ATRCell

ATRCell(in_dims => out_dims;
    use_bias=true, train_state=false, init_bias=nothing,
    init_recurrent_bias=nothing, init_weight=nothing,
    init_recurrent_weight=nothing, init_state=zeros32)

Addition-subtraction twin-gated recurrent cell.

Equations

\[\begin{aligned} \mathbf{p}(t) &= \mathbf{W}_{ih} \mathbf{x}(t) + \mathbf{b}_{ih}, \\ \mathbf{q}(t) &= \mathbf{W}_{ih} \mathbf{h}(t-1) + \mathbf{b}_{hh}, \\ \mathbf{i}(t) &= \sigma(\mathbf{p}(t) + \mathbf{q}(t)), \\ \mathbf{f}(t) &= \sigma(\mathbf{p}(t) - \mathbf{q}(t)), \\ \mathbf{h}(t) &= \mathbf{i}(t) \circ \mathbf{p}(t) + \mathbf{f}(t) \circ \mathbf{h}(t-1). \end{aligned}\]

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_weight: Initializer for input to hidden weights $\mathbf{W}_{ih}$. 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 recurrent 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_state: Initializer for hidden state. Default set to zeros32.
• init_memory: Initializer for memory. Default set to zeros32.

Inputs

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

Returns

• Tuple containing

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

• Updated model state

Parameters

• weight_ih: Concatenated weights to map from input to the hidden state $\mathbf{W}_{ih}$.
• weight_hh: Concatenated weights to map from hidden to the hidden state $\mathbf{W}_{hh}$.
• 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) $\mathbf{b}_{hh}$.
• hidden_state: Initial hidden state vector (not present if train_state=false)

States

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