coRNNCell

coRNNCell(in_dims => out_dims;
    use_bias=true, train_state=false, train_memory=false,
    init_bias=nothing, init_recurrent_bias=nothing, init_cell_bias=nothing,
    init_weight=nothing, init_recurrent_weight=nothing,
    init_cell_weight=nothing, init_state=zeros32, init_memory=zeros32,
    gamma=0.0, epsilon=0.0, dt=1.0)

Coupled oscillatory recurrent neural unit.

Equations

\[\begin{aligned} \mathbf{c}(t) &= \mathbf{c}(t-1) + \Delta t \, \sigma\left( \mathbf{W}_{ih} \mathbf{x}(t) + \mathbf{b}_{ih} + \mathbf{W}_{hh} \mathbf{h}(t-1) + \mathbf{b}_{hh} + \mathbf{W}_{ch} \mathbf{c}(t-1) + \mathbf{b}_{ch} \right) - \Delta t \, \gamma \, \mathbf{h}(t-1) - \Delta t \, \epsilon \, \mathbf{c}(t), \\ \mathbf{h}(t) &= \mathbf{h}(t-1) + \Delta t \, \mathbf{c}(t) \end{aligned}\]

Arguments

• in_dims: Input Dimension
• out_dims: Output (Hidden State & Memory) Dimension

Keyword Arguments

• use_bias: Flag to use bias in the computation. Default set to true.
• train_state: Flag to set the initial hidden state as trainable. Default set to false.
• train_memory: Flag to set the initial memory state as trainable. Default set to false.
• init_bias: Initializer for input to hidden bias $\mathbf{b}_{ih}$. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound] where bound = inv(sqrt(out_dims)). Default is nothing.
• init_recurrent_bias: Initializer for hidden to hidden bias $\mathbf{b}_{hh}$. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound] where bound = inv(sqrt(out_dims)). Default is nothing.
• init_cell_bias: Initializer for cell to hidden bias $\mathbf{b}_{ch}$. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound] where bound = inv(sqrt(out_dims)). Default is nothing.
• init_weight: Initializer for input to hidden weight $\mathbf{W}_{ih}$. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound] where bound = inv(sqrt(out_dims)). Default is nothing.
• init_recurrent_weight: Initializer for hidden to hidden weight $\mathbf{W}_{hh}$. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound] where bound = inv(sqrt(out_dims)). Default is nothing.
• init_cell_weight: Initializer for cell to hidden weight $\mathbf{W}_{ch}$. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound] where bound = inv(sqrt(out_dims)). Default is nothing.
• init_state: Initializer for hidden state. Default set to zeros32.
• init_memory: Initializer for memory. Default set to zeros32.
• dt: time step. Default is 1.0.
• gamma: Damping for state. Default is 0.0.
• epsilon: Damping for candidate state. Default is 0.0.

Inputs

• Case 1a: Only a single input x of shape (in_dims, batch_size), train_state is set to false, train_memory is set to false - Creates a hidden state using init_state, hidden memory using init_memory and proceeds to Case 2.
• Case 1b: Only a single input x of shape (in_dims, batch_size), train_state is set to true, train_memory is set to false - Repeats hidden_state vector from the parameters to match the shape of x, creates hidden memory using init_memory and proceeds to Case 2.
• Case 1c: Only a single input x of shape (in_dims, batch_size), train_state is set to false, train_memory is set to true - Creates a hidden state using init_state, repeats the memory vector from parameters to match the shape of x and proceeds to Case 2.
• Case 1d: Only a single input x of shape (in_dims, batch_size), train_state is set to true, train_memory is set to true - Repeats the hidden state and memory vectors from the parameters to match the shape of x and proceeds to Case 2.
• Case 2: Tuple (x, (h, c)) is provided, then the output and a tuple containing the updated hidden state and memory is returned.

Returns

• Tuple Containing

  • Output $h_{new}$ of shape (out_dims, batch_size)
  • Tuple containing new hidden state $h_{new}$ and new memory $c_{new}$

• Updated model state

Parameters

• weight_ih: Weights to map the input to the hidden state $\mathbf{W}_{ih}$.
• weight_hh: Weights to map the hidden state to the hidden state $\mathbf{W}_{hh}$.
• weight_ch: Weights to map the cell state to the hidden state $\mathbf{W}_{ch}$.
• bias_ih: Bias vector for the input-hidden connection (not present if use_bias=false) $\mathbf{b}_{ih}$
• bias_hh: Bias vector for the hidden-hidden connection (not present if use_bias=false) $\mathbf{b}_{hh}$
• bias_ch: Bias vector for the cell-hidden connection (not present if use_bias=false) $\mathbf{b}_{ch}$
• hidden_state: Initial hidden state vector (not present if train_state=false)
• memory: Initial memory vector (not present if train_memory=false)

States

• rng: Controls the randomness (if any) in the initial state generation