logistic_mapping

logistic_mapping([rng], [T], dims...;
    amplitude=0.3, sine_divisor=5.9, logistic_parameter=3.7,
    return_sparse=false)

Generate an input weight matrix using a logistic mapping (Wang et al., 2022) The first row is initialized using a sine function:

\[ W[1, j] = \text{amplitude} \cdot \sin(j \cdot \pi / (\text{sine_divisor} \cdot in_size))\]

for each input index j, with in_size being the number of columns provided in dims. Subsequent rows are generated recursively using the logistic map recurrence:

\[ W[i+1, j] = \text{logistic_parameter} \cdot W(i, j) \cdot (1 - W[i, j])\]

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

• amplitude: Scaling parameter used in the sine initialization of the first row. Default is 0.3.
• sine_divisor: Parameter used to adjust the phase in the sine initialization. Default is 5.9.
• logistic_parameter: The parameter in the logistic mapping recurrence that governs the dynamics. Default is 3.7.
• return_sparse: If true, returns the resulting matrix as a sparse matrix. Default is false.

Examples

julia> logistic_mapping(8, 3)
8×3 Matrix{Float32}:
 0.0529682  0.104272  0.1523
 0.185602   0.345578  0.477687
 0.559268   0.836769  0.923158
 0.912003   0.50537   0.262468
 0.296938   0.924893  0.716241
 0.772434   0.257023  0.751987
 0.650385   0.70656   0.69006
 0.841322   0.767132  0.791346