# Rethinking Reservoir Pruning: A Dynamical Perspective for Echo State Networks

arXiv: https://arxiv.org/abs/2608.04593 · HTML: https://mlsanity.com/paper/2608.04593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 18 of 18)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [ZipLM: Inference-Aware Structured Pruning of Language Models](https://mlsanity.com/paper/2302.04089/) (2023)
- [SPDY: Accurate Pruning with Speedup Guarantees](https://mlsanity.com/paper/2201.13096/) (2022)
- [Topology-Aware Network Pruning using Multi-stage Graph Embedding and Reinforcement Learning](https://mlsanity.com/paper/2102.03214/) (2021)
- [Sparse Double Descent: Where Network Pruning Aggravates Overfitting](https://mlsanity.com/paper/2206.08684/) (2022)
- [Data-Efficient Structured Pruning via Submodular Optimization](https://mlsanity.com/paper/2203.04940/) (2022)
- [Fantastic Weights and How to Find Them: Where to Prune in Dynamic Sparse Training](https://mlsanity.com/paper/2306.12230/) (2023)
- [One-Shot Pruning of Recurrent Neural Networks by Jacobian Spectrum Evaluation](https://mlsanity.com/paper/1912.00120/) (2019)
- [Centrality Measures in Networks](https://mlsanity.com/paper/1608.05845/) (2016)
- [Layer-Adaptive State Pruning for Deep State Space Models](https://mlsanity.com/paper/2411.02824/) (2024)
- [Investigating echo state networks dynamics by means of recurrence analysis](https://mlsanity.com/paper/1601.07381/) (2016)
- [No Free Prune: Information-Theoretic Barriers to Pruning at Initialization](https://mlsanity.com/paper/2402.01089/) (2024)
- [Chasing the Echo State Property](https://mlsanity.com/paper/1811.10892/) (2018)
- [BMRS: Bayesian Model Reduction for Structured Pruning](https://mlsanity.com/paper/2406.01345/) (2024)
- [Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics](https://mlsanity.com/paper/2507.06050/) (2025)
- [Centrality-Based Pruning for Efficient Echo State Networks](https://mlsanity.com/paper/2603.20684/) (2026)

## Abstract (arXiv)

Echo State Networks (ESNs) offer an efficient framework for temporal prediction, but their randomly initialized reservoirs are often over-parameterized and dynamically redundant. Existing pruning methods largely rely on static connectivity or activation statistics, which may overlook neurons that shape input-driven state transitions. We propose Dynamical Mode Pruning (DMP), a reservoir pruning method that ranks neurons by their contribution to dominant transition modes obtained from a trajectory-averaged Jacobian Gramian. DMP removes low-impact units and retrains only the readout. Experiments on chaotic and real-world time-series benchmarks show that DMP improves or preserves forecasting accuracy while reducing redundant reservoir components. Our results suggest that dynamical influence is a useful criterion for reservoir refinement beyond static structural importance alone.