UnICORNN

UnICORNN(input_size => hidden_size, [dt];
    alpha=0.0, return_state=false, init_kernel = glorot_uniform,
    init_recurrent_kernel = glorot_uniform, bias = true)

Undamped independent controlled oscillatory recurrent neural network (Rusch and Mishra, 18–24 Jul 2021). See UnICORNNCell for a layer that processes a single sequence.

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.
• return_state: Option to return the last state together with the output. Default is false.

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

unicornn(inp, (state, zstate))
unicornn(inp)

Arguments

• inp: The input to the unicornn. It should be a vector of size input_size x len or a matrix of size input_size x len x batch_size.
• (state, cstate): A tuple containing the hidden and cell states of the UnICORNN. 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

• New hidden states new_states as an array of size hidden_size x len x batch_size. When return_state = true it returns a tuple of the hidden stats new_states and the last state of the iteration.