Although the residuals for each of the four component matrices (after removing the first two principal components) are both small and seem to be noise, proving that there’s no structure that causes the noise to interact constructively when we multiply the matrices and “blow up” is hard.
Have you tried replacing what you believe is noise with actual random noise, with similar statistical properties, and then testing the performance of the resulting model? You may not be able to prove the original model is safe, but you can produce a model that has had all potential structure that you hypothesize is just noise replaced, where you know the noise hypothesis is true.
I believe what you describe is effectively Casual Scrubbing.
Edit: Note that it is not exactly the same as causal scrubbing, which picks looks at the activations for another input sampled at random.
On our particular model, doing this replacement shows us that the noise bound in our particular model is actually about 4 standard deviations worse than random, probably because the training procedure (sequences chosen uniformly at random) means we care a lot more about large possible maxes than small ones. (See Appendix H.1.2 for some very sparse details.)
On other toy models we’ve looked at (modular addition in particular, writeup forthcoming), we have (very) preliminary evidence suggesting that randomizing the noise has a steep drop-off in bound-tightness (as a function of how compact a proof the noise term comes from) in a very similar fashion to what we see with proofs. There seems to be a pretty narrow band of hypotheses for which the noise is structureless but we can’t prove it. This is supported by a handful of comments about how causal scrubbing indicates that many existing mech interp hypotheses in fact don’t capture enough of the behavior.
That sounds very promising, especially that in some cases you can demonstrate that it really is just noise, and in others it seems more like it’s behavior you don’t yet understand so looks like noise. and replacing it with noise degrades performance — that sounds like a very useful diagnostic.
Have you tried replacing what you believe is noise with actual random noise, with similar statistical properties, and then testing the performance of the resulting model? You may not be able to prove the original model is safe, but you can produce a model that has had all potential structure that you hypothesize is just noise replaced, where you know the noise hypothesis is true.
I believe what you describe is effectively Casual Scrubbing. Edit: Note that it is not exactly the same as causal scrubbing, which picks looks at the activations for another input sampled at random.
On our particular model, doing this replacement shows us that the noise bound in our particular model is actually about 4 standard deviations worse than random, probably because the training procedure (sequences chosen uniformly at random) means we care a lot more about large possible maxes than small ones. (See Appendix H.1.2 for some very sparse details.)
On other toy models we’ve looked at (modular addition in particular, writeup forthcoming), we have (very) preliminary evidence suggesting that randomizing the noise has a steep drop-off in bound-tightness (as a function of how compact a proof the noise term comes from) in a very similar fashion to what we see with proofs. There seems to be a pretty narrow band of hypotheses for which the noise is structureless but we can’t prove it. This is supported by a handful of comments about how causal scrubbing indicates that many existing mech interp hypotheses in fact don’t capture enough of the behavior.
That sounds very promising, especially that in some cases you can demonstrate that it really is just noise, and in others it seems more like it’s behavior you don’t yet understand so looks like noise. and replacing it with noise degrades performance — that sounds like a very useful diagnostic.