LSTMCell

class brainpy.dyn.LSTMCell(num_in, num_out, Wi_initializer=XavierNormal(scale=1.0, mode=fan_avg, in_axis=-2, out_axis=-1, distribution=truncated_normal, rng=[3949182063 2081860855]), Wh_initializer=XavierNormal(scale=1.0, mode=fan_avg, in_axis=-2, out_axis=-1, distribution=truncated_normal, rng=[3949182063 2081860855]), b_initializer=ZeroInit, state_initializer=ZeroInit, activation='tanh', mode=None, train_state=False, name=None)

Long short-term memory (LSTM) RNN core.

The implementation is based on (zaremba, et al., 2014) [1]. Given \(x_t\) and the previous state \((h_{t-1}, c_{t-1})\) the core computes

\[\begin{split}\begin{array}{ll} i_t = \sigma(W_{ii} x_t + W_{hi} h_{t-1} + b_i) \\ f_t = \sigma(W_{if} x_t + W_{hf} h_{t-1} + b_f) \\ g_t = \tanh(W_{ig} x_t + W_{hg} h_{t-1} + b_g) \\ o_t = \sigma(W_{io} x_t + W_{ho} h_{t-1} + b_o) \\ c_t = f_t c_{t-1} + i_t g_t \\ h_t = o_t \tanh(c_t) \end{array}\end{split}\]

where \(i_t\), \(f_t\), \(o_t\) are input, forget and output gate activations, and \(g_t\) is a vector of cell updates.

The output is equal to the new hidden, \(h_t\).

Notes

Forget gate initialization: Following (Jozefowicz, et al., 2015) [2] we add 1.0 to \(b_f\) after initialization in order to reduce the scale of forgetting in the beginning of the training.

Parameters:

• num_in (int) – The dimension of the input vector

• num_out (int) – The number of hidden unit in the node.

• state_initializer (callable, Initializer, bm.ndarray, jax.numpy.ndarray) – The state initializer.

• Wi_initializer (callable, Initializer, bm.ndarray, jax.numpy.ndarray) – The input weight initializer.

• Wh_initializer (callable, Initializer, bm.ndarray, jax.numpy.ndarray) – The hidden weight initializer.

• b_initializer (optional, callable, Initializer, bm.ndarray, jax.numpy.ndarray) – The bias weight initializer.

• activation (str, callable) – The activation function. It can be a string or a callable function. See brainpy.math.activations for more details.

References

[1]

Zaremba, Wojciech, Ilya Sutskever, and Oriol Vinyals. “Recurrent neural network regularization.” arXiv preprint arXiv:1409.2329 (2014).

[2]

Jozefowicz, Rafal, Wojciech Zaremba, and Ilya Sutskever. “An empirical exploration of recurrent network architectures.” In International conference on machine learning, pp. 2342-2350. PMLR, 2015.

property c

Memory cell.

property h

Hidden state.

update(x)

The function to specify the updating rule.