chainer.functions.slstm(c_prev1, c_prev2, x1, x2)[source]

S-LSTM units as an activation function.

This function implements S-LSTM unit. It is an extension of LSTM unit applied to tree structures. The function is applied to binary trees. Each node has two child nodes. It gets four arguments, previous cell states c_prev1 and c_prev2, and input arrays x1 and x2.

First both input arrays x1 and x2 are split into eight arrays \(a_1, i_1, f_1, o_1\), and \(a_2, i_2, f_2, o_2\). They have the same shape along the second axis. It means that x1 and x2 ‘s second axis must have 4 times the length of c_prev1 and c_prev2.

The split input arrays are corresponding to:

  • \(a_i\) : sources of cell input

  • \(i_i\) : sources of input gate

  • \(f_i\) : sources of forget gate

  • \(o_i\) : sources of output gate

It computes the updated cell state c and the outgoing signal h as:

\[\begin{split}c &= \tanh(a_1 + a_2) \sigma(i_1 + i_2) + c_{\text{prev}1} \sigma(f_1) + c_{\text{prev}2} \sigma(f_2), \\ h &= \tanh(c) \sigma(o_1 + o_2),\end{split}\]

where \(\sigma\) is the elementwise sigmoid function. The function returns c and h as a tuple.

  • c_prev1 (Variable or N-dimensional array) – Variable that holds the previous cell state of the first child node. The cell state should be a zero array or the output of the previous call of LSTM.

  • c_prev2 (Variable or N-dimensional array) – Variable that holds the previous cell state of the second child node.

  • x1 (Variable or N-dimensional array) – Variable that holds the sources of cell input, input gate, forget gate and output gate from the first child node. It must have the second dimension whose size is four times of that of the cell state.

  • x2 (Variable or N-dimensional array) – Variable that holds the input sources from the second child node.


Two Variable objects c and h. c is the cell state. h indicates the outgoing signal.

Return type


See detail in paper: Long Short-Term Memory Over Tree Structures.


Assuming c1, c2 is the previous cell state of children, and h1, h2 is the previous outgoing signal from children. Each of c1, c2, h1 and h2 has n_units channels. Most typical preparation of x1, x2 is:

>>> n_units = 100
>>> h1 = chainer.Variable(np.zeros((1, n_units), np.float32))
>>> h2 = chainer.Variable(np.zeros((1, n_units), np.float32))
>>> c1 = chainer.Variable(np.zeros((1, n_units), np.float32))
>>> c2 = chainer.Variable(np.zeros((1, n_units), np.float32))
>>> model1 = chainer.Chain()
>>> with model1.init_scope():
...   model1.w = L.Linear(n_units, 4 * n_units)
...   model1.v = L.Linear(n_units, 4 * n_units)
>>> model2 = chainer.Chain()
>>> with model2.init_scope():
...   model2.w = L.Linear(n_units, 4 * n_units)
...   model2.v = L.Linear(n_units, 4 * n_units)
>>> x1 = model1.w(c1) + model1.v(h1)
>>> x2 = model2.w(c2) + model2.v(h2)
>>> c, h = F.slstm(c1, c2, x1, x2)

It corresponds to calculate the input array x1, or the input sources \(a_1, i_1, f_1, o_1\) from the previous cell state of first child node c1, and the previous outgoing signal from first child node h1. Different parameters are used for different kind of input sources.