TLSTMCell

TLSTMCell(in_dims => out_dims;
    use_bias=true, use_recurrent_bias=true,
    train_state=false, train_memory=false,
    init_bias=nothing, init_recurrent_bias=nothing,
    init_weight=nothing, init_recurrent_weight=nothing,
    init_state=zeros32, init_memory=zeros32)

Strongly typed long short term memory cell.

Equations

\[\begin{aligned} \mathbf{z}(t) &= \mathbf{W}_{mh}^{z} \mathbf{x}(t{-}1) + \mathbf{b}_{mh}^{z} + \mathbf{W}_{ih}^{z} \mathbf{x}(t) + \mathbf{b}_{ih}^{z} \\ \mathbf{f}(t) &= \sigma\left( \mathbf{W}_{mh}^{f} \mathbf{x}(t{-}1) + \mathbf{b}_{mh}^{f} + \mathbf{W}_{ih}^{f} \mathbf{x}(t) + \mathbf{b}_{ih}^{f} \right) \\ \mathbf{o}(t) &= \tau\left( \mathbf{W}_{mh}^{o} \mathbf{x}(t{-}1) + \mathbf{b}_{mh}^{o} + \mathbf{W}_{ih}^{o} \mathbf{x}(t) + \mathbf{b}_{ih}^{o} \right) \\ \mathbf{c}(t) &= \mathbf{f}(t) \circ \mathbf{c}(t{-}1) + \left(1 - \mathbf{f}(t)\right) \circ \mathbf{z}(t) \\ \mathbf{h}(t) &= \mathbf{c}(t) \circ \mathbf{o}(t) \end{aligned}\]

Arguments

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

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.
• train_memory: Flag to set the initial memory state as trainable. Default set to false.
• init_bias: Initializer for input-to-hidden biases $\mathbf{b}_{ih}^{z}, \mathbf{b}_{ih}^{f}, \mathbf{b}_{ih}^{o}$. Must be a tuple containing 3 functions. If a single value is passed, it is copied into a 3-element tuple. If set to nothing, biases are initialized from a uniform distribution within [-bound, bound], where bound = \mathrm{inv}(\sqrt{\mathrm{out\_dims}}). The functions are applied in order to initialize $\mathbf{b}_{ih}^{z}$, $\mathbf{b}_{ih}^{f}$, \mathbf{b}_{ih}^{o}$. Default set to nothing.
• init_recurrent_bias: Initializer for memory-to-hidden biases $\mathbf{b}_{mh}^{z}, \mathbf{b}_{mh}^{f}, \mathbf{b}_{mh}^{o}$. Must be a tuple containing 3 functions. If a single value is passed, it is copied into a 3-element tuple. If set to nothing, biases are initialized from a uniform distribution within [-bound, bound], where bound = \mathrm{inv}(\sqrt{\mathrm{out\_dims}}). The functions are applied in order to initialize $\mathbf{b}_{mh}^{z}$, $\mathbf{b}_{mh}^{f}$, \mathbf{b}_{mh}^{o}$. Default set to nothing.
• init_weight: Initializer for input-to-hidden weights $\mathbf{W}_{ih}^{z}, \mathbf{W}_{ih}^{f}, \mathbf{W}_{ih}^{o}$. Must be a tuple containing 3 functions. If a single value is passed, it is copied into a 3-element tuple. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound], where bound = \mathrm{inv}(\sqrt{\mathrm{out\_dims}}). The functions are applied in order to initialize $\mathbf{W}_{ih}^{z}$, $\mathbf{W}_{ih}^{f}$, \mathbf{W}_{ih}^{o}$. Default set to nothing.
• init_recurrent_weight: Initializer for memory-to-hidden weights $\mathbf{W}_{mh}^{z}, \mathbf{W}_{mh}^{f}, \mathbf{W}_{mh}^{o}$. Must be a tuple containing 3 functions. If a single value is passed, it is copied into a 3-element tuple. If set to nothing, weights are initialized from a uniform distribution within [-bound, bound], where bound = \mathrm{inv}(\sqrt{\mathrm{out\_dims}}). The functions are applied in order to initialize $\mathbf{W}_{mh}^{z}$, $\mathbf{W}_{mh}^{f}$, \mathbf{W}_{mh}^{o}$. Default set to 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, 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: Concatenated weights for input-to-hidden transformations $\{ \mathbf{W}_{ih}^{z}, \mathbf{W}_{ih}^{f}, \mathbf{W}_{ih}^{o} \}$.
• weight_mh: Concatenated weights for memory-to-hidden transformations $\{ \mathbf{W}_{mh}^{z}, \mathbf{W}_{mh}^{f}, \mathbf{W}_{mh}^{o} \}$.
• bias_ih: Concatenated bias vector for input-to-hidden transformations $\{ \mathbf{b}_{ih}^{z}, \mathbf{b}_{ih}^{f}, \mathbf{b}_{ih}^{o} \}$. Not present if use_bias = false.
• bias_mh: Concatenated bias vector for memory-to-hidden transformations $\{ \mathbf{b}_{mh}^{z}, \mathbf{b}_{mh}^{f}, \mathbf{b}_{mh}^{o} \}$. Not present if use_bias = false.
• hidden_state: Initial hidden state vector. Not present if train_state = false.
• memory: Initial memory state vector. Not present if train_memory = false.

States

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