No, the animal vectors are all fully spanned by the fifty attribute features.
Is this just saying that there’s superposition noise, so everything is spanning everything else? If so that doesn’t seem like it should conflict with being able to use a dictionary, dictionary learning should work with superposition noise as long as the interference doesn’t get too massive.
The animal features are sparse. The attribute features are not sparse.
If you mean that the attributes are a basis in the sense that the neurons are a basis, then I don’t see how you can say there’s a unique “label” direction for each animal that’s separate from the the underlying attributes such that you can set any arbitrary combination of attributes, including all attributes turned on at once or all turned off since they’re not sparse, and still read off the animal label without interference. It seems like that would be like saying that the elephant direction = [1, 0, −1], but you can change arbitrarily all 3 of those numbers to any other numbers and still be the elephant direction.
Is this just saying that there’s superposition noise, so everything is spanning everything else? If so that doesn’t seem like it should conflict with being able to use a dictionary, dictionary learning should work with superposition noise as long as the interference doesn’t get too massive.
If you mean that the attributes are a basis in the sense that the neurons are a basis, then I don’t see how you can say there’s a unique “label” direction for each animal that’s separate from the the underlying attributes such that you can set any arbitrary combination of attributes, including all attributes turned on at once or all turned off since they’re not sparse, and still read off the animal label without interference. It seems like that would be like saying that the elephant direction = [1, 0, −1], but you can change arbitrarily all 3 of those numbers to any other numbers and still be the elephant direction.