Neurophysiological Markers of Statistical Learning in Music and Language: Hierarchy, Entropy, and Uncertainty

Perceptual Expectations Are Reflected by Early Alpha Power Reduction

The predictability of a stimulus can be characterized by its transitional probability. Perceptual expectations derived from the transitional probability of the stimulus were found to modulate the early alpha oscillations in the sensory regions of the brain when neural responses to expected versus unexpected stimuli were compared. The objective of our study was to find out the extent to which this low-frequency oscillation reflects stimulus predictability. We aimed to detect the alpha-power difference with smaller differences in transitional probabilities by comparing expected stimuli with neutral ones. We studied the effect of expectation on perception by applying an unsupervised visual statistical learning paradigm with expected and neutral stimuli embedded in an image sequence while recording EEG. Time-frequency analysis showed that expected stimuli elicit lower alpha power in the window of 8-12 Hz and 0-400 msec after stimulus presentation, appearing in the centroparietal region. Comparing previous findings of expectancy-based alpha-band modulation with our results suggests that early alpha oscillation shows an inverse relationship with stimulus predictability. Although current data are insufficient to determine the origin of the alpha power reduction, this could be a potential sign of expectation suppression in cortical oscillatory activity.

Seeking the neural representation of statistical properties in print during implicit processing of visual words

Statistical learning (SL) plays a key role in literacy acquisition. Studies have increasingly revealed the influence of distributional statistical properties of words on visual word processing, including the effects of word frequency (lexical level) and mappings between orthography, phonology, and semantics (sub-lexical level). However, there has been scant evidence to directly confirm that the statistical properties contained in print can be directly characterized by neural activities. Using time-resolved representational similarity analysis (RSA), the present study examined neural representations of different types of statistical properties in visual word processing. From the perspective of predictive coding, an equal probability sequence with low built-in prediction precision and three oddball sequences with high built-in prediction precision were designed with consistent and three types of inconsistent (orthographically inconsistent, orthography-to-phonology inconsistent, and orthography-to-semantics inconsistent) Chinese characters as visual stimuli. In the three oddball sequences, consistent characters were set as the standard stimuli (probability of occurrence p = 0.75) and three types of inconsistent characters were set as deviant stimuli (p = 0.25), respectively. In the equal probability sequence, the same consistent and inconsistent characters were presented randomly with identical occurrence probability (p = 0.25). Significant neural representation activities of word frequency were observed in the equal probability sequence. By contrast, neural representations of sub-lexical statistics only emerged in oddball sequences where short-term predictions were shaped. These findings reveal that the statistical properties learned from long-term print environment continues to play a role in current word processing mechanisms and these mechanisms can be modulated by short-term predictions.

Temporal dynamics of statistical learning in children's song contributes to phase entrainment and production of novel information in multiple cultures

Statistical learning is thought to be linked to brain development. For example, statistical learning of language and music starts at an early age and is shown to play a significant role in acquiring the delta-band rhythm that is essential for language and music learning. However, it remains unclear how auditory cultural differences affect the statistical learning process and the resulting probabilistic and acoustic knowledge acquired through it. This study examined how children's songs are acquired through statistical learning. This study used a Hierarchical Bayesian statistical learning (HBSL) model, mimicking the statistical learning processes of the brain. Using this model, I conducted a simulation experiment to visualize the temporal dynamics of perception and production processes through statistical learning among different cultures. The model learned from a corpus of children's songs in MIDI format, which consists of English, German, Spanish, Japanese, and Korean songs as the training data. In this study, I investigated how the probability distribution of the model is transformed over 15 trials of learning in each song. Furthermore, using the probability distribution of each model over 15 trials of learning each song, new songs were probabilistically generated. The results suggested that, in learning processes, chunking and hierarchical knowledge increased gradually through 15 rounds of statistical learning for each piece of children's songs. In production processes, statistical learning led to the gradual increase of delta-band rhythm (1-3 Hz). Furthermore, by combining the acquired chunks and hierarchy through statistical learning, statistically novel music was generated gradually in comparison to the original songs (i.e. the training songs). These findings were observed consistently, in multiple cultures. The present study indicated that the statistical learning capacity of the brain, in multiple cultures, contributes to the acquisition and generation of delta-band rhythm, which is critical for acquiring language and music. It is suggested that cultural differences may not significantly modulate the statistical learning effects since statistical learning and slower rhythm processing are both essential functions in the human brain across cultures. Furthermore, statistical learning of children's songs leads to the acquisition of hierarchical knowledge and the ability to generate novel music. This study may provide a novel perspective on the developmental origins of creativity and the importance of statistical learning through early development.

Prerequisites of language acquisition in the newborn brain

Learning to decode and produce speech is one of the most demanding tasks faced by infants. Nevertheless, infants typically utter their first words within a year, and phrases soon follow. Here we review cognitive abilities of newborn infants that promote language acquisition, focusing primarily on studies tapping neural activity. The results of these studies indicate that infants possess core adult auditory abilities already at birth, including statistical learning and rule extraction from variable speech input. Thus, the neonatal brain is ready to categorize sounds, detect word boundaries, learn words, and separate speech streams: in short, to acquire language quickly and efficiently from everyday linguistic input.

Flexible structure learning under uncertainty

Experience is known to facilitate our ability to interpret sequences of events and make predictions about the future by extracting temporal regularities in our environments. Here, we ask whether uncertainty in dynamic environments affects our ability to learn predictive structures. We exposed participants to sequences of symbols determined by first-order Markov models and asked them to indicate which symbol they expected to follow each sequence. We introduced uncertainty in this prediction task by manipulating the: (a) probability of symbol co-occurrence, (b) stimulus presentation rate. Further, we manipulated feedback, as it is known to play a key role in resolving uncertainty. Our results demonstrate that increasing the similarity in the probabilities of symbol co-occurrence impaired performance on the prediction task. In contrast, increasing uncertainty in stimulus presentation rate by introducing temporal jitter resulted in participants adopting a strategy closer to probability maximization than matching and improving in the prediction tasks. Next, we show that feedback plays a key role in learning predictive statistics. Trial-by-trial feedback yielded stronger improvement than block feedback or no feedback; that is, participants adopted a strategy closer to probability maximization and showed stronger improvement when trained with trial-by-trial feedback. Further, correlating individual strategy with learning performance showed better performance in structure learning for observers who adopted a strategy closer to maximization. Our results indicate that executive cognitive functions (i.e., selective attention) may account for this individual variability in strategy and structure learning ability. Taken together, our results provide evidence for flexible structure learning; individuals adapt their decision strategy closer to probability maximization, reducing uncertainty in temporal sequences and improving their ability to learn predictive statistics in variable environments.

Neural correlates of statistical learning in developmental dyslexia: An electroencephalography study

The human brain extracts statistical regularities from the surrounding environment in a process called statistical learning. Behavioural evidence suggests that developmental dyslexia affects statistical learning. However, surprisingly few studies have assessed how developmental dyslexia affects the neural processing underlying this type of learning. We used electroencephalography to explore the neural correlates of an important aspect of statistical learning - sensitivity to transitional probabilities - in individuals with developmental dyslexia. Adults diagnosed with developmental dyslexia (n = 17) and controls (n = 19) were exposed to a continuous stream of sound triplets. Every so often, a triplet ending had a low transitional probability given the triplet's first two sounds ("statistical deviants"). Furthermore, every so often a triplet ending was presented from a deviant location ("acoustic deviants"). We examined mismatch negativity elicited by statistical deviants (sMMN), and MMN elicited by location deviants (i.e., acoustic changes). Acoustic deviants elicited a MMN which was larger in the control group than in the developmental dyslexia group. Statistical deviants elicited a small, yet significant, sMMN in the control group, but not in the developmental dyslexia group. However, the difference between the groups was not significant. Our findings indicate that the neural mechanisms underlying pre-attentive acoustic change detection and implicit statistical auditory learning are both affected in developmental dyslexia.

Order of statistical learning depends on perceptive uncertainty

Statistical learning (SL) is an innate mechanism by which the brain automatically encodes the n-th order transition probability (TP) of a sequence and grasps the uncertainty of the TP distribution. Through SL, the brain predicts a subsequent event (e _n+1 ) based on the preceding events (e _n ) that have a length of "n". It is now known that uncertainty modulates prediction in top-down processing by the human predictive brain. However, the manner in which the human brain modulates the order of SL strategies based on the degree of uncertainty remains an open question. The present study examined how uncertainty modulates the neural effects of SL and whether differences in uncertainty alter the order of SL strategies. It used auditory sequences in which the uncertainty of sequential information is manipulated based on the conditional entropy. Three sequences with different TP ratios of 90:10, 80:20, and 67:33 were prepared as low-, intermediate, and high-uncertainty sequences, respectively (conditional entropy: 0.47, 0.72, and 0.92 bit, respectively). Neural responses were recorded when the participants listened to the three sequences. The results showed that stimuli with lower TPs elicited a stronger neural response than those with higher TPs, as demonstrated by a number of previous studies. Furthermore, we found that participants adopted higher-order SL strategies in the high uncertainty sequence. These results may indicate that the human brain has an ability to flexibly alter the order based on the uncertainty. This uncertainty may be an important factor that determines the order of SL strategies. Particularly, considering that a higher-order SL strategy mathematically allows the reduction of uncertainty in information, we assumed that the brain may take higher-order SL strategies when encountering high uncertain information in order to reduce the uncertainty. The present study may shed new light on understanding individual differences in SL performance across different uncertain situations.

Modality, presentation, domain and training effects in statistical learning

While several studies suggest that the nature and properties of the input have significant effects on statistical learning, they have rarely been investigated systematically. In order to understand how input characteristics and their interactions impact statistical learning, we explored the effects of modality (auditory vs. visual), presentation type (serial vs. simultaneous), domain (linguistic vs. non-linguistic), and training type (random, starting small, starting big) on artificial grammar learning in young adults (N = 360). With serial presentation of stimuli, learning was more effective in the auditory than in the visual modality. However, with simultaneous presentation of visual and serial presentation of auditory stimuli, the modality effect was not present. We found a significant domain effect as well: a linguistic advantage over nonlinguistic material, which was driven by the domain effect in the auditory modality. Overall, the auditory linguistic condition had an advantage over other modality-domain types. Training types did not have any overall effect on learning; starting big enhanced performance only in the case of serial visual presentation. These results show that input characteristics such as modality, presentation type, domain and training type influence statistical learning, and suggest that their effects are also dependent on the specific stimuli and structure to be learned.

Cancer Segmentation by Entropic Analysis of Ordered Gene Expression Profiles

The availability of massive gene expression data has been challenging in terms of how to cure, process, and extract useful information. Here, we describe the use of entropic measures as discriminating criteria in cancer using the whole data set of gene expression levels. These methods were applied in classifying samples between tumor and normal type for 13 types of tumors with a high success ratio. Using gene expression, ordered by pathways, results in complexity-entropy diagrams. The map allows the clustering of the tumor and normal types samples, with a high success rate for nine of the thirteen, studied cancer types. Further analysis using information distance also shows good discriminating behavior, but, more importantly, allows for discriminating between cancer types. Together, our results allow the classification of tissues without the need to identify relevant genes or impose a particular cancer model. The used procedure can be extended to classification problems beyond the reported results.

Brain-correlates of processing local dependencies within a statistical learning paradigm

Statistical learning refers to the implicit mechanism of extracting regularities in our environment. Numerous studies have investigated the neural basis of statistical learning. However, how the brain responds to violations of auditory regularities based on prior (implicit) learning requires further investigation. Here, we used functional magnetic resonance imaging (fMRI) to investigate the neural correlates of processing events that are irregular based on learned local dependencies. A stream of consecutive sound triplets was presented. Unbeknown to the subjects, triplets were either (a) standard, namely triplets ending with a high probability sound or, (b) statistical deviants, namely triplets ending with a low probability sound. Participants (n = 33) underwent a learning phase outside the scanner followed by an fMRI session. Processing of statistical deviants activated a set of regions encompassing the superior temporal gyrus bilaterally, the right deep frontal operculum including lateral orbitofrontal cortex, and the right premotor cortex. Our results demonstrate that the violation of local dependencies within a statistical learning paradigm does not only engage sensory processes, but is instead reminiscent of the activation pattern during the processing of local syntactic structures in music and language, reflecting the online adaptations required for predictive coding in the context of statistical learning.

Relevance to the higher order structure may govern auditory statistical learning in neonates

Hearing is one of the earliest senses to develop and is quite mature by birth. Contemporary theories assume that regularities in sound are exploited by the brain to create internal models of the environment. Through statistical learning, internal models extrapolate from patterns to predictions about subsequent experience. In adults, altered brain responses to sound enable us to infer the existence and properties of these models. In this study, brain potentials were used to determine whether newborns exhibit context-dependent modulations of a brain response that can be used to infer the existence and properties of internal models. Results are indicative of significant context-dependence in the responsivity to sound in newborns. When common and rare sounds continue in stable probabilities over a very long period, neonates respond to all sounds equivalently (no differentiation). However, when the same common and rare sounds at the same probabilities alternate over time, the neonate responses show clear differentiations. The context-dependence is consistent with the possibility that the neonate brain produces more precise internal models that discriminate between contexts when there is an emergent structure to be discovered but appears to adopt broader models when discrimination delivers little or no additional information about the environment.

Unpredictability of the “when” influences prediction error processing of the “what” and “where”

The capability to establish accurate predictions is an integral part of learning. Whether predictions about different dimensions of a stimulus interact with each other, and whether such an interaction affects learning, has remained elusive. We conducted a statistical learning study with EEG (electroencephalography), where a stream of consecutive sound triplets was presented with deviants that were either: (a) statistical, depending on the triplet ending probability, (b) physical, due to a change in sound location or (c) double deviants, i.e. a combination of the two. We manipulated the predictability of stimulus-onset by using random stimulus-onset asynchronies. Temporal unpredictability due to random onsets reduced the neurophysiological responses to statistical and location deviants, as indexed by the statistical mismatch negativity (sMMN) and the location MMN. Our results demonstrate that the predictability of one stimulus attribute influences the processing of prediction error signals of other stimulus attributes, and thus also learning of those attributes.

Does auditory deprivation impairs statistical learning in the auditory modality?

Early sensory deprivation allows assessing the extent of reorganisation of cognitive functions, well beyond sensory processing. As such, it is a good model to explore the links between sensory experience and cognitive functions. One of these functions, statistical learning - the ability to extract and use regularities present in the environment - is suspected to be impaired in prelingually deaf children with a cochlear implant. However, empirical evidence supporting this claim is very scarce and studies have reported contradictory results. This might be because previous studies have tested statistical learning only in the visual modality and did not make clear distinctions between multiple types of statistical regularities. To overcome these problems, we designed a modified serial reaction time task where cochlear implanted children and normal hearing children had to react to auditory sequences that embed multiple statistical regularities, namely transition probabilities of 0^th, 1^st or 2^nd order. We compared the reaction times of the children with the output of a simple computational model that learns transition probabilities. First, 6-12 years old children were able to learn 0^th and 1^st order transition probabilities but not 2^nd order ones. Second, there were no differences between cochlear implanted children and their normal hearing peers. These results indicate that auditory statistical learning is preserved in congenitally deaf children with cochlear implants. This suggests in turn that early auditory deprivation might not be crucially detrimental for the normal development of statistical learning.

Perceptual uncertainty modulates auditory statistical learning: A magnetoencephalography study

Statistical learning allows comprehension of structured information, such as that in language and music. The brain computes a sequence's transition probability and predicts future states to minimise sensory reaction and derive entropy (uncertainty) from sequential information. Neurophysiological studies have revealed that early event-related neural responses (P1 and N1) reflect statistical learning - when the brain encodes transition probability in stimulus sequences, it predicts an upcoming stimulus with a high transition probability and suppresses the early event-related responses to a stimulus with a high transition probability. This amplitude difference between high and low transition probabilities reflects statistical learning effects. However, how a sequence's transition probability ratio affects neural responses contributing to statistical learning effects remains unknown. This study investigated how transition-probability ratios or conditional entropy (uncertainty) in auditory sequences modulate the early event-related neuromagnetic responses of P1m and N1m. Sequence uncertainties were manipulated using three different transition-probability ratios: 90:10%, 80:20%, and 67:33% (conditional entropy: 0.47, 0.72, and 0.92 bits, respectively). Neuromagnetic responses were recorded when participants listened to sequential sounds with these three transition probabilities. Amplitude differences between lower and higher probabilities were larger in sequences with transition-probability ratios of 90:10% and smaller in sequences with those of 67:33%, compared to sequences with those of 80:20%. This suggests that the transition-probability ratio finely tunes P1m and N1m. Our study also showed larger amplitude differences between frequent- and rare-transition stimuli in P1m than in N1m. This indicates that information about transition-probability differences may be calculated in earlier cognitive processes.

Neurophysiological and functional neuroanatomical coding of statistical and deterministic rule information during sequence learning

Humans are capable of acquiring multiple types of information presented in the same information stream. It has been suggested that at least two parallel learning processes are important during learning of sequential patterns-statistical learning and rule-based learning. Yet, the neurophysiological underpinnings of these parallel learning processes are not fully understood. To differentiate between the simultaneous mechanisms at the single trial level, we apply a temporal EEG signal decomposition approach together with sLORETA source localization method to delineate whether distinct statistical and rule-based learning codes can be distinguished in EEG data and can be related to distinct functional neuroanatomical structures. We demonstrate that concomitant but distinct aspects of information coded in the N2 time window play a role in these mechanisms: mismatch detection and response control underlie statistical learning and rule-based learning, respectively, albeit with different levels of time-sensitivity. Moreover, the effects of the two learning mechanisms in the different temporally decomposed clusters of neural activity also differed from each other in neural sources. Importantly, the right inferior frontal cortex (BA44) was specifically implicated in visuomotor statistical learning, confirming its role in the acquisition of transitional probabilities. In contrast, visuomotor rule-based learning was associated with the prefrontal gyrus (BA6). The results show how simultaneous learning mechanisms operate at the neurophysiological level and are orchestrated by distinct prefrontal cortical areas. The current findings deepen our understanding on the mechanisms of how humans are capable of learning multiple types of information from the same stimulus stream in a parallel fashion.

Musical Expertise Is Associated with Improved Neural Statistical Learning in the Auditory Domain

 

It is poorly known whether musical training is associated with improvements in general cognitive abilities, such as statistical learning (SL). In standard SL paradigms, musicians have shown better performances than nonmusicians. However, this advantage could be due to differences in auditory discrimination, in memory or truly in the ability to learn sequence statistics. Unfortunately, these different hypotheses make similar predictions in terms of expected results. To dissociate them, we developed a Bayesian model and recorded electroencephalography (EEG). Our results confirm that musicians perform approximately 15% better than nonmusicians at predicting items in auditory sequences that embed either low or high-order statistics. These higher performances are explained in the model by parameters governing the learning of high-order statistics and the selection stage noise. EEG recordings reveal a neural underpinning of the musician's advantage: the P300 amplitude correlates with the surprise elicited by each item, and so, more strongly for musicians. Finally, early EEG components correlate with the surprise elicited by low-order statistics, as opposed to late EEG components that correlate with the surprise elicited by high-order statistics and this effect is stronger for musicians. Overall, our results demonstrate that musical expertise is associated with improved neural SL in the auditory domain.

SIGNIFICANCE STATEMENT

It is poorly known whether musical training leads to improvements in general cognitive skills. One fundamental cognitive ability, SL, is thought to be enhanced in musicians, but previous studies have reported mixed results. This is because such musician's advantage can embrace very different explanations, such as improvement in auditory discrimination or in memory. To solve this problem, we developed a Bayesian model and recorded EEG to dissociate these explanations. Our results reveal that musical expertise is truly associated with an improved ability to learn sequence statistics, especially high-order statistics. This advantage is reflected in the electroencephalographic recordings, where the P300 amplitude is more sensitive to surprising items in musicians than in nonmusicians.

Statistical Properties of Musical Creativity: Roles of Hierarchy and Uncertainty in Statistical Learning

Creativity is part of human nature and is commonly understood as a phenomenon whereby something original and worthwhile is formed. Owing to this ability, humans can produce innovative information that often facilitates growth in our society. Creativity also contributes to esthetic and artistic productions, such as music and art. However, the mechanism by which creativity emerges in the brain remains debatable. Recently, a growing body of evidence has suggested that statistical learning contributes to creativity. Statistical learning is an innate and implicit function of the human brain and is considered essential for brain development. Through statistical learning, humans can produce and comprehend structured information, such as music. It is thought that creativity is linked to acquired knowledge, but so-called "eureka" moments often occur unexpectedly under subconscious conditions, without the intention to use the acquired knowledge. Given that a creative moment is intrinsically implicit, we postulate that some types of creativity can be linked to implicit statistical knowledge in the brain. This article reviews neural and computational studies on how creativity emerges within the framework of statistical learning in the brain (i.e., statistical creativity). Here, we propose a hierarchical model of statistical learning: statistically chunking into a unit (hereafter and shallow statistical learning) and combining several units (hereafter and deep statistical learning). We suggest that deep statistical learning contributes dominantly to statistical creativity in music. Furthermore, the temporal dynamics of perceptual uncertainty can be another potential causal factor in statistical creativity. Considering that statistical learning is fundamental to brain development, we also discuss how typical versus atypical brain development modulates hierarchical statistical learning and statistical creativity. We believe that this review will shed light on the key roles of statistical learning in musical creativity and facilitate further investigation of how creativity emerges in the brain.

Beta-Band Activity Is a Signature of Statistical Learning

Through statistical learning (SL), cognitive systems may discover the underlying regularities in the environment. Testing human adults (n = 35, 21 females), we document, in the context of a classical visual SL task, divergent rhythmic EEG activity in the interstimulus delay periods within patterns versus between patterns (i.e., pattern transitions). Our findings reveal increased oscillatory activity in the beta band (∼20 Hz) at triplet transitions that indexes learning: it emerges with increased pattern repetitions; and importantly, it is highly correlated with behavioral learning outcomes. These findings hold the promise of converging on an online measure of learning regularities and provide important theoretical insights regarding the mechanisms of SL and prediction.SIGNIFICANCE STATEMENT Statistical learning has become a major theoretical construct in cognitive science, providing the primary means by which organisms learn about regularities in the environment. As such, it is a critical building block for basic and higher-order cognitive functions. Here we identify, for the first time, a spectral neural index in the time window before stimulus presentation, which evolves with increased pattern exposure, and is predictive of learning performance. The manifestation of learning that is revealed, not in stimulus processing but in the blank interval between stimuli, makes a direct link between the fields of statistical learning on the one hand and either prediction or consolidation on the other hand, suggesting a possible mechanistic account of visual statistical learning.

Statistical Properties in Jazz Improvisation Underline Individuality of Musical Representation

Statistical learning is an innate function in the brain and considered to be essential for producing and comprehending structured information such as music. Within the framework of statistical learning the brain has an ability to calculate the transitional probabilities of sequences such as speech and music, and to predict a future state using learned statistics. This paper computationally examines whether and how statistical learning and knowledge partially contributes to musical representation in jazz improvisation. The results represent the time-course variations in a musician’s statistical knowledge. Furthermore, the findings show that improvisational musical representation might be susceptible to higher- but not lower-order statistical knowledge (i.e., knowledge of higher-order transitional probability). The evidence also demonstrates the individuality of improvisation for each improviser, which in part depends on statistical knowledge. Thus, this study suggests that statistical properties in jazz improvisation underline individuality of musical representation.

Advances in the Neurocognition of Music and Language

Neurocomparative music and language research has seen major advances over the past two decades. The goal of this Special Issue “Advances in the Neurocognition of Music and Language” was to showcase the multiple neural analogies between musical and linguistic information processing, their entwined organization in human perception and cognition and to infer the applicability of the combined knowledge in pedagogy and therapy. Here, we summarize the main insights provided by the contributions and integrate them into current frameworks of rhythm processing, neuronal entrainment, predictive coding and cognitive control.

Statistical learning and the uncertainty of melody and bass line in music

Statistical learning is the ability to learn based on transitional probability (TP) in sequential information, which has been considered to contribute to creativity in music. The interdisciplinary theory of statistical learning examines statistical learning as a mechanism of human learning. This study investigated how TP distribution and conditional entropy in TP of the melody and bass line in music interact with each other, using the highest and lowest pitches in Beethoven’s piano sonatas and Johann Sebastian Bach’s Well-Tempered Clavier. Results for the two composers were similar. First, the results detected specific statistical characteristics that are unique to each melody and bass line as well as general statistical characteristics that are shared between the melody and bass line. Additionally, a correlation of the conditional entropies sampled from the TP distribution could be detected between the melody and bass line. This suggests that the variability of entropies interacts between the melody and bass line. In summary, this study suggested that TP distributions and the entropies of the melody and bass line interact with but are partly independent of each other.

Tonality Tunes the Statistical Characteristics in Music: Computational Approaches on Statistical Learning

Statistical learning is a learning mechanism based on transition probability in sequences such as music and language. Recent computational and neurophysiological studies suggest that the statistical learning contributes to production, action, and musical creativity as well as prediction and perception. The present study investigated how statistical structure interacts with tonalities in music based on various-order statistical models. To verify this in all 24 major and minor keys, the transition probabilities of the sequences containing the highest pitches in Bach's Well-Tempered Clavier, which is a collection of two series (No. 1 and No. 2) of preludes and fugues in all of the 24 major and minor keys, were calculated based on nth-order Markov models. The transition probabilities of each sequence were compared among tonalities (major and minor), two series (No. 1 and No. 2), and music types (prelude and fugue). The differences in statistical characteristics between major and minor keys were detected in lower- but not higher-order models. The results also showed that statistical knowledge in music might be modulated by tonalities and composition periods. Furthermore, the principal component analysis detected the shared components of related keys, suggesting that the tonalities modulate statistical characteristics in music. The present study may suggest that there are at least two types of statistical knowledge in music that are interdependent on and independent of tonality, respectively.

Concurrent Statistical Learning of Ignored and Attended Sound Sequences: An MEG Study

In an auditory environment, humans are frequently exposed to overlapping sound sequences such as those made by human voices and musical instruments, and we can acquire information embedded in these sequences via attentional and nonattentional accesses. Whether the knowledge acquired by attentional accesses interacts with that acquired by nonattentional accesses is unknown, however. The present study examined how the statistical learning (SL) of two overlapping sound sequences is reflected in neurophysiological and behavioral responses, and how the learning effects are modulated by attention to each sequence. SL in this experimental paradigm was reflected in a neuromagnetic response predominantly in the right hemisphere, and the learning effects were not retained when attention to the tone streams was switched during the learning session. These results suggest that attentional and nonattentional learning scarcely interact with each other and that there may be a specific system for nonattentional learning, which is independent of attentional learning.

Depth and the Uncertainty of Statistical Knowledge on Musical Creativity Fluctuate Over a Composer's Lifetime

Brain models music as a hierarchy of dynamical systems that encode probability distributions and complexity (i.e., entropy and uncertainty). Through musical experience over lifetime, a human is intrinsically motivated in optimizing the internalized probabilistic model for efficient information processing and the uncertainty resolution, which has been regarded as rewords. Human's behavior, however, appears to be not necessarily directing to efficiency but sometimes act inefficiently in order to explore a maximum rewards of uncertainty resolution. Previous studies suggest that the drive for novelty seeking behavior (high uncertain phenomenon) reflects human's curiosity, and that the curiosity rewards encourage humans to create and learn new regularities. That is to say, although brain generally minimizes uncertainty of music structure, we sometimes derive pleasure from music with uncertain structure due to curiosity for novelty seeking behavior by which we anticipate the resolution of uncertainty. Few studies, however, investigated how curiosity for uncertain and novelty seeking behavior modulates musical creativity. The present study investigated how the probabilistic model and the uncertainty in music fluctuate over a composer's lifetime (all of the 32 piano sonatas by Ludwig van Beethoven). In the late periods of the composer's lifetime, the transitional probabilities (TPs) of sequential patterns that ubiquitously appear in all of his music (familiar phrase) were decreased, whereas the uncertainties of the whole structure were increased. Furthermore, these findings were prominent in higher-, rather than lower-, order models of TP distribution. This may suggest that the higher-order probabilistic model is susceptible to experience and psychological phenomena over the composer's lifetime. The present study first suggested the fluctuation of uncertainty of musical structure over a composer's lifetime. It is suggested that human's curiosity for uncertain and novelty seeking behavior may modulate optimization and creativity in human's brain.

When the statistical MMN meets the physical MMN

How do listeners respond to prediction errors within patterned sequence of sounds? To answer this question we carried out a statistical learning study using electroencephalography (EEG). In a continuous auditory stream of sound triplets the deviations were either (a) statistical, in terms of transitional probability, (b) physical, due to a change in sound location (left or right speaker) or (c) a double deviants, i.e. a combination of the two. Statistical and physical deviants elicited a statistical mismatch negativity and a physical MMN respectively. Most importantly, we found that effects of statistical and physical deviants interacted (the statistical MMN was smaller when co-occurring with a physical deviant). Results show, for the first time, that processing of prediction errors due to statistical learning is affected by prediction errors due to physical deviance. Our findings thus show that the statistical MMN interacts with the physical MMN, implying that prediction error processing due to physical sound attributes suppresses processing of learned statistical properties of sounds.

Entropy, Uncertainty, and the Depth of Implicit Knowledge on Musical Creativity: Computational Study of Improvisation in Melody and Rhythm

Recent neurophysiological and computational studies have proposed the hypothesis that our brain automatically codes the nth-order transitional probabilities (TPs) embedded in sequential phenomena such as music and language (i.e., local statistics in nth-order level), grasps the entropy of the TP distribution (i.e., global statistics), and predicts the future state based on the internalized nth-order statistical model. This mechanism is called statistical learning (SL). SL is also believed to contribute to the creativity involved in musical improvisation. The present study examines the interactions among local statistics, global statistics, and different levels of orders (mutual information) in musical improvisation interact. Interactions among local statistics, global statistics, and hierarchy were detected in higher-order SL models of pitches, but not lower-order SL models of pitches or SL models of rhythms. These results suggest that the information-theoretical phenomena of local and global statistics in each order may be reflected in improvisational music. The present study proposes novel methodology to evaluate musical creativity associated with SL based on information theory.

Musical Creativity and Depth of Implicit Knowledge: Spectral and Temporal Individualities in Improvisation

It has been suggested that musical creativity is mainly formed by implicit knowledge. However, the types of spectro-temporal features and depth of the implicit knowledge forming individualities of improvisation are unknown. This study, using various-order Markov models on implicit statistical learning, investigated spectro-temporal statistics among musicians. The results suggested that lower-order models on implicit knowledge represented general characteristics shared among musicians, whereas higher-order models detected specific characteristics unique to each musician. Second, individuality may essentially be formed by pitch but not rhythm, whereas the rhythms may allow the individuality of pitches to strengthen. Third, time-course variation of musical creativity formed by implicit knowledge and uncertainty (i.e., entropy) may occur in a musician's lifetime. Individuality of improvisational creativity may be formed by deeper but not superficial implicit knowledge of pitches, and that the rhythms may allow the individuality of pitches to strengthen. Individualities of the creativity may shift over a musician's lifetime via experience and training.

Motor Reproduction of Time Interval Depends on Internal Temporal Cues in the Brain: Sensorimotor Imagery in Rhythm

How the human brain perceives time intervals is a fascinating topic that has been explored in many fields of study. This study examined how time intervals are replicated in three conditions: with no internalized cue (PT), with an internalized cue without a beat (AS), and with an internalized cue with a beat (RS). In PT, participants accurately reproduced the time intervals up to approximately 3 s. Over 3 s, however, the reproduction errors became increasingly negative. In RS, longer presentations of over 5.6 s and 13 beats induced accurate time intervals in reproductions. This suggests longer exposure to beat presentation leads to stable internalization and efficiency in the sensorimotor processing of perception and reproduction. In AS, up to approximately 3 s, the results were similar to those of RS whereas over 3 s, the results shifted and became similar to those of PT. The time intervals between the first two stimuli indicate that the strategies of time-interval reproduction in AS may shift from RS to PT. Neural basis underlying the reproduction of time intervals without a beat may depend on length of time interval between adjacent stimuli in sequences.