3 ms·

> We can do this by computing the projection of c out onto ^r, and then subtracting this projection away That looks exactly equivalent to multiplying by a matr

by amluto 3y ago

> We can do this by computing the projection of c out onto ^r, and then subtracting this projection away That looks exactly equivalent to multiplying by a matrix that nulls out that vector and preserves everything else. (This is trivial linear algebra!) One could presumably multiply such a matrix into the model weights to get exactly the same effect, and then one could run the model using any inference engine. Of course, the project-and-subtract formulation is faster for each projection, and one could premultiply the matrices by projecting-and-subtracting each row or column (depending on which side one wants to multiply on) using the project-and-subtract trick. This would make computing the new weights very fast, even with a slow CPU and no GPU.

HanClinto 3y ago
> That looks exactly equivalent to multiplying by a matrix that nulls out that vector and preserves everything else. (This is trivial linear algebra!) One could presumably multiply such a matrix into the model weights to get exactly the same effect, and then one could run the model using any inference engine. Oh fascinating -- so almost like LoRa weight-adjustment being added to a fully trained model after-the-fact?
- amluto 3y ago
  It’s certainly a low rank fine-tune — the weight difference would be rank 1! But I think it’s more useful to think of it as a multiplicative change, not an additive change.
  - HanClinto 3y ago
    Nice, thank you! You're adding to my reading list, and I appreciate that! :) I'm still mulling over how difficult it would be to reimplement this with "stock" llama.cpp. It feels like the first step would be to essentially get the "super-embeddings" for each prompt -- instead of grabbing just the text embeddings (which I understand is usually only the narrowest layer?) -- we would want to store off the activations for every layer. Then save them all to a list, average them together, and then figure out a way to use that to modify the weights of the model -- either at runtime (I imagine this much like a current guidance-vector would be loaded), or else (as you suggested) write a script to bake the modifications into the core model (but using multiplication rather than addition). Does that match your understanding? Thank you very much for helping me think this through!

by amluto 3y ago

HanClinto 3y ago

> That looks exactly equivalent to multiplying by a matrix that nulls out that vector and preserves everything else. (This is trivial linear algebra!) One could presumably multiply such a matrix into the model weights to get exactly the same effect, and then one could run the model using any inference engine. Oh fascinating -- so almost like LoRa weight-adjustment being added to a fully trained model after-the-fact?

amluto 3y ago
It’s certainly a low rank fine-tune — the weight difference would be rank 1! But I think it’s more useful to think of it as a multiplicative change, not an additive change.
- HanClinto 3y ago
  Nice, thank you! You're adding to my reading list, and I appreciate that! :) I'm still mulling over how difficult it would be to reimplement this with "stock" llama.cpp. It feels like the first step would be to essentially get the "super-embeddings" for each prompt -- instead of grabbing just the text embeddings (which I understand is usually only the narrowest layer?) -- we would want to store off the activations for every layer. Then save them all to a list, average them together, and then figure out a way to use that to modify the weights of the model -- either at runtime (I imagine this much like a current guidance-vector would be loaded), or else (as you suggested) write a script to bake the modifications into the core model (but using multiplication rather than addition). Does that match your understanding? Thank you very much for helping me think this through!