I've ran into this multiple times, each time reason was labels are not between 0 and 1

The reason that you are seeing this is because nn.CrossEntropyLoss accepts logits and targets, a.k.a X should be logits, but is already between 0 and 1. X should be much bigger, because after softmax it will go between 0 and 1.

ce_loss(X * 1000, torch.argmax(X,dim=1)) # tensor(0.)

nn.CrossEntropyLoss works with logits, to make use of the log sum trick.

The way you are currently trying after it gets activated, your predictions become about [0.73, 0.26].

Binary cross entropy example works since it accepts already activated logits. By the way, you probably want to use nn.Sigmoid for activating binary cross entropy logits. For the 2-class example, softmax is also ok.

is there an equivalent PyTorch loss function for TensorFlow's softmax_cross_entropy_with_logits?

torch.nn.functional.cross_entropy

This takes logits as inputs (performing log_softmax internally). Here "logits" are just some values that are not probabilities (i.e. not necessarily in the interval [0,1]).

But, logits are also the values that will be converted to probabilities. If you consider the name of the tensorflow function you will understand it is pleonasm (since the with_logits part assumes softmax will be called).

In the PyTorch implementation looks like this:

loss = F.cross_entropy(x, target)

Which is equivalent to :

lp = F.log_softmax(x, dim=-1)
loss = F.nll_loss(lp, target)

It is not F.binary_cross_entropy_with_logits because this function assumes multi label classification:

F.sigmoid + F.binary_cross_entropy = F.binary_cross_entropy_with_logits

It is not torch.nn.functional.nll_loss either because this function takes log-probabilities (after log_softmax()) not logits.

The loss of a single sample is the sum of the $J$ nodes' predictions, so for each sample, the loss is a scalar value.

The expression $-\sum_j^J y_j \log p_j$ has only one nonzero term, because only one element of $y$ is nonzero. This is the correct loss for a classification problem; we can prove that this is correct by writing out the likelihood of the categorical distribution and taking the negative of its logarithm to get the cross-entropy. It's merely a special case that we can re-write the binary classification problem in terms of one probability $p$ and one binary label $y$ in the convenient form $-y \log p - (1-y)\log (1-p)$.

Let's write out a concrete example. We have predictions $[0.4,0.3,0.2]$ and label $[1,0,0]$. By inspection, we know that the loss is $-\log(0.4)$ because this is the only entry with a nonzero label.