WMCLSTMCell

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

Long short term memory cell with working memory connections.

Equations

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

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 biases $\mathbf{b}_{ih}^{i}, \mathbf{b}_{ih}^{f}, \mathbf{b}_{ih}^{c}, \mathbf{b}_{ih}^{o}$. Must be a tuple containing 4 functions. If a single value is passed, it is copied into a 4-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: the first initializes $\mathbf{b}_{ih}^{i}$, the second $\mathbf{b}_{ih}^{f}$, the third $\mathbf{b}_{ih}^{c}$, the fourth $\mathbf{b}_{ih}^{o}$. Default set to nothing.
• init_recurrent_bias: Initializer for hidden-to-hidden biases $\mathbf{b}_{hh}^{i}, \mathbf{b}_{hh}^{f}, \mathbf{b}_{hh}^{o}$. 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: the first initializes $\mathbf{b}_{hh}^{i}$, the second $\mathbf{b}_{hh}^{f}$, the third $\mathbf{b}_{hh}^{o}$. Default set to nothing.
• init_memory_bias: Initializer for memory-to-hidden biases $\mathbf{b}_{mh}^{i}, \mathbf{b}_{mh}^{f}, \mathbf{b}_{mh}^{o}$. 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: the first initializes $\mathbf{b}_{mh}^{i}$, the second $\mathbf{b}_{mh}^{f}$, the third $\mathbf{b}_{mh}^{o}$. Default set to nothing.
• init_weight: Initializer for input-to-hidden weights $\mathbf{W}_{ih}^{i}, \mathbf{W}_{ih}^{f}, \mathbf{W}_{ih}^{c}, \mathbf{W}_{ih}^{o}$. Must be a tuple containing 4 functions. If a single value is passed, it is copied into a 4-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: the first initializes $\mathbf{W}_{ih}^{i}$, the second $\mathbf{W}_{ih}^{f}$, the third $\mathbf{W}_{ih}^{c}$, the fourth $\mathbf{W}_{ih}^{o}$. Default set to nothing.
• init_recurrent_weight: Initializer for hidden-to-hidden weights $\mathbf{W}_{hh}^{i}, \mathbf{W}_{hh}^{f}, \mathbf{W}_{hh}^{o}$. 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: the first initializes $\mathbf{W}_{hh}^{i}$, the second $\mathbf{W}_{hh}^{f}$, the third $\mathbf{W}_{hh}^{o}$. Default set to nothing.
• init_memory_weight: Initializer for memory-to-hidden weights $\mathbf{W}_{mh}^{i}, \mathbf{W}_{mh}^{f}, \mathbf{W}_{mh}^{o}$. 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: the first initializes $\mathbf{W}_{mh}^{i}$, the second $\mathbf{W}_{mh}^{f}$, the third $\mathbf{W}_{mh}^{o}$. 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 to map from input space $\{ \mathbf{W}_{ih}^{f}, \mathbf{W}_{ih}^{c}, \mathbf{W}_{ih}^{i}, \mathbf{W}_{ih}^{o} \}$.
• weight_hh: Concatenated weights to map from hidden space $\{ \mathbf{W}_{hh}^{f}, \mathbf{W}_{hh}^{c}, \mathbf{W}_{hh}^{i}, \mathbf{W}_{hh}^{o} \}$.
• weight_mh: Concatenated weights to map from memory space $\{ \mathbf{W}_{mh}^{f}, \mathbf{W}_{mh}^{c}, \mathbf{W}_{mh}^{i} \}$.
• bias_ih: Concatenated bias vector for the input-hidden connection (not present if use_bias=false) $\{ \mathbf{b}_{ih}^{f}, \mathbf{b}_{ih}^{c}, \mathbf{b}_{ih}^{i}, \mathbf{b}_{ih}^{o} \}$.
• bias_hh: Concatenated bias vector for the hidden-hidden connection (not present if use_bias=false) $\{ \mathbf{b}_{hh}^{f}, \mathbf{b}_{hh}^{i}, \mathbf{b}_{hh}^{o} \}$.
• bias_mh: Concatenated bias vector for the memory-hidden connection (not present if use_bias=false) $\{ \mathbf{b}_{mh}^{f}, \mathbf{b}_{mh}^{i}, \mathbf{b}_{mh}^{o} \}$.
• 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