# AutoSchA: Automatic Hierarchical Music Representations via Multi-Relational Node Isolation

arXiv: https://arxiv.org/abs/2512.18232 · HTML: https://mlsanity.com/paper/2512.18232/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 20 Dec 2025.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Counterpoint by Convolution](https://mlsanity.com/paper/1903.07227/) (2019)
- [Towards Interpretable Sparse Graph Representation Learning with Laplacian Pooling](https://mlsanity.com/paper/1905.11577/) (2019)
- [Multi-GCN: Graph Convolutional Networks for Multi-View Networks, with Applications to Global Poverty](https://mlsanity.com/paper/1901.11213/) (2019)
- [A Hierarchical Recurrent Neural Network for Symbolic Melody Generation](https://mlsanity.com/paper/1712.05274/) (2017)
- [Predicting Music Hierarchies with a Graph-Based Neural Decoder](https://mlsanity.com/paper/2306.16955/) (2023)
- [A New Dataset, Notation Software, and Representation for Computational Schenkerian Analysis](https://mlsanity.com/paper/2408.07184/) (2024)

## Abstract (arXiv)

Hierarchical representations provide powerful and principled approaches for analyzing many musical genres. Such representations have been broadly studied in music theory, for instance via Schenkerian analysis (SchA). Hierarchical music analyses, however, are highly cost-intensive; the analysis of a single piece of music requires a great deal of time and effort from trained experts. The representation of hierarchical analyses in a computer-readable format is a further challenge. Given recent developments in hierarchical deep learning and increasing quantities of computer-readable data, there is great promise in extending such work for an automatic hierarchical representation framework. This paper thus introduces a novel approach, AutoSchA, which extends recent developments in graph neural networks (GNNs) for hierarchical music analysis. AutoSchA features three key contributions: 1) a new graph learning framework for hierarchical music representation, 2) a new graph pooling mechanism based on node isolation that directly optimizes learned pooling assignments, and 3) a state-of-the-art architecture that integrates such developments for automatic hierarchical music analysis. We show, in a suite of experiments, that AutoSchA performs comparably to human experts when analyzing Baroque fugue subjects.