What is the description of the custom LSTM cell used in the code?

[ritwikmishra]

I see that the code calls for a custom LSTM cell defined by

  def __call__(self, inputs, state, scope=None):
    """Long short-term memory cell (LSTM)."""
    with tf.variable_scope(scope or type(self).__name__):  # "CustomLSTMCell"
      c, h = state
      h *= self._dropout_mask
      concat = projection(tf.concat([inputs, h], 1), 3 * self.output_size, initializer=self._initializer)
      i, j, o = tf.split(concat, num_or_size_splits=3, axis=1)
      i = tf.sigmoid(i)
      new_c = (1 - i) * c  + i * tf.tanh(j)
      new_h = tf.tanh(new_c) * tf.sigmoid(o)
      new_state = tf.contrib.rnn.LSTMStateTuple(new_c, new_h)
      return new_h, new_state

Equations of LSTM are:

i = sigmoid(x_t * U^i + h_{t-1} * W^i ) # input_gate_t
f = sigmoid(x_t * U^f + h_{t-1} * W^f ) # forget_gate_t
o = sigmoid(x_t * U^o + h_{t-1} * W^o ) # output_gate_t

new_c = f * c + i * tanh(x_t * U^g + h_{t-1} * W^g)
new_h = o * tanh(new_c)

Then why new_c is different in the code?

Why f (forget_gate) equals to 1 - i (1 minus input_gate) ?

Why x_t * U^g + h_{t-1} * W^g equals to forget_gate ?