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Echo State Network

Recurrent neural network architecture where only the output layer is trained, with the reservoir remaining fixed and random.

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Reservoir

Collection of untrained recurrent neurons generating a rich and non-linear representation of the system's input history.

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Echo state

Fundamental condition where the current reservoir states asymptotically depend only on recent past inputs and not on initial conditions.

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Spectral radius

Maximum eigenvalue in magnitude of the reservoir weight matrix, controlling the memory dynamics and fade-out of the network.

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Echo property

Essential characteristic ensuring that the influence of initial conditions disappears exponentially in favor of the input history.

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Readout layer

Trainable linear output layer combining reservoir states to generate the final network prediction.

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Reservoir computing

Computational paradigm using a fixed dynamic reservoir to project data into a high-dimensional space before classification.

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Leaky integration

Mechanism controlling the update speed of reservoir states through a leak parameter between 0 and 1, adjusting temporal memory.

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Reservoir connectivity

Density of non-zero connections in the reservoir weight matrix, typically low (1-10%) to ensure network sparsity.

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Input matrix

Fixed weight matrix projecting input signals into the high-dimensional space of the reservoir with a controlled input scale.

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Internal states

Vector of reservoir neuron activations at a given time, encapsulating the past temporal information of the system.

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Input noise

Random perturbation added to inputs to improve reservoir robustness and avoid unwanted attractors in the dynamics.

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Linear regression

Optimization method used to calculate output weights by minimizing the squared error between predictions and targets.

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Memory capacity

Quantitative measure of the reservoir's ability to retain and retrieve information over varying time delays in inputs.

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Time scale

Parameter determining the effective temporal memory window of the reservoir, controlled by the spectral radius and leak rate.

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Chaotic dynamics

Operational regime of the reservoir where the spectral radius > 1, generating complex dynamics sensitive to initial conditions.

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