# Topology Structure Optimization of Reservoirs Using GLMY Homology

arXiv: https://arxiv.org/abs/2509.11612 · HTML: https://mlsanity.com/paper/2509.11612/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Weight Agnostic Neural Networks](https://mlsanity.com/paper/1906.04358/) (2019)
- [Confidence sets for persistence diagrams](https://mlsanity.com/paper/1303.7117/) (2013)
- [A Review of Designs and Applications of Echo State Networks](https://mlsanity.com/paper/2012.02974/) (2020)
- [Reservoir Topology in Deep Echo State Networks](https://mlsanity.com/paper/1909.11022/) (2019)
- [Path homologies of deep feedforward networks](https://mlsanity.com/paper/1910.07617/) (2019)
- [An efficient algorithm for 1-dimensional (persistent) path homology](https://mlsanity.com/paper/2001.09549/) (2020)
- [Path homology and temporal networks](https://mlsanity.com/paper/2008.11885/) (2020)
- [Analyzing Singular Patterns in Discrete Planar Vector Fields via Persistent Path Homology](https://mlsanity.com/paper/2404.01007/) (2024)

## Abstract (arXiv)

Reservoir is an efficient network for time series processing. It is well known that network structure is one of the determinants of its performance. However, the topology structure of reservoirs, as well as their performance, is hard to analyzed, due to the lack of suitable mathematical tools. In this paper, we study the topology structure of reservoirs using persistent GLMY homology theory, and develop a method to improve its performance. Specifically, it is found that the reservoir performance is closely related to the one-dimensional GLMY homology groups. Then, we develop a reservoir structure optimization method by modifying the minimal representative cycles of one-dimensional GLMY homology groups. Finally, by experiments, it is validated that the performance of reservoirs is jointly influenced by the reservoir structure and the periodicity of the dataset.