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truedoublecycle

ReservoirComputing.true_doublecycle — Function
true_doublecycle([rng], [T], dims...;
    cycle_weight=0.1, second_cycle_weight=0.1, radius=nothing,
    return_sparse=false, cycle_kwargs=(), second_cycle_kwargs=())

Creates a true double cycle reservoir, ispired by (Fu et al., 2023), with cycles built on the definition by (Rodan and Tino, 2011).

\[W_{i,j} = \begin{cases} r_1, & \text{if } i = j + 1,\;\; j \in [1, D_{\mathrm{res}} - 1], \\[4pt] r_1, & \text{if } i = 1,\;\; j = D_{\mathrm{res}}, \\[6pt] r_2, & \text{if } j = i + 1,\;\; i \in [1, D_{\mathrm{res}} - 1], \\[4pt] r_2, & \text{if } i = D_{\mathrm{res}},\;\; j = 1, \\[6pt] 0, & \text{otherwise.} \end{cases}\]

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

  • cycle_weight: Weight of the upper cycle connections in the reservoir matrix. Default is 0.1.

  • second_cycle_weight: Weight of the lower cycle connections in the reservoir matrix. Default is 0.1.

  • radius: The desired spectral radius of the reservoir. If nothing is passed, no scaling takes place. Defaults to nothing.

  • return_sparse: flag for returning a sparse matrix. true requires SparseArrays to be loaded. Default is false.

  • cycle_kwargs, and second_cycle_kwargs: named tuples that control the kwargs for the weights generation. The kwargs are as follows:

Examples

Default call:

julia> res_matrix = true_doublecycle(5, 5)
5×5 Matrix{Float32}:
 0.0  0.1  0.0  0.0  0.1
 0.1  0.0  0.1  0.0  0.0
 0.0  0.1  0.0  0.1  0.0
 0.0  0.0  0.1  0.0  0.1
 0.1  0.0  0.0  0.1  0.0

Changing weights:

julia> res_matrix = true_doublecycle(5, 5; cycle_weight = 0.1, second_cycle_weight = 0.3)
5×5 Matrix{Float32}:
 0.0  0.3  0.0  0.0  0.1
 0.1  0.0  0.3  0.0  0.0
 0.0  0.1  0.0  0.3  0.0
 0.0  0.0  0.1  0.0  0.3
 0.3  0.0  0.0  0.1  0.0

Changing weights to custom arrays:

julia> cycle_weights = Float32[0.2, 0.4, 0.6, 0.8, 1.0];

julia> second_cycle_weights = -Float32[0.1, 0.3, 0.5, 0.7, 0.9];

julia> res_matrix = true_doublecycle(5, 5; cycle_weight = cycle_weights, second_cycle_weight = second_cycle_weights);

julia> size(res_matrix) == (5, 5) && eltype(res_matrix) == Float32 && count(!iszero, res_matrix) == 10
true

Changing sign of the weights with different sign patterns:

julia> res_matrix = true_doublecycle(5, 5; cycle_kwargs=(;signs = IrrationalDigitSigns()))
5×5 Matrix{Float32}:
  0.0  0.1   0.0   0.0  -0.1
 -0.1  0.0   0.1   0.0   0.0
  0.0  0.1   0.0   0.1   0.0
  0.0  0.0  -0.1   0.0   0.1
  0.1  0.0   0.0  -0.1   0.0

julia> res_matrix = true_doublecycle(5, 5; second_cycle_kwargs=(;signs = RandomSigns()))
5×5 Matrix{Float32}:
 0.0  -0.1  0.0   0.0  0.1
 0.1   0.0  0.1   0.0  0.0
 0.0   0.1  0.0  -0.1  0.0
 0.0   0.0  0.1   0.0  0.1
 0.1   0.0  0.0   0.1  0.0

Returning as sparse:

julia> res_matrix = true_doublecycle(5, 5; return_sparse=true)
5×5 SparseMatrixCSC{Float32, Int64} with 10 stored entries:
  ⋅   0.1   ⋅    ⋅   0.1
 0.1   ⋅   0.1   ⋅    ⋅
  ⋅   0.1   ⋅   0.1   ⋅
  ⋅    ⋅   0.1   ⋅   0.1
 0.1   ⋅    ⋅   0.1   ⋅
source

References