forward_connection

forward_connection([rng], [T], dims...;
    weight=0.1, selfloop_weight=0.1,
    return_sparse=false)

Creates a reservoir based on a forward connection of weights (Elsarraj et al., 2019).

This architecture is referred to as TP5 in the original paper.

Equations

\[W_{i,j} = \begin{cases} r, & \text{if } j = i - 2 \text{ for } i = 3 \dots N \\ 0, & \text{otherwise} \end{cases}\]

Arguments

• rng: Random number generator. Default is Utils.default_rng() from WeightInitializers.
• T: Type of the elements in the reservoir matrix. Default is Float32.
• dims: Dimensions of the reservoir matrix.

Keyword arguments

• weight: Weight of the cycle connections in the reservoir matrix. This can be provided as a single value or an array. In case it is provided as an array please make sure that the length of the array matches the length of the sub-diagonal you want to populate. Default is 0.1.
• return_sparse: flag for returning a sparse matrix. Default is false.
• sampling_type: Sampling that decides the distribution of weight negative numbers. If set to :no_sample the sign is unchanged. If set to :bernoulli_sample! then each weight can be positive with a probability set by positive_prob. If set to :irrational_sample! the weight is negative if the decimal number of the irrational number chosen is odd. If set to :regular_sample!, each weight will be assigned a negative sign after the chosen strides. strides can be a single number or an array. Default is :no_sample.
• positive_prob: probability of the weight being positive when sampling_type is set to :bernoulli_sample!. Default is 0.5.
• irrational: Irrational number whose decimals decide the sign of weight. Default is pi.
• start: Which place after the decimal point the counting starts for the irrational sign counting. Default is 1.
• strides: number of strides for assigning negative value to a weight. It can be an integer or an array. Default is 2.

Examples

julia> reservoir_matrix = forward_connection(5, 5)
5×5 Matrix{Float32}:
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.1  0.0  0.0  0.0  0.0
 0.0  0.1  0.0  0.0  0.0
 0.0  0.0  0.1  0.0  0.0

julia> reservoir_matrix = forward_connection(5, 5; weight=0.5)
5×5 Matrix{Float32}:
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.5  0.0  0.0  0.0  0.0
 0.0  0.5  0.0  0.0  0.0
 0.0  0.0  0.5  0.0  0.0