Deep symbolic processing of human-performed musical sequences

Artificial music tutors are needed for assisting a performer during his/her practice time whenever a human tutor is not available. But for these artificial tutors to be intelligent and fulfill the role of a music tutor, they have to be able to identify errors made by the performer while playing a musical sequence. This task is not a trivial one, since all musical activities are considered as open-ended domains. Therefore, not only there is no unique correct way of performing a musical sequence, but also the analysis made by the tutor has to consider the development level of the performer, the difficulty level of the performed musical sequence, and many other variables. This paper describes an ongoing research that uses cascading connected layers of symbolic processing as the core of a human-performed error identification and characterization module able to overcome the complexity of the studied open-ended domain.

Experience as cognition: musical sense-making and the ‘in-time/ outside-of-time’ dichotomy

Musical sense-making relies on two distinctive strategies: tracking the moment-to-moment history of the actual unfolding and recollecting actual and previous sounding events in a kind of synoptic overview. Both positions are not opposed but complement each other. The aim of this contribution, therefore, is to provide a comprehensive framework that provides both conceptual and operational tools for coping with the sounds. Five major possibilities are proposed in this regard: (i) the concepts of perspective and resolution, which refer to the distance the listener takes with respect to the sounding music and the fine-grainedness of his/her discriminative abilities; (ii) the continuous/discrete dichotomy which conceives of the music as one continuous flow as against a division in separate and distinct elements; (iii) the in time/outside-of-time distinction, with the former proceeding in real time and the latter proceeding outside of the time of unfolding; (iv) the deictic approach to musical sense-making, which conceives of an act of mental pointing to the music, and (v) the levels of processing, which span a continuum between primitive sensory reactivity to actual sounding stimuli and high-level symbolic processing.

Training neural networks to encode symbols enables combinatorial generalization

Combinatorial generalization—the ability to understand and produce novel combinations of already familiar elements—is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body of research suggests that conventional neural networks cannot solve this problem unless they are endowed with mechanisms specifically engineered for the purpose of representing symbols. In this paper, we introduce a novel way of representing symbolic structures in connectionist terms—the vectors approach to representing symbols (VARS), which allows training standard neural architectures to encode symbolic knowledge explicitly at their output layers. In two simulations, we show that neural networks not only can learn to produce VARS representations, but in doing so they achieve combinatorial generalization in their symbolic and non-symbolic output. This adds to other recent work that has shown improved combinatorial generalization under some training conditions, and raises the question of whether specific mechanisms or training routines are needed to support symbolic processing. This article is part of the theme issue ‘Towards mechanistic models of meaning composition’.

Spatial–numerical associations: Shared symbolic and non-symbolic numerical representations

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial–numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.