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Generative musical models often comprise of multiple levels of structure, presuming that the process of composition moves between background to foreground, or between generating musical surface and some deeper and reduced representation that governs hidden or latent dimensions of music. In this paper we are using a recently proposed framework called Deep Musical Information Dynamics (DMID) to explore information contents of deep neural models of music through rate reduction of latent representation streams, which is contrasted with hight rate information dynamics of the musical surface. This approach is partially motivated by rate-distortion theories of human cognition, providing a framework for exploring possible relations between imaginary anticipations existing in the listener's or composer's mind, and the information dynamics of the sensory (acoustic) or symbolic score data. In the paper the DMID framework is demonstrated using several experiments with symbolic (MIDI) and acoustic (spectral) music representations. We use variational encoding to learn a latent representation of the musical surface. This embedding is further reduced using a bit-allocation method into a second stream of low bit-rate encoding. The combined loss includes temporal information in terms of predictive properties for each encoding stream, and accuracy loss measured in terms of mutual information between the encoding at low rate and the high rate surface representations. For the case of counterpoint, we also study the mutual information between two voices in a musical piece at different levels of information reduction. The DMID framework allows to explore aspects of computational creativity in terms of juxtaposition of latent/imaginary surprisal aspects of deeper structure with music surprisal on the surface level, done in a manner that is quantifiable and computationally tractable. The relevant information theory modeling and analysis methods are discussed in the paper, suggesting that a trade off between compression and prediction play an important factor in the analysis and design of creative musical systems.

Capturing long-term statistics of signals and time series is important for modeling recurrent phenomena, especially when such recurrences are a-periodic and can be characterized by the approximate repetition of variable length motifs, such as patterns in human gestures and trends in financial time series or musical melodies. Regressive and auto-regressive models that are common in such problems, both analytically derived and neural network-based, often suffer from limited memory or tend to accumulate errors, making them sensitive during training. Moreover, such models often assume stationary signal statistics, which makes it difficult to deal with switching regimes or conditional signal dynamics. In this paper, we describe a method for time series modeling that is based on adaptive symbolization that maximizes the predictive information of the resulting sequence. Using approximate string-matching methods, the initial vectorized sequence is quantized into a discrete representation with a variable quantization threshold. Finding an optimal signal embedding is formulated in terms of a predictive bottleneck problem that takes into account the trade-off between representation and prediction accuracy. Several downstream applications based on discrete representation are described in this paper, which includes an analysis of the symbolic dynamics of recurrence statistics, motif extraction, segmentation, query matching, and the estimation of transfer entropy between parallel signals.