UnICORNNCell

UnICORNNCell(input_size => hidden_size, [dt];
    alpha=0.0, init_kernel = glorot_uniform,
    init_recurrent_kernel = glorot_uniform,
    init_control_kernel = glorot_uniform,
    bias = true, recurrent_bias = true,
    independent_recurrence = false, integration_mode = :addition)

Undamped independent controlled oscillatory recurrent neural unit (Rusch and Mishra, 18–24 Jul 2021). See UnICORNN for a layer that processes entire sequences.

Arguments

• input_size => hidden_size: input and inner dimension of the layer.
• dt: time step. Default is 1.0.

Keyword arguments

• alpha: Control parameter. Default is 0.0.
• init_kernel: initializer for the input to hidden weights. Default is glorot_uniform.
• init_recurrent_kernel: initializer for the hidden to hidden weights. Default is glorot_uniform.
• init_control_kernel: initializer for the control to hidden weights. Default is glorot_uniform.
• bias: include input to recurrent bias or not. Default is true.
• recurrent_bias: include recurrent to recurrent bias or not. Default is true.
• independent_recurrence: flag to toggle independent recurrence. If true, the recurrent to recurrent weights are a vector instead of a matrix. Default false.
• integration_mode: determines how the input and hidden projections are combined. The options are :addition and :multiplicative_integration. Defaults to :addition.

Equations

\[\begin{aligned} \mathbf{z}(t) &= \mathbf{z}(t-1) - \Delta t \, \hat{\sigma}(\mathbf{c}) \odot \left[ \sigma\left( \mathbf{w} \odot \mathbf{h}(t-1) + \mathbf{W}_{ih} \mathbf{x}(t) + \mathbf{b} \right) + \alpha \, \mathbf{h}(t-1) \right] \\ \mathbf{h}(t) &= \mathbf{h}(t-1) + \Delta t \, \hat{\sigma}(\mathbf{c}) \odot \mathbf{z}(t) \end{aligned}\]

Forward

unicornncell(inp, (state, cstate))
unicornncell(inp)

Arguments

• inp: The input to the unicornncell. It should be a vector of size input_size or a matrix of size input_size x batch_size.
• (state, cstate): A tuple containing the hidden and cell states of the UnICORNNCell. They should be vectors of size hidden_size or matrices of size hidden_size x batch_size. If not provided, they are assumed to be vectors of zeros, initialized by Flux.initialstates.

Returns

• A tuple (output, state), where output = new_state is the new hidden state and state = (new_state, new_cstate) is the new hidden and cell state. They are tensors of size hidden_size or hidden_size x batch_size.