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Topology Structure Optimization of Reservoirs Using GLMY Homology

arXiv 2509.11612 ↗First posted 15 Sep 2025cs.LGcited by 0

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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.

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.

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12 of 55 references.

References · 12

  1. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  2. 2017Methods for Interpreting and Understanding Deep Neural Networkscited by 345
  3. 2020Topology of deep neural networkscited by 112
  4. 2018Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topologycited by 73
  5. 2019Weight Agnostic Neural Networkscited by 71
  6. 2013Confidence sets for persistence diagramscited by 17
  7. 2020A Review of Designs and Applications of Echo State Networkscited by 11
  8. 2019Reservoir Topology in Deep Echo State Networkscited by 6
  9. 2019Path homologies of deep feedforward networkscited by 6
  10. 2020An efficient algorithm for 1-dimensional (persistent) path homologycited by 1
  11. 2020Path homology and temporal networkscited by 1
  12. 2024Analyzing Singular Patterns in Discrete Planar Vector Fields via Persistent Path Homologycited by 1

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