Deep Reservoir Computing with Linear Readout for Audio Data

A PyTorch implementation of Deep Echo State Networks (DeepESN) and related reservoir computing models, designed for efficient sequence representation with a fixed recurrent backbone and a linear ridge readout. Ref. accepted paper: C. Baccheschi and P. Dazzi, “An Analysis of Untrained Deep Reservoir Networks for Audio Surveillance,” in Proceedings of the IEEE International Conference on Advanced Video and Signal-Based Surveillance (AVSS), Lecce(Italy), 2026, forthcoming.

This repository focuses on the following idea:

• use a reservoir backbone as a nonlinear temporal feature extractor;
• keep the recurrent layers untrained;
• train only a linear readout, making the approach particularly attractive for large-scale settings where full backpropagation through time may be expensive.

The core implementation is provided in deepesn.py.

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Overview

This repository implements:

• single-layer ESN
• deep ESN
• bidirectional DeepESN
• ridge-based linear readout
• support for sequence-to-sequence and sequence-to-one/sequence-to-vector tasks
• support for (mean)pooled or last-state outputs
• support for large datasets through a readout fitting procedure based on sufficient statistics

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Repository Structure

.
├── deepesn.py      # main DeepESN model
├── reservoir.py    # reservoir cell and bidirectional wrapper
├── readout.py      # linear readout + ridge fitting utilities
└── ...

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Example usage

Create a DeepESN model

The main constructor is:

model = DeepESN(
    input_size=your_input,
    units=100,
    num_layers=2,
    input_scaling=1.0,
    bias_scaling=1.0,
    spectral_radius=0.9,
    leaky=1.0,
    bias_scaling_hidden=1.0,
    spectral_radius_hidden=0.9,
    input_scaling_hidden=1.0,
    leaky_hidden=1.0,
    readout_regularizer=[0,1e-4,1e-3,1e-2,1,10,100],   # they will be used in sequence to find the best regularizer for the readout !
    type="bi", # bidirectional or nobi
    score="accuracy",
    last_layer=False,
    sequences=False, # extracting the last state returning 2D tensor
    mean=False,
)

1. Extract reservoir features

reservoir_states, all_states = model(x)

2. Train the readout

Find the best validation performance and the best lambda

For multiclassification, remember to give to the readout the onehot representation. Conversely, for the binary case, just encode in {+1, -1}

val_error, fit_time_s, fit_time_ms = model.fit(
    train=reservoir_statest_train,
    labels=labels,
    num_targets=num_classes,
    validation_data=(reservoir_statest_val, val_labels),
    verbose=True,
    device=cpu|cuda
)

3. Predict

predictions = model.predict(test_data)

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Authors

-Prof. Claudio Gallicchio — original DeepESN formulation and deep reservoir computing research

-Dr. Corrado Baccheschi — PyTorch implementation and extensions

Cite

If you use this code entirely or partially please cite the following:

Gallicchio, Claudio, Alessio Micheli, and Luca Pedrelli. "Deep reservoir computing: A critical experimental analysis." Neurocomputing 268 (2017): 87-99.

and

@inproceedings{baccheschidazzi2026,
  author    = {Corrado Baccheschi and Patrizio Dazzi},
  title     = {An Analysis of Untrained Deep Reservoir Networks for Audio Surveillance},
  booktitle = {Proceedings of the IEEE International Conference on Advanced Visual and Signal-Based Systems (AVSS)},
  year      = {2026},
  note      = {accepted, forthcoming}
}