esnfed 1.6.0

Echo State Networks for Federated Learning: reservoirs, topologies and federated strategies

esnfed — a federated reservoir computing toolkit

esnfed is a small, dependency-light Python library for training Echo State Networks (reservoir computing) in a federated setting — where several parties jointly train a model without sharing their raw data. It accompanies the Final Degree Project Ensemble of Recurrent Networks for Federated Learning (ETSINF, Universitat Politècnica de València).

The core library depends only on NumPy and NetworkX.

Why this and not ReservoirPy? ReservoirPy is the mature, full-featured library for building and tuning reservoir computing models, and esnfed does not try to replace it. esnfed focuses on the part ReservoirPy does not cover: federating reservoir models across parties. You can design a reservoir in ReservoirPy and federate it here in one line (see Interoperability below).

Gallery

All four plots below are produced by esnfed.viz (see Visualising your ESN).

Reservoir topology	Eigenvalue spectrum
Reservoir activations	Forecast vs. actual

Features

• Echo State Network with leaky-integrator neurons and a closed-form ridge readout (EchoStateNetwork).
• Federated strategies:
  • federated_ridge — exact federated training for a shared reservoir (clients exchange only ridge sufficient statistics; provably equal to pooled training, in one communication round);
  • fedavg — iterative FedAvg on the readout;
  • ensemble_predict — prediction ensemble for heterogeneous reservoirs;
  • structural_alignment — interpolate reservoirs toward a shared structure.
• Reservoir topologies: Erdős–Rényi, small-world, scale-free, ring.
• Data: synthetic benchmarks (NARMA-10, Mackey-Glass, Lorenz) and real data — a bundled counterparty-risk series (the TED spread) plus generic loaders (from_array, load_csv, load_fred).
• Interoperability: adapters for ReservoirPy reservoirs and an example integration with the Flower federated-learning framework.

Installation

pip install esnfed                  # core (numpy + networkx)
pip install "esnfed[viz]"           # + plotly/matplotlib/seaborn plots
pip install "esnfed[experiments]"   # + matplotlib/pandas/scipy/scikit-learn
pip install "esnfed[reservoirpy]"   # + ReservoirPy interop
pip install "esnfed[flower]"        # + Flower integration

Quick start

Federated counterparty-risk forecasting (real data)

Several institutions jointly forecast the TED spread (a classic gauge of interbank/counterparty credit risk) without sharing their data. Exact federated ridge equals pooled training in a single round:

from esnfed import datasets, federated, topologies, metrics

u, y = datasets.load_ted_spread()                 # bundled real series (FRED)
u_tr, y_tr, u_te, y_te = datasets.split(u, y, 0.7)
parts = datasets.partition_iid(u_tr, y_tr, n_clients=8)   # 8 "institutions"

W = topologies.random_reservoir(200, density=0.1, rng=0)
esn_kw = dict(spectral_radius=0.9, leaking_rate=0.5, washout=100, ridge=1e-6)
clients, ref = federated.make_shared_clients(W, parts, input_seed=0, esn_kwargs=esn_kw)

W_out = federated.federated_ridge(clients, ref)   # one round, exact, private
Z_test = ref.harvest(u_te)[ref.washout:]
print("federated NRMSE:", metrics.nrmse(y_te[ref.washout:], Z_test @ W_out))

Need another series? datasets.load_fred("BAMLH0A0HYM2") pulls a high-yield credit spread from FRED; datasets.from_array(my_series) or datasets.load_csv("my.csv") turn any series into a forecasting task.

Train a single ESN

import numpy as np
from esnfed import EchoStateNetwork, datasets, topologies, metrics

u, y = datasets.narma10(3000, rng=0)
u_tr, y_tr, u_te, y_te = datasets.split(u, y)
W = topologies.random_reservoir(200, density=0.1, rng=0)
esn = EchoStateNetwork(1, 1, W, spectral_radius=0.9, washout=100).fit(u_tr, y_tr)
print("NRMSE:", metrics.nrmse(y_te[100:], esn.predict(u_te)[100:]))

Interoperability

ReservoirPy — design there, federate here

from reservoirpy.nodes import Reservoir
from esnfed import interop, datasets, federated

res = Reservoir(200, sr=0.9, lr=0.5, input_dim=1)   # design/tune in ReservoirPy
esn = interop.to_esn(res, n_inputs=1)               # -> esnfed EchoStateNetwork
W = interop.reservoir_matrix(res)                   # ... then federate it

Flower — a real FL framework

examples/flower_federated_ridge.py shows the exact federated-ridge scheme as a Flower NumPyClient + custom Strategy: each client's fit returns its ridge sufficient statistics and the server sums them and solves once. The Flower-routed result is identical to federated_ridge to numerical precision.

Visualising your ESN

The optional esnfed.viz module (pip install "esnfed[viz]") provides four plots. The default backend is Plotly (interactive); pass backend="matplotlib" or backend="seaborn" for static figures. Each function returns the native figure object.

from esnfed import EchoStateNetwork, topologies, viz

W = topologies.small_world_reservoir(100, k=6, p=0.1, rng=0)
esn = EchoStateNetwork(1, 1, W, spectral_radius=0.9).fit(u_tr, y_tr)

viz.plot_reservoir(esn).show()           # connectivity graph (degree-coloured)
viz.plot_spectrum(esn).show()            # eigenvalues + unit circle + ρ
viz.plot_states(esn, u_te).show()        # reservoir activations over time
viz.plot_forecast(y_te, esn.predict(u_te), washout=100).show()
viz.save(viz.plot_spectrum(esn), "spectrum.html")   # or .png (needs kaleido)

Function	Shows
plot_reservoir	reservoir connectivity as a network graph
plot_spectrum	eigenvalues in the complex plane (echo state property)
plot_states	a sample of reservoir activations over time
plot_forecast	predicted vs. actual with NRMSE

Modules

Module	Contents
esnfed.esn	EchoStateNetwork, ridge helpers
esnfed.topologies	reservoir generators + graph_metrics
esnfed.datasets	NARMA-10, Mackey-Glass, Lorenz; from_array, load_csv, load_ted_spread, load_fred
esnfed.metrics	nrmse, rmse, mse, r2_score
esnfed.federated	Client, federated_ridge, fedavg, ensemble_predict, structural_alignment
esnfed.interop	ReservoirPy adapters (to_esn, reservoir_matrix)
esnfed.viz	plot_reservoir, plot_spectrum, plot_states, plot_forecast

Reproducing the research experiments

pip install -e ".[experiments,reservoirpy,flower,viz]"
python -m pytest                    # 53 tests
python experiments/run_all.py       # synthetic-benchmark figures and tables
python experiments/exp6_finance.py  # federated counterparty-risk (TED spread)

Data attribution

The bundled TED spread is sourced from the Federal Reserve Bank of St. Louis (FRED, series TEDRATE) and is used for demonstration under FRED's terms.

Citation

@thesis{benites2026esnfed,
  author = {Benites Aldaz, Dairon Andres},
  title  = {Ensemble of Recurrent Networks for Federated Learning},
  school = {Universitat Politecnica de Valencia (ETSINF)},
  year   = {2026},
  type   = {Bachelor's thesis},
}

License

MIT — see LICENSE.