datasets.narma doesn't return input series about reservoirpy

[PAUL-BERNARD]

Hello @DS-Liu 👋
Thank you for your issue.
Timeseries in the datasets module of ReservoirPy all have the shape (n_timesteps, n_features), as they are timeseries. Echo State Networks can be used on those timeseries to predict the following timesteps, considering the previous ones.

If you want to convert a timeseries into an (input, output) tuple for a prediction task, you can use the to_forecasting method.

[DS-Liu]

I'm new to reservoir computing. But I think the input of the narma task should be the u(t) sampled uniformly from [0, 0.5], am I wrong?

[PAUL-BERNARD]

I think the confusion comes from the naming convention between the reservoir computing litterature where u(t) usually represents the input timeseries, and u(t) in the NARMA recurrent relation which stands for "uniform", and that is simply a sample from a uniform distribution and that is not meant to be used elsewhere.

In the end, the NARMA timeseries is a single timeseries of shape (n_timesteps, 1), and you can use reservoir computing to make predictions.

Let me know if the misunderstanding persists

[DS-Liu]

The $n$-th order narma task is defined as
$$y_{k+1} = \alpha y_k + \beta y_k\left(\sum_{j=0}^{n-1}y_{k-j}\right) + \gamma u_{k-n+1}u_k + \delta,$$
where $(\alpha,\beta,\gamma,\delta)$ are set to $(0.3,0.05,1.5,0.1)$, respectively.

In the literatures of quantum reservoir computing, such as

1. Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning.
2. Boosting Computational Power through Spatial Multiplexing in Quantum Reservoir Computing.
3. Learning nonlinear input–output maps with dissipative quantum systems.
4. Higher-Order Quantum Reservoir Computing.
5. Dynamical Phase Transitions in Quantum Reservoir Computing.
6. Unifying framework for information processing in stochastically driven dynamical systems.

the input to the reservoir at time step $k$ is the $u_k$ which is sampled uniformly from [0, 0.2] to assure the stability of the narma task.

I think this is reasonable since the narma system is driven by $u_k$.

However, you mentioned that

If you want to convert a timeseries into an (input, output) tuple for a prediction task, you can use the to_forecasting method.

which means that for the narma task, the echo state at time $k$ is driven by its previous output $y_{k-1}$. This is equivalent to the case that the echo state has no input, but has an output feedback connection.

Are these literatures wrongly performed the narma task?

[PAUL-BERNARD]

Hello again, and thank you for your well-placed perseverance :)
Indeed, many papers use the uniformly distributed timeseries as an input for benchmarking. This will be fixed in the ReservoirPy v0.3.11.

In the meantime, if you want to use the NARMA task for your benchmarking, you can re-implement the function that returns u(t):

def narma(
    n_timesteps: int,
    order: int = 30,
    a1: float = 0.2,
    a2: float = 0.04,
    b: float = 1.5,
    c: float = 0.001,
    x0: Union[list, np.ndarray] = [0.0],
    seed: Union[int, RandomState] = None,
) -> np.ndarray:
    if seed is None:
        seed = get_seed()
    rs = rand_generator(seed)

    y = np.zeros((n_timesteps + order, 1))

    x0 = check_vector(np.atleast_2d(np.asarray(x0)))
    y[: x0.shape[0], :] = x0

    u = rs.uniform(0, 0.5, size=(n_timesteps + order, 1))
    for t in range(order, n_timesteps + order - 1):
        y[t + 1] = (
            a1 * y[t]
            + a2 * y[t] * np.sum(y[t - order : t])
            + b * u[t - order] * u[t]
            + c
        )
    return u, y[order:, :]

Sorry for my misunderstanding, and thank you again for your issue