Explicitly initialize RNN/LSTM/GRU states

[gvtulder]

Description of changes:

The current from-scratch implementations of the RNN, LSTM and GRU do some complicated juggling with the initial states of the recurrent module.

Example for the current LSTM:

d2l-en/chapter_recurrent-modern/lstm.md

Lines 286 to 304 in f4432f3

	@d2l.add_to_class(LSTMScratch)
	def forward(self, inputs, H_C=None):
	H, C = None, None if H_C is None else H_C
	outputs = []
	for X in inputs:
	I = d2l.sigmoid(d2l.matmul(X, self.W_xi) + (
	d2l.matmul(H, self.W_hi) if H is not None else 0) + self.b_i)
	if H is None:
	H, C = d2l.zeros_like(I), d2l.zeros_like(I)
	F = d2l.sigmoid(d2l.matmul(X, self.W_xf) +
	d2l.matmul(H, self.W_hf) + self.b_f)
	O = d2l.sigmoid(d2l.matmul(X, self.W_xo) +
	d2l.matmul(H, self.W_ho) + self.b_o)
	C_tilde = d2l.tanh(d2l.matmul(X, self.W_xc) +
	d2l.matmul(H, self.W_hc) + self.b_c)
	C = F * C + I * C_tilde
	H = O * d2l.tanh(C)
	outputs.append(H)
	return outputs, (H, C)

While this is clever and avoids a little bit of code, it has a few downsides:

• The initial state is initialized inside the for loop, which requires an if H is None block that runs at every time step, but only does something in the first step of the RNN. From a good programming perspective, this if should be placed outside the loop.
• This lazy initialization obscures the fact that we need to initialize the state of the RNN to something before the first time step. I think this makes the model more difficult to understand than necessary. (For example, I had a discussion with a student where this initialization led to some confusion.)

With this pull request, I'd like to suggest some changes to initialize the states explicitly before the for loop. This requires one or two extra lines of code, but I think it would look cleaner and might make the models easier to follow.

Note that I added a self.num_hiddens to the RNN/LSTM/GRU classes. This is isn't absolutely necessary, you could also get this from the shape of the weights, but I think giving it a name might help.

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[d2l-bot]

Job d2l-en/PR-2314/1 is complete.
Check the results at http://preview.d2l.ai/d2l-en/PR-2314/

[astonzhang]

Thanks. I removed self.num_hiddens = num_hiddens because it's automatically done by self.save_hyperparameters()

[astonzhang]

@gvtulder We've added your name in our acknowledgement https://github.com/d2l-ai/d2l-en/blob/master/chapter_preface/index.md
Feel free to send another PR if there's any mistake in the name :)