Nope. Try it out. If you attempt to split the activation vector into 1050 vectors for animals + attributes, you can’t get the dictionary activations to equal the feature activations ci(x), c′i(x).
Is the central point here that a given input will activate it’s representation in both the size 1000 and size 50 sub-dictionaries, meaning the reconstruction will be 2x too big?
If the animal specific features form an overcomplete basis, isn’t the set of animals + attributes just an even more overcomplete basis?
Nope. Try it out. If you attempt to split the activation vector into 1050 vectors for animals + attributes, you can’t get the dictionary activations to equal the feature activations ci(x), c′i(x).
Is the central point here that a given input will activate it’s representation in both the size 1000 and size 50 sub-dictionaries, meaning the reconstruction will be 2x too big?
Yes.