Physical Reservoir Computing with (iontronic) Leaky-Integrator Neurons

Abstract

This repository provides an Echo State Network (ESN) and Band-pass Network (BPN) framework based on a physical circuit. The code is designed for both continuous data streams and sets of shorter pulses, each with a single label. The networks contain (iontronic) memristors, whose dynamic conductance exhibit the behaviour of leaky-integrator neurons. The physical (sigmoidal) steady-state conductance $g_{\text{inf}}(V)$ of the memristor nodes takes on the role of the activation function, while its conductance memory exhibits the same dynamics as leaky integrator nodes.

Unique Contribution

Our approach handles both:

1. Single time series (predicting at each step).
2. Multiple shorter series (pulses) (predicting a single label at the end of each pulse).

The leaky-integrator neurons and the integrated operator $g_{\text{inf}}$ allow for flexible state evolution that aligns with many practical tasks.

usage

1. Clone or download this repository.
2. Install required libraries: console pip install -r .\requirements.txt
3. Open and run the demo notebook included in the repository.

EchoStateNetwork Core Parameters

| Parameter | Type | Default | Description | |-------------------------|------------|---------|-------------| | input_dim | int | - | Dimension of input features | | reservoir_size | int | - | Number of neurons in reservoir | | output_dim | int | - | Dimension of output targets | | leaking_rate | float | 1.0 | Self-coupling constant (a ∈ (0,1]) | | step_size | float | 0.3 | Discrete time step (δ) | | time_scale | float | 1.0 | Base timescale (c) | | spectral_radius | float | 0.9 | Spectral radius of Wres | | sparsity | float | 0.5 | Fraction of zero weights in Wres | | input_scaling | float | 1.0 | Scaling factor applied to input | | regularization | float | 1e-4 | Ridge regression regularization | | washout | int | 100 | Initial timesteps to discard during training | | washout_inference | int | 0 | Initial timesteps to discard during prediction | | weight_seed | int | 42 | Random seed for weight initialization | | activation | callable | np.tanh | Nonlinear activation function | | guarantee_ESP | bool | True | Enforce Echo State Property | | progress_bar | bool | True | Show training progress bars | | apply_dynamics_per_step_size | int | 1 | Number of substeps per Δt | | choose_W_in | bool | False | Use custom input weights | | W_in_input | np.ndarray | None | If choose_W_in = True: Custom Win matrix (shape [reservoirsize, input_dim]) |

BandPassNetwork Additional Parameters

| Parameter | Type | Default | Description | |-------------------------|------------|---------|-------------| | time_scale_std | float | 1.0 | Standard deviation of per-neuron timescale distribution | | choose_timescales | bool | False | Use custom timescale array | | timescale_array_input | np.ndarray | None | If choose_timescales = True: Custom timescales (shape [reservoir_size,]) |

Physical Interpretation

Key physical relationships: - Physical timescale: τ = time_scale/leaking_rate = c/a - Physical conductance as activation: activation can be set to physical dynamic conductance

Figures

Optimization

The parameters of the ESN can be optimized for a dataset using optuna. Example files for optimization are included in the repository in the optimization folder. Use optuna-dashboard sqlite:///optuna_esn.db to visualize the results.

This code requires the optuna library. Install it using pip install optuna. The dashboard requires the optuna-dashboard library. Install it using pip install optuna-dashboard.

Authors

Tim Kamsma

Jelle Jasper Teijema

License

This extension is released under the MIT License.

Contact

This work is part of https://doi.org/10.48550/arXiv.2505.13451. For questions, please contact t.m.kamsma@uu.nl