>And finally, there are already picture and video embeddings that are gradient-friendly and reusable.
I have been thinking about such things for a while and considered things like giving each of R rows and each of C columns a vector, and using the inner product of row_i and col_i as that pixel's intensity (in the simplest demonstrative case monochromatic, but reordering the floats in each vector before taking the inner product allows many more channels).
But this is just my quick shallow concoction. If I look at the konicq10k dataset, there are 10373 images 1024 x 768 totaling to 5.3GB. Thats ~511KB per image. 511KB / ( 1024 + 768 ) = 285 bytes for each row or column. Dividing by 4 for standard floats that gives each column and each row a vector of 71 (32-bit) floats. This would use absolutely no prior knowledge about human visual perception, so fitting these float vectors inner products (and their permutations for different channels) to the image by the most naive metric (average per pixel residual error) will probably not result in great images. But I'm curious how bad it performs. Perhaps I will try it out in a few hours.
Do you have any references for such or similar simplistic embeddings? I don't want to force you to dig for me, but if you happen to know of a few such papers or perhaps even a review paper that would be welcome!