architecture of predictive learning processes in the human brain. Neural representations in the higher levels of cortical hierarchies can be used to predict plausible representations in the lower levels in a top-down manner and are then compared between the hierarchies to assess the prediction error (i.e., a mismatch between a prior prediction and the actual sensory input) (Mumford, 1992; Rao and Ballard, 1999; Kiebel et al., 2008). The resulting mismatched signal is passed back up the hierarchy to update higher representations and yield better predictions. Over the long term, this recursive exchange of signals reduces the prediction error and uncertainty in the environment. In this framework, the reliability of the prior prediction is also controlled by the precision (confidence) of prediction at higher levels of a hierarchical model (Friston, 2008). This precision can be estimated by the variance of any possible sensory input, which is sometimes referred to as perceptual uncertainty (information entropy, Shannon, 1948). In other words, the brain perceives and suppresses the uncertainty. The expected reduction of uncertainty has generally been referred to as salience, evaluated from the gap between the prior and posterior distributions (i.e., Kullback–Leibler divergence or relative entropy).

Statistical learning mechanisms in the brain appear to agree with this predictive process (Harrison et al., 2006). Statistical learning is an automatic computing system by which the human brain extracts statistical regularities from the world and predicts a future state to minimize sensory reactions and uncertainty over the environment. Specifically, the brain calculates the transitional probability and precisely perceives the uncertainty of its probability distribution. This internalized probabilistic model allows us to generate prior predictions of future states and continually update the internal model (prior distribution) for better prediction and precision (Daikoku et al., 2017) by integrating sensory input with prior distribution. Evidence has also suggested that human pitch prediction of novel melodies is closely linked to statistical models of transitional probability sampled from a large corpus of music (Pearce and Wiggins, 2006, 2012; Pearce et al., 2010). This may imply that human brains acquire a statistically universal model of music through musical statistical learning.

Some researchers have suggested two interdependent processes as hallmarks of statistical learning (Rogers and McClelland, 2004; Altmann, 2017; Daikoku, 2019a,b): the chunking of statistically coherent events and the sequential combination of the chunked units. They indicated that an individual’s experience is abstracted on a statistical basis to generate a chunk that captures the statistical common and shareable denominator across individually experienced information (Sloutsky, 2010). This suggests that statistical learning underlying chunk formation and word acquisition consists of statistical accumulation across multiple episodes. However, an opposing statistical learning process appears to occur simultaneously: chunked units can be integrated to generate novel information through statistical learning (Altmann, 2017). Thus, language/music learning requires a route from the individual experience of statistical abstraction as a shareable knowledge unit (e.g., word), while comprehension and creation (e.g., grammar and sentences) require the integration of several units. Therefore, these two interdependent processes are necessary for a complete account of statistical learning and production that results therefrom (Thiessen et al., 2013; Wiggins and Sanjekdar, 2019; Wiggins, 2020).

Recent studies claim that statistical learning contributes to creative behaviors and learning, such as music composition (Daikoku, 2019b; Zioga et al., 2019); however, the underlying mechanisms remain unclear. In this study, we refer as creativity stemming from statistical learning as statistical creativity and propose two potential keys to statistical creativity. The first is the interplay between the chunking of statistically coherent events into a unit and the integration of several units. This process forms a hierarchical structure in statistical learning (hierarchical statistical learning). The second is the fluctuation of the perceptual uncertainty. The brain appears to seek a suboptimal solution of uncertainty for creativity based on prior predictions, which results in fluctuations in uncertainty. Furthermore, it is assumed that these two key factors interact with each other.

We emphasize that statistical learning plays a key role in musical creativity. In particular, we propose two important roles for statistical learning in musical creativity. The first is a hierarchy of shallow and deep statistical learning. As discussed, small-scale (shallow) statistical learning (Figure 1A) may fundamentally provide general and common knowledge, while large-scale (deep) statistical learning contributes to individual knowledge of music (Daikoku, 2019a,b). In general, deep statistical learning is a mechanism for the integration of chunked units acquired by shallow statistical learning. That is, deep statistical learning of music could occur after persons have robust shallow statistical models of chunks. From the information theoretical perspective, as the order of transitional probability in the Markov chain becomes higher (i.e., the scale is larger), transition patterns can also be subdivided (for more detail, see Figure 3B of Daikoku, 2018c). That is, there are more sequential patterns in the deeper model. This leads to a diversity of patterns and individuality in music and possibly leads to musical creativity. Thus, deep statistical learning (integration of chunked units) may allow for the creation of a novel melody and rhythm even in the absence of any prior knowledge.

The second is a fluctuation in uncertainty. In general, creativity is defined as a process of producing something that is both original and worthwhile (Lubart and Mouchiroud, 2003; Kozbelt et al., 2010; Robert, 2011). Due to its novelty, creative information is often unpredictable and uncertain. It has been suggested that novel and uncertain musical information emerges through hierarchical statistical learning. However, there is still little understanding as to why such uncertain information can be accepted as creative. In other words, highly uncertain information is not necessarily creative. For example, a random tone sequence is highly uncertain, but in general, we do not approve of a random time sequence as creative music. Hence, it is assumed that appreciation of musical creativity may be associated with certain forms of suboptimality between uncertainty and certainty (Figure 3). We hypothesize that such competitive pursuits of uncertainty and certainty may induce fluctuations in uncertainty and that fluctuations in uncertainty may contribute to musical creativity.

Evidence has revealed that musicians are good statistical learners (Francois and Schön, 2011; Paraskevopoulos et al., 2012; Elmer and Lutz, 2018; Daikoku and Yumoto, 2020), allowing the brain to precisely grasp the temporal dynamics of uncertainty in music perception and production (Hansen and Pearce, 2014; Daikoku, 2019b; Zioga et al., 2019). We hypothesize that such proficiency in precision in perceptual uncertainty may also allow musicians to control the uncertainties in music finely by manipulating several musical components such as rhythm, melody, and harmony. Musical tensions can be created by establishing a predictable pattern in rhythm and melody and subsequently denying the prediction from it (Meyer, 2008). We can derive pleasure from deviant and uncertain musical patterns once a predictive pattern is established. Evidence suggests that so-called “music chills” are correlated with violations of expectation (Sloboda, 1991) and underpin musical appreciation (Huron, 2006). A neural study revealed that music chills increase brain activity in reward areas (ventral striatum) and decrease activity in the amygdala and ventromedial prefrontal cortex (Blood and Zatorre, 2001). This suggests that we derive rewards from violations of expectations, as well as from confirmed predictions. It is suggested that such esthetic appreciation can be reflected in the temporal dynamics of uncertainty.

Alternatively, musicians who have trained for a long period may have robust internal statistical models of music (Hansen and Pearce, 2014). Furthermore, a study has suggested that the characteristics of internal models respond to one’s own musical culture, such as Japanese and Western classical music (Daikoku et al., 2020). This may lead to cultural fixation of statistical knowledge and even bolster productivity instead of creativity. Statistical learning has been shown to be ubiquitously performed regardless of the intention (Perruchet and Pacton, 2006; Tsogli et al., 2019). This suggests that statistical knowledge is influenced by surrounding environmental information. Nevertheless, such musicians aptly exhibit pathways of high creativity (Kleinmintz, 2017; Przysinda et al., 2017; Zioga et al., 2019). One possible reason is that the knowledge and behavior that results from statistical learning involve implicit mechanisms with less intention (Perruchet and Pacton, 2006; Paraskevopoulos et al., 2012; Koelsch et al., 2016; Christiansen, 2019) but can transform into explicit knowledge through long-term training and experience (Batterink et al., 2015; Moser et al., 2020). Statistical learning of behavior is also considered as procedural learning that takes place without explicit knowledge (Kóbor et al., 2018). Therefore, we hypothesize that musical creativity resulting from statistical learning is mainly involved in intuitive performance, such as musical improvisation, in which musicians intuitively play new melodies and rhythms (Daikoku, 2018b).

Musical creativity is likely to be correlated with general creativity. A previous study examined how jazz improvisers, non-improvising musicians, and non-musicians perform the domain-general task of divergent thinking as well as the musical task of preference ratings for chord progressions that vary in expectation (Przysinda et al., 2017). The results showed that jazz musicians preferred unexpected (unpredicted) chord progressions. Further, the unexpected stimuli elicited larger music expectancy-related neural responses (early right-anterior negativity: ERAN) and another event-related potential (ERP) of P3b, followed by smaller long-latency responses (late positivity potential) in jazz musicians. This implies that people who can predict precisely a musical event prefer an unpredictable one, possibly because they can correctly discriminate between familiar and novel musical events (i.e., creative). Notably, these neural effects were significantly correlated with fluency and originality in the divergent thinking task. This suggests that the precision of (prior) prediction is crucial for general and musical creativity.

Frontal lobe functions are considered to be one of the most important keys to understanding creativity in the brain (Flaherty, 2005) and is generally involved in the top-down control of executive functions and decision-making (Gold and Shadlen, 2007; Dosenbach et al., 2008; Heekeren et al., 2008; Dalley et al., 2011). Recent studies have suggested that the prefrontal lobe (e.g., the inferior frontal gyrus, IFG) and dorsal connectivity between the prefrontal and sensory areas are associated with the formation of internal Bayesian models and prior predictions (Friston et al., 2016; Cope et al., 2017; Park et al., 2018). According to their studies, Bayesian models (i.e., prior prediction) could be generated in IFG and/or frontal motor speech regions and conveyed to auditory sensory regions through synaptic connections to instantiate plausible representations.

This hypothesis may also be explained by the developmental processes. A recent study indicated that this prefrontal-auditory connectivity is better developed in human adults than in newborns and macaques (Friederici et al., 2017). They also showed that in newborns, only the dorsal stream terminates in the premotor cortex (PMC). This partially supports the computational hypothesis that infants may have a prior prediction. That is, the development of the brain allows us to switch from a strong reliance on sensory input and weak reliance on prior predictions (hypo-prior) at an early learning stage to proper integration of sensory information with prior prediction (internal model) at later learning stages, becoming robust against disturbances in the uncertain phenomena (Philippsen and Nagai, 2019). Infants may have hypo-prior prediction due to the prematurity of dorsal prefrontal-sensory connectivity, which is essential for generating prior prediction and integrating prior prediction with sensory input. Together, many pieces of evidence suggest that prefrontal function may contribute to strong dependence on top-down prior prediction in perceiving and producing information. Such predictions can be generated by the acquired knowledge and experience. Hence, the strong dependence on prior prediction is partially interpreted as a strong reliance on certain acquired knowledge. Neural evidence has shown that both large- (deep) and small-scale (shallow) statistical learning involve top-down prior prediction (Daikoku et al., 2017). The magnetoencephalographic (MEG) study suggested that both mechanisms combine statistically chunks into a unit (small-scale statistical learning) and several units (large-scale statistical learning) that are reflected in mismatch responses.

However, prior predictions may sometimes inhibit creativity. Creativity is a phenomenon whereby something new and uncertain is formed, even if creativity is intricately linked to acquired knowledge. Therefore, the inhibition of prefrontal function may partially induce creative and uncertain information production (Chrysikou, 2018), possibly because of less dependence on prior prediction and certain knowledge. The neural evidence seems to agree with this hypothesis. Electroencephalography (EEG) (Fink et al., 2006, 2009; Lustenberger et al., 2015) and functional magnetic resonance imaging (fMRI) studies (Bengtsson et al., 2007; Berkowitz and Ansari, 2008; Limb and Braun, 2008; de Manzano and Ullén, 2012a,b) have examined brain activity during exposure to fixed melodies (less creative) or free-improvised melodies (more creative). The results indicate that more creative conditions lead to stronger alpha power (Fink et al., 2006; Lustenberger et al., 2015; Lopata et al., 2017) in the right frontal and parietal regions (Fink et al., 2009). The increased oscillatory activity in the alpha band is considered to reflect inhibition of the top-down process (Klimesch, 2012). However, other studies have suggested that alpha power reflects internally oriented attention, in which external bottom-up stimulation is also suppressed (Fink and Benedek, 2014). One study that investigated both the neural and genetic correlates of creativity suggested that a system of interaction between strong top-down and weak bottom-up processes underpins creativity, which is modulated by competition between the glutamate and GABA neurotransmitter systems (Liu et al., 2018). Furthermore, a computational model (Collins and Koechlin, 2012) inspired the hypothesis that the frontal lobes create an expanding repertoire of flexible behavioral strategies for driving action in uncertain, changing, and open-ended environments and suggested that frontal lobe function, including executive control and decision-making, somewhat supports the integration of reasoning, learning, and creativity through uncertainty monitoring. Green et al. (2017) also suggested that neural activity in the frontopolar cortex facilitates creative intelligence.

The contradiction between these two opposing findings on inhibition and enhancement of top-down control may be explained by the different tasks set in the different studies (Adhikari et al., 2016). In fMRI studies (Pinho et al., 2015), improvisation using a defined pitch set resulted in activation of the dorsolateral prefrontal cortex (dlPFC) because participants had to maintain available note choices in their working memory. In contrast, free improvisation leads to deactivation of the dlPFC because participants are able to take advantage of their implicit learning systems to create improvisations in which top-down control from the dlPFC would be disadvantageous (Dhakal et al., 2019). Using fMRI, Liu et al. (2015) examined brain mechanisms during poetry composition and the assessment (revision) process. The results indicated that dlPFC activity was attenuated during composition and reengaged during revision, whereas the medial prefrontal cortex (MPFC), which is associated with multiple cognitive functions such as motivation (Kouneiher et al., 2009) and unconscious decision-making (Soon et al., 2008), was active during both phases. Furthermore, expert poets showed significantly stronger deactivation of the dlPFC during composition, but there was no significant difference in the activity of the MPFC. Thus, expert poets may more effectively suspend top-down control while maintaining their motivation. Together, these findings show that open-ended creative and uncertain behaviors may suppress top-down controls, as expressed through the dlPFC activity level, while maintaining motivation, as expressed through MPFC activity level, whereas fixed behaviors enhance top-down control.

Evidence suggests that the temporal dynamics of creativity processes are reflected in three types of neuronal networks (Beaty et al., 2018). First, the default mode network (DMN), which consists of the cortical midline and posterior inferior parietal regions, underpins spontaneous idea generation, episodic future thinking, and mind-wandering, among others (Mason et al., 2007; Zabelina and Andrews-Hanna, 2016). Second, the executive control network (ECN), which involves the lateral prefrontal and anterior inferior parietal regions, contributes to idea evaluation and executive function (Beaty et al., 2016). Third, the salience network (SN), which consists of the bilateral insula and anterior cingulate cortex, plays a role in conveying candidate ideas originating from the DMN to the ECN for idea evaluation (Beaty et al., 2016, 2018).

A previous study demonstrated that creative people show higher global efficiency within these networks, that is, a smaller number of paths traverse between brain regions (Beaty et al., 2015). In other words, the efficiency of the interplay between idea generation and evaluation is higher in creative people (Kleinmintz et al., 2019). Importantly, the perceptions of novelty (and surprise) are involved in both idea generation and evaluation processes, but not either of them; when generating a new idea, they need to recognize that it is a novel idea, not to mention when evaluating. This previous finding may explain the contradiction between inhibition and enhancement of frontal activity during creative behavior, as discussed in section A Role of Frontal Cortex in Prior Prediction and Creativity.” Creative people have the ability to simultaneously engage these large-scale brain networks, including the DMN, ECN, and SN (Boccia et al., 2015; Beaty et al., 2018). It is assumed that creativity is not just free and uncontrolled activities but rather elaborate collaboration between uncontrolled/uncertain mind activity (i.e., DMN), which is less dependent on frontal function, and the top-down executive control of free thinking, including frontal function (i.e., ECN).

Together, the prefrontal function and three types of neural networks may have an important role in statistical creativity, particularly in terms of perceptual uncertainty. We hypothesize that the inhibition of prefrontal function may induce creative and uncertain information production, possibly because of the weakened dependence of prior knowledge. Besides, it is assumed that sophisticated creativity is not just free-thinking activities uncontrolled by prior knowledge but rather an elaborate collaboration between uncontrolled/uncertain mind activity (i.e., DMN), which is less dependent on frontal function, and top-down executive control of free thinking, including frontal function (i.e., ECN).