modified_lm

modified_lm([rng], [T], dims...;
    factor, amplitude=0.3, sine_divisor=5.9, logistic_parameter=2.35,
    return_sparse=false)

Generate a input weight matrix based on the logistic mapping (Viehweg et al., 2025). Thematrix is built so that each input is transformed into a high-dimensional feature space via a recursive logistic map. For each input, a chain of weights is generated as follows:

• The first element of the chain is initialized using a sine function:

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

where j is the index corresponding to the input and n is the number of inputs.

• Subsequent elements are recursively computed using the logistic mapping:

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

The resulting matrix has dimensions (factor * in_size) x in_size, where in_size corresponds to the number of columns provided in dims. If the provided number of rows does not match factor * in_size the number of rows is overridden.

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

• factor: The number of logistic map iterations (chain length) per input, determining the number of rows per input.
• amplitude: Scaling parameter A for the sine-based initialization of the first element in each logistic chain. Default is 0.3.
• sine_divisor: Parameter B used to adjust the phase in the sine initialization. Default is 5.9.
• logistic_parameter: The parameter r in the logistic recurrence that governs the chain dynamics. Default is 2.35.
• return_sparse: If true, returns the resulting matrix as a sparse matrix. Default is false.

Examples

julia> modified_lm(20, 10; factor=2)
20×10 SparseArrays.SparseMatrixCSC{Float32, Int64} with 18 stored entries:
⎡⢠⠀⠀⠀⠀⎤
⎢⠀⢣⠀⠀⠀⎥
⎢⠀⠀⢣⠀⠀⎥
⎢⠀⠀⠀⢣⠀⎥
⎣⠀⠀⠀⠀⢣⎦

julia> modified_lm(12, 4; factor=3)
12×4 SparseArrays.SparseMatrixCSC{Float32, Int64} with 9 stored entries:
  ⋅    ⋅          ⋅          ⋅ 
  ⋅    ⋅          ⋅          ⋅ 
  ⋅    ⋅          ⋅          ⋅ 
  ⋅   0.0133075   ⋅          ⋅ 
  ⋅   0.0308564   ⋅          ⋅ 
  ⋅   0.070275    ⋅          ⋅ 
  ⋅    ⋅         0.0265887   ⋅ 
  ⋅    ⋅         0.0608222   ⋅ 
  ⋅    ⋅         0.134239    ⋅ 
  ⋅    ⋅          ⋅         0.0398177
  ⋅    ⋅          ⋅         0.0898457
  ⋅    ⋅          ⋅         0.192168