selfloopfeedbackcycle

selfloop_backward_cycle([rng], [T], dims...;
    cycle_weight=0.1, selfloop_weight=0.1,
    fb_weight = 0.1, radius=nothing, return_sparse=false)

Creates a cycle reservoir with feedback connections on even neurons and self loops on odd neurons (Elsarraj et al., 2019).

This architecture is referred to as TP2 in the original paper.

\[W_{i,j} = \begin{cases} r, & \text{if } j = i - 1 \text{ for } i = 2 \dots N \\ r, & \text{if } i = 1, j = N \\ ll, & \text{if } i = j \text{ and } i \text{ is odd} \\ r, & \text{if } j = i + 1 \text{ and } i \text{ is even}, i \neq N \\ 0, & \text{otherwise} \end{cases}\]

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

• cycle_weight: Weight of the cycle 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. Default is 0.1.
• fb_weight: Weight of the self loops 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.

Examples

julia> reservoir_matrix = selfloop_backward_cycle(5, 5)
5×5 Matrix{Float32}:
 0.1  0.1  0.0  0.0  0.1
 0.1  0.0  0.0  0.0  0.0
 0.0  0.1  0.1  0.1  0.0
 0.0  0.0  0.1  0.0  0.0
 0.0  0.0  0.0  0.1  0.1

julia> reservoir_matrix = selfloop_backward_cycle(5, 5; self_loop_weight=0.5)
5×5 Matrix{Float32}:
 0.5  0.1  0.0  0.0  0.1
 0.1  0.0  0.0  0.0  0.0
 0.0  0.1  0.5  0.1  0.0
 0.0  0.0  0.1  0.0  0.0
 0.0  0.0  0.0  0.1  0.5