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PreprintCC BY 4.0HAL

Bridging Denotator Theory and Sheaf Neural Networks for Symbolic Music Generation

  • Mariana Montiel
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Abstract

This framework provides a rigorous mathematical bridge between Guerino Mazzola's algebraic Denotator Theory and modern Sheaf Neural Networks (SNNs). By adapting hierarchical musical structures into cellular stalks and linear restriction matrices over incidence posets, we demonstrate how categorical limits and colimits govern local counterpoint restrictions and macroscopic temporal synthesis. We present a clear operational contrast between deterministic Baroque counterpoint constraints and continuous parallel transport operators in modern modal jazz, providing an explicit formulation to instantiate these properties within structural machine learning environments.

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Cite

BibTeXRIS
BibTeX
@misc{montiel2026bridging,
  title = {{Bridging Denotator Theory and Sheaf Neural Networks for Symbolic Music Generation}},
  author = {Mariana Montiel},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  url = {https://hal.science/hal-05846010v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bridging Denotator Theory and Sheaf Neural Networks for Symbolic Music Generation
AU  - Mariana Montiel
PY  - 2026
DA  - 2026/11/02
PB  - HAL
UR  - https://hal.science/hal-05846010v1
AB  - This framework provides a rigorous mathematical bridge between Guerino Mazzola's algebraic Denotator Theory and modern Sheaf Neural Networks (SNNs). By adapting hierarchical musical structures into cellular stalks and linear restriction matrices over incidence posets, we demonstrate how categorical limits and colimits govern local counterpoint restrictions and macroscopic temporal synthesis. We present a clear operational contrast between deterministic Baroque counterpoint constraints and continuous parallel transport operators in modern modal jazz, providing an explicit formulation to instantiate these properties within structural machine learning environments.
ER  -