selfloopdelaylinebackward

selfloop_delayline_backward([rng], [T], dims...;
    delay_weight=0.1, selfloop_weight=0.1, fb_weight=0.1,
    fb_shift=2, delya_shift=1, radius=nothing, return_sparse=false,
    fb_kwargs=(), selfloop_kwargs=(), delay_kwargs=())

Creates a reservoir based on a delay line with the addition of self loops and backward connections shifted by one (Elsarraj et al., 2019).

This architecture is referred to as TP3 in the original paper.

\[W_{i,j} = \begin{cases} ll, & \text{if } i = j \text{ for } i = 1 \dots N \\ r, & \text{if } j = i - 1 \text{ for } i = 2 \dots N \\ r, & \text{if } j = i - 2 \text{ for } i = 3 \dots N \\ 0, & \text{otherwise} \end{cases}\]

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

• delay_weight: Weight of the delay line 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 cycle you want to populate. Default is 0.1.

• selfloop_weight: Weight of the self loops 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 diagonal you want to populate. Default is 0.1.

• fb_weight: Weight of the feedback 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 diagonal you want to populate. Default is 0.1.

• fb_shift: How far the backward connection will be from the diagonal. Default is 1.

• delay_shift: delay line shift relative to the diagonal. Default is 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.

• delay_kwargs, selfloop_kwargs, and fb_kwargs: named tuples that control the kwargs for the weights generation. The kwargs are as follows:

  • signs: Controls sign flips. Use RandomSigns, RegularSigns, or IrrationalDigitSigns. Pass nothing to leave signs unchanged. Default is nothing.

Examples

Default call:

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

Changing weights:

julia> res_matrix = selfloop_delayline_backward(5, 5; selfloop_weight=0.3, fb_weight=0.99, delay_weight=-0.5)
5×5 Matrix{Float32}:
  0.3   0.0   0.99   0.0   0.0
 -0.5   0.3   0.0    0.99  0.0
  0.0  -0.5   0.3    0.0   0.99
  0.0   0.0  -0.5    0.3   0.0
  0.0   0.0   0.0   -0.5   0.3

Changing weights to custom arrays:

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

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

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

julia> res_matrix = selfloop_delayline_backward(5, 5;
           selfloop_weight = selfloop_weights, fb_weight = feedback_weights,
           delay_weight = delay_weights);

julia> size(res_matrix) == (5, 5) && eltype(res_matrix) == Float32 &&
       all(weight -> any(==(weight), diag(res_matrix)), selfloop_weights)
true

Changing sign of the weights with different sign patterns:

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

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

julia> res_matrix = selfloop_delayline_backward(5, 5; fb_kwargs=(;signs = RegularSigns()))
5×5 Matrix{Float32}:
 0.1  0.0  0.1   0.0  0.0
 0.1  0.1  0.0  -0.1  0.0
 0.0  0.1  0.1   0.0  0.1
 0.0  0.0  0.1   0.1  0.0
 0.0  0.0  0.0   0.1  0.1

Shifting the delay and the backward line:

julia> res_matrix = selfloop_delayline_backward(5, 5; delay_shift=3, fb_shift=2)
5×5 Matrix{Float32}:
 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
 0.0  0.1  0.0  0.0  0.1

Returning as sparse:

julia> using SparseArrays

julia> res_matrix = selfloop_delayline_backward(5, 5; return_sparse=true)
5×5 SparseMatrixCSC{Float32, Int64} with 12 stored entries:
 0.1   ⋅   0.1   ⋅    ⋅
 0.1  0.1   ⋅   0.1   ⋅
  ⋅   0.1  0.1   ⋅   0.1
  ⋅    ⋅   0.1  0.1   ⋅
  ⋅    ⋅    ⋅   0.1  0.1