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This paper applies Smooth-L1 regularization to the readout layer of Echo State Networks to make them sparser, and extends the approach to federated training with a Newton-step aggregation. The reported results are sparsity of roughly 75-95% with accuracy within about 1-2 points of dense baselines on seven time-series benchmarks, which is a useful trade-off for edge and IoT settings. Readers should weigh these gains against the modest benchmark scope and the fact that the comparisons are against dense ESN baselines rather than other compression methods.
Sparse Federated Echo State Networks for Time-Series Classification via Smooth-L1 Regularization
arXiv:2610.21742v1 Announce Type: new Abstract: Echo State Networks (ESNs), as lightweight implementations of reservoir computing, provide efficient solutions for temporal data processing in resource-constrained environments. While standard ESNs offer computational efficiency, their dense readout layers inflate the stored model and the per-sample inference cost. This paper introduces a Smooth-L1 regularized ESN (SL1ESN) that promotes sparsity in the readout layer while preserving differentiability for gradient-based optimization. The method employs a twice-differentiable Smooth-L1 approximation compatible with Newton's method, which we exploit both for centralized training and for a second-order (Newton-step) federated aggregation scheme. Under a single fixed shrinkage threshold shared by every dataset and both settings, experiments on seven time-series classification benchmarks show that SL1ESN learns readouts that are $77$--$95\%$ sparse in the centralized setting and $75$--$95\%$ sparse in the federated one, while staying within $0.7$ accuracy points of the strongest dense baseline on five of the seven benchmarks in the centralized setting and within $1.6$ points on the same five in the federated one, and the second-order federated update converges in only a few rounds. The resulting sparsity compresses the stored model, the per-sample inference cost, and the server-to-client broadcast by a comparable factor. These results demonstrate the practical value of sparse readouts for edge computing and IoT deployments.
Abstract:Echo State Networks (ESNs), as lightweight implementations of reservoir computing, provide efficient solutions for temporal data processing in resource-constrained environments. While standard ESNs offer computational efficiency, their dense readout layers inflate the stored model and the per-sample inference cost. This paper introduces a Smooth-L1 regularized ESN (SL1ESN) that promotes sparsity in the readout layer while preserving differentiability for gradient-based optimization. The method employs a twice-differentiable Smooth-L1 approximation compatible with Newton's method, which we exploit both for centralized training and for a second-order (Newton-step) federated aggregation scheme. Under a single fixed shrinkage threshold shared by every dataset and both settings, experiments on seven time-series classification benchmarks show that SL1ESN learns readouts that are $77$--$95\%$ sparse in the centralized setting and $75$--$95\%$ sparse in the federated one, while staying within $0.7$ accuracy points of the strongest dense baseline on five of the seven benchmarks in the centralized setting and within $1.6$ points on the same five in the federated one, and the second-order federated update converges in only a few rounds. The resulting sparsity compresses the stored model, the per-sample inference cost, and the server-to-client broadcast by a comparable factor. These results demonstrate the practical value of sparse readouts for edge computing and IoT deployments.
30 pages, 8 figures, 7 tables. Extended version of a paper presented at IDEAL 2025. Code: this https URL
Machine Learning (cs.LG)
arXiv:2610.21742 [cs.LG]
(or arXiv:2610.21742v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.21742 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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