GatedAntisymmetricRNNCell

GatedAntisymmetricRNNCell(in_dims => out_dims, [activation];
    use_bias=true, use_recurrent_bias=true,
    train_state=false, init_bias=nothing,
    init_recurrent_bias=nothing, init_weight=nothing,
    init_recurrent_weight=nothing, init_state=zeros32,
    epsilon=1.0, gamma=0.0)

Antisymmetric recurrent cell with gating.

Equations

\[\begin{aligned} \mathbf{z}(t) &= \sigma\left( (\mathbf{W}_{hh} - \mathbf{W}_{hh}^\top - \gamma \cdot \mathbf{I}) \mathbf{h}(t-1) + \mathbf{b}_{hh} + \mathbf{W}_{ih}^z \mathbf{x}(t) + \mathbf{b}_{ih}^z \right), \\ \mathbf{h}(t) &= \mathbf{h}(t-1) + \epsilon \cdot \mathbf{z}(t) \circ \tanh\left( (\mathbf{W}_{hh} - \mathbf{W}_{hh}^\top - \gamma \cdot \mathbf{I}) \mathbf{h}(t-1) + \mathbf{b}_{hh} + \mathbf{W}_{ih}^x \mathbf{x}(t) + \mathbf{b}_{ih}^h \right). \end{aligned}\]

Arguments

• in_dims: Input Dimension
• out_dims: Output (Hidden State & Memory) Dimension
• activation: activation function. Default is tanh

Keyword arguments

• use_bias: Flag to use bias $\mathbf{b}_{ih}$ in the computation. Default set to true.
• use_recurrent_bias: Flag to use recurrent bias $\mathbf{b}_{hh}$ in the computation. Default set to true.
• use_recurrent_bias: Flag to use recurrent bias $\mathbf{b}_{hh}$ in the computation. Default set to true.
• train_state: Flag to set the initial hidden state as trainable. Default set to false.
• init_bias: Initializer for input to hidden bias $\mathbf{b}_{ih}^z, \mathbf{b}_{ih}^h$. Must be a tuple containing 2 functions, e.g., (glorot_normal, kaiming_uniform). If a single function fn is provided, it is automatically expanded into a 2-element tuple (fn, fn). 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 $\mathbf{W}_{ih}^z, \mathbf{W}_{ih}^x$. Must be a tuple containing 2 functions, e.g., (glorot_normal, kaiming_uniform). If a single function fn is provided, it is automatically expanded into a 2-element tuple (fn, fn). 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.
• epsilon: step size. Default is 1.0.
• gamma: strength of diffusion. Default is 0.0.

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. $\{ \mathbf{W}_{ih}^z, \mathbf{W}_{ih}^h \}$ The initializers in init_weight are applied in the order they appear: the first function is used for $\mathbf{W}_{ih}^z$, and the second for $\mathbf{W}_{ih}^h$.
• weight_hh: Weights to map the hidden state to the hidden state $\mathbf{W}_{hh}$.
• bias_ih: Bias vector for the input-hidden connection (not present if use_bias=false) $\{ \mathbf{b}_{ih}^z, \mathbf{b}_{ih}^h \}$ The initializers in init_bias are applied in the order they appear: the first function is used for $\mathbf{b}_{ih}^z$, and the second for $\mathbf{b}_{ih}^h$.
• 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