FastGRNNCell

FastGRNNCell(input_size => hidden_size, [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,
    init_zeta=1.0, init_nu=4.0)

Fast gated recurrent neural network cell.

Equations

\[\begin{aligned} \mathbf{z}(t) &= \sigma\left( \mathbf{W}_{ih} \mathbf{x}(t) + \mathbf{b}_{ih}^{z} + \mathbf{W}_{hh} \mathbf{h}(t-1) + \mathbf{b}_{hh}^{z} \right), \\ \tilde{\mathbf{h}}(t) &= \tanh\left( \mathbf{W}_{ih} \mathbf{x}(t) + \mathbf{b}_{ih}^{h} + \mathbf{W}_{hh} \mathbf{h}(t-1) + \mathbf{b}_{hh}^{h} \right), \\ \mathbf{h}(t) &= \left( \left( \sigma(\zeta) (1 - \mathbf{z}(t)) + \sigma(\nu) \right) \circ \tilde{\mathbf{h}}(t) \right) + \mathbf{z}(t) \circ \mathbf{h}(t-1) \end{aligned}\]

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.
• 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 $\mathbf{b}_{hh}^z, \mathbf{b}_{hh}^h$. 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_weight: Initializer for 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 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_zeta: initializer for the $\zeta$ learnable parameter. Default is 1.0.
• init_nu: initializer for the $\nu$ learnable parameter. Default is 4.0.

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 $\mathbf{W}_{ih}$.
• 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) $\{ \mathbf{b}_{ih}^z, \mathbf{b}_{ih}^h \}$ 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) $\{ \mathbf{b}_{hh}^z, \mathbf{b}_{hh}^h \}$ The initializers in init_bias are applied in the order they appear: the first function is used for $\mathbf{b}_{hh}^z$, and the second for $\mathbf{b}_{hh}^h$.
• hidden_state: Initial hidden state vector (not present if train_state=false)
• zeta: Learnable scalar to modulate candidate state.
• nu: Learnable scalar to modulate previous state.

States

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