Implementation of `torchdeq.utils.mixed_init` different from original paper

[jklim01]

From the paper:
"we experimented with initializing the hidden states with zeros on half of the examples in the batch, and with standard Gaussian noise on the rest of the examples"

"Mixed initialization: During each training forward pass, each sample was assigned with either zero initialization (i.e. the fixed point was initialized with the 0 vector) or standard normal distribution (i.e. ...) using a Bernoulli random variable of probability 0.5 (i.e. the examples that were run with zero vs. normal initializations were roughly half-half."

Current implementation:

torchdeq/torchdeq/utils/init.py

Lines 4 to 21 in 4f6bd5f

	def mixed_init(z_shape, device=None):
	"""
	Initializes a tensor with a shape of `z_shape` with half Gaussian random values and hald zeros.
	Proposed in the paper, `Path Independent Equilibrium Models Can Better Exploit Test-Time Computation <https://arxiv.org/abs/2211.09961>`_,
	for better path independence.
	Args:
	z_shape (tuple): Shape of the tensor to be initialized.
	device (torch.device, optional): The desired device of returned tensor. Default None.
	Returns:
	torch.Tensor: A tensor of shape `z_shape` with values randomly initialized and zero masked.
	"""
	z_init = torch.randn(*z_shape, device=device)
	mask = torch.zeros_like(z_init, device=device).bernoulli_(0.5)
	return z_init * mask

It seems more appropriate to do this instead to match the paper.

*mask_shape, _ = z_shape
mask = torch.empty(*mask_shape, device=device).bernoulli_(0.5).unsqueeze(-1)

This form has the disadvantage of assuming that all but the last dimension are batch dimensions. But this seems to be quite a reasonable assumption, and downstream users can easily adjust to this by reshaping and rearranging the dimensions.