Suppose we have a training set of 3 classes of image: 1.Cats, 2.Dogs, 3.Neither cats nor dogs. We're only really bothered about detecting whether an image is a cat/dog, or neither, but we don't care whether it's a cat or a dog, just that it's one of the two.
Is it inherently "better" to train a binary class CNN by merging the Dog and Cat classes into a single "positive" class rather than train a 3-class CNN?
If it is, does it then follow that if we did care about whether the image was a dog or cat, it would also be better to first run the binary classifier to decide if it was a dog/cat or not, then run a second binary classifier trained on just cats and dogs to decide which of the two it actually is?