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Artificial Neural Networks Solve Musical Problems With Fourier Phase Spaces.

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Artificial neural networks trained on musical tasks surprisingly encode musical properties using discrete Fourier phase spaces. This suggests Fourier components may play a key role in the brain's musical cognition.

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Area of Science:

  • Cognitive Neuroscience
  • Computational Musicology
  • Artificial Intelligence

Background:

  • The brain's representation of musical properties remains a significant question in cognitive neuroscience.
  • Artificial neural networks offer biologically plausible models for understanding cognitive processes.
  • Interpreting the internal structure of neural networks is challenging, often leading to a focus on their outputs rather than their internal representations.

Purpose of the Study:

  • To investigate how artificial neural networks encode musical properties when trained on musical tasks.
  • To explore the relationship between network connection weights and established methods for representing musical information.
  • To determine if neural networks can reveal novel insights into the neural basis of musical cognition.

Main Methods:

  • Training artificial neural networks to perform musical tasks.
  • Analyzing the connection weights within the trained networks.
  • Correlating network weights with discrete Fourier phase spaces used for musical set representation.

Main Results:

  • A remarkably high correlation was found between network connection weights and discrete Fourier phase spaces.
  • The networks spontaneously discovered and utilized Fourier phase spaces without explicit programming.
  • This discovery occurred despite the absence of a clear mathematical link between network learning rules and Fourier analysis.

Conclusions:

  • Discrete Fourier phase spaces appear to be a fundamental tool for representing musical information, extending beyond formal music theory.
  • The presence of these phase spaces in neural network models strongly suggests that Fourier components are plausible neural codes for musical cognition.
  • This research opens new avenues for understanding the neural mechanisms underlying music perception and processing.