weighted_minimal

weighted_minimal([rng], [T], dims...;
    weight=0.1, return_sparse=false,
    sampling_type=:no_sample)

Create and return a minimal weighted input layer matrix. This initializer generates a weighted input matrix with equal, deterministic elements in the same construction as [weighted_minimal](@ref), inspired by (Lu et al., 2017).

Please note that this initializer computes its own reservoir size! If the computed reservoir size is different than the provided one it will raise a warning.

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 matrix. Should follow res_size x in_size.

Keyword arguments

• weight: The value for all the weights in the input matrix. Defaults to 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> res_input = weighted_minimal(8, 3)
┌ Warning: Reservoir size has changed!
│
│     Computed reservoir size (6) does not equal the provided reservoir size (8).
│
│     Using computed value (6). Make sure to modify the reservoir initializer accordingly.
│
└ @ ReservoirComputing ~/.julia/dev/ReservoirComputing/src/esn/esn_inits.jl:159
6×3 Matrix{Float32}:
 0.1  0.0  0.0
 0.1  0.0  0.0
 0.0  0.1  0.0
 0.0  0.1  0.0
 0.0  0.0  0.1
 0.0  0.0  0.1

julia> res_input = weighted_minimal(9, 3; weight = 0.99)
9×3 Matrix{Float32}:
 0.99  0.0   0.0
 0.99  0.0   0.0
 0.99  0.0   0.0
 0.0   0.99  0.0
 0.0   0.99  0.0
 0.0   0.99  0.0
 0.0   0.0   0.99
 0.0   0.0   0.99
 0.0   0.0   0.99

julia> res_input = weighted_minimal(9, 3; sampling_type = :bernoulli_sample!)
9×3 Matrix{Float32}:
  0.1  -0.0  -0.0
 -0.1  -0.0  -0.0
  0.1  -0.0   0.0
 -0.0   0.1   0.0
  0.0   0.1  -0.0
  0.0   0.1   0.0
 -0.0  -0.0  -0.1
 -0.0  -0.0   0.1
  0.0  -0.0   0.1