How Do Artificial Neural Networks Classify Musical Triads? A Case Study in Eluding Bonini's Paradox.

Area of Science:

• Cognitive Science
• Computational Neuroscience
• Music Theory

Background:

• Cognitive scientists frequently employ artificial neural networks (ANNs) to model cognitive processes.
• However, the internal representations learned by ANNs are often not deeply investigated.
• This limits understanding of how complex cognitive functions, like music perception, might be implemented.

Purpose of the Study:

• To investigate how artificial neural networks (ANNs) represent musical properties, specifically musical chords.
• To interpret the internal structure of ANNs to uncover the representations they develop.
• To explore the potential of ANNs to inform cognitive science theories of musical cognition.

Main Methods:

• Training ANNs to classify musical chords.
• Analyzing the connection weights between input and hidden units.
• Interpreting network structures using Fourier phase spaces and signal analysis.
• Examining the role of different unit activation functions in information processing.

Main Results:

• Connection weights between input and hidden units can be described using Fourier phase spaces.
• The total signal through weighted connections measures similarity between Fourier structures of weights and stimuli.
• Different activation functions lead to varied utilization of this similarity measure by units.
• The ANNs' processing is related to, but distinct from, traditional Fourier analyses in musical set theory.

Conclusions:

• Fourier representations of music extend beyond traditional musical set theory.
• ANNs offer a valuable framework for exploring Fourier representations in musical cognition.
• Understanding network structure is crucial for interpreting ANN-based models of cognition and stimulus-response conversion.