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

Abstract

Statistical learning (SL) is a method of learning based on the transitional probabilities embedded in sequential phenomena such as music and language. It has been considered an implicit and domain-general mechanism that is innate in the human brain and that functions independently of intention to learn and awareness of what has been learned. SL is an interdisciplinary notion that incorporates information technology, artificial intelligence, musicology, and linguistics, as well as psychology and neuroscience. A body of recent study has suggested that SL can be reflected in neurophysiological responses based on the framework of information theory. This paper reviews a range of work on SL in adults and children that suggests overlapping and independent neural correlations in music and language, and that indicates disability of SL. Furthermore, this article discusses the relationships between the order of transitional probabilities (TPs) (i.e., hierarchy of local statistics) and entropy (i.e., global statistics) regarding SL strategies in human's brains; claims importance of information-theoretical approaches to understand domain-general, higher-order, and global SL covering both real-world music and language; and proposes promising approaches for the application of therapy and pedagogy from various perspectives of psychology, neuroscience, computational studies, musicology, and linguistics.

Keywords: Markov model; domain generality; entropy; implicit learning; information theory; n-gram; order; statistical learning; uncertainty; word segmentation.

Figure 1

Example of n-gram and Markov models in statistical learning (SL) of language (a) and music (b) based on information theory. The top are examples of sequences, and the others explain how to calculate TPs (P(e_n+1|e_n)) based on zero- to second-order Markov models. They are based on the conditional probability of an event e_n+1, given the preceding n events based on Bayes’ theorem. For instance, in language ((a), This is a sentence), the second-order Markov model represents that the “a” can be predicted based on the last subsequent two words of “This” and “is”. In music ((b), C4, D4, E4, F4), second-order Markov model represents that the “E” can be predicted based on the last subsequent two tones of “C” and “D”.

Figure 2

SL models and the sequences used in neural studies. All of the models and paradigms in sequences based on concatenation of words (a), Markov model of tone (b) and word (c), and concatenation of words with different TPs of the last stimuli in words (d) are simplified so that the characteristics of paradigms can be compared. In the example of word-segmentation paradigm (a), the same words do not successively appear. TP—transitional probability.

Figure 3

The entropy (uncertainty) of predictability in the framework of SL. The uncertainties depend on (a) TP ratios in a first-order Markov model (i.e., bigram model) and (b) orders of models in the TP ratio of 10% vs. 90%.

Figure 4

Representative equivalent current dipole (ECD) locations (dots) and orientations (bars) for the N100 m responses superimposed on the magnetic resonance images (a) (Daikoku et al., 2014 [32]; and the SL effects (b) (Daikoku et al., 2015 [10]) (NS = not significant). When the brain encodes the TP in a sequence, it expects a probable future stimulus with a high TP and inhibits the neural response to predictable stimuli. In the end, the SL effects manifest as a difference in amplitudes of neural responses to stimuli with lower and higher TPs (b).