As you already know, the main culprit here is the large number of classes (50k). For every sample data, you have a label of size 50k. Even if a sample only belongs to a single class, the label will still be of size 50k.
For example, sample1 has a label of A and B while sample2 has a label of A. Sample3 on the other hand has C for its label and sample4 has A. We can visualize it like this:
sample1 - [1, 1, 0, 0, 0, 0, ..., 0]
sample2 - [1, 0, 0, 0, 0, 0, ..., 0]
sample3 - [0, 0, 1, 0, 0, 0, ..., 0]
sample4 - [1, 0, 0, 0, 0, 0, ..., 0]
One solution here is to use Siamese neural network. This takes in two input at a time. Instead of training directly to learn classes as the output, we are training to learn the similarity between two samples. We first select random pairs. We use the label 1 if two samples belong to the same class; else 0.
sample1 & sample2 - 1
sample1 & sample3 - 0
sample2 & sample4 - 1
sample3 & sample4 - 0
This way, even if there is a lot of classes, you are only training with 2 labels, 1 or 0, thus, avoiding memory error.
The problem now is that you are doing a multi-classification task. For instance, sample1 and sample 2 are the same class A but sample1 also belongs to class B. My suggestion, but I'm not totally sure here, is to add multiple instance of that pair.
sample1 & sample2 - 1
sample1 & sample2 - 0
sample1 & sample3 - 0
sample2 & sample4 - 1
sample3 & sample4 - 0
As for the large number of training samples (1 million), this can be handled by using small batches during training.
