Andrew Ilyas

And so what you'd expect, if that was your mental model,

what you would expect is for things to generally get worse as the projection dimension goes down, because you're progressively losing more and more information from these random projections.

What we find, though, is that there's actually sort of like this peaking behavior, where for a while, making the random projection smaller actually gets better and better, and then it starts getting worse.

And so what that indicates is that there's actually some non-compression effect of the random projections that we're doing.

They're adding something.

And so there's a lot of really interesting work out of a couple of groups in the statistics community that suggests that actually doing the influence function on randomly projected vectors is equivalent to doing some sort of regularized influence function on the original vectors.

And so there's some regularization element or something like that happening that we didn't originally account for when we were writing the track paper.

Yeah, so that's probably my favorite application from the track paper is that we took this data set, which is this brilliantly designed data set out of MIT.

I think Ekin Akurek is the lead author on that, of Jacob Andreas' group.

But they designed this really cool data set called Ftrace.

And the idea behind Ftrace is that they construct this artificial data set where you have a test set that contains a bunch of facts and a train set of Wikipedia abstracts.

And they have annotations for which abstracts entail which facts.

So for example, in your training set, if you have, you know, like France is a country whose capital is Paris, blah, blah, blah, blah, blah.

And then in your test set, it says like, what's the capital of France?

Paris.

Then like that would be labeled with a logical entailment.

And so the really nice thing about this data set is it sort of gives you this technique for evaluating different data attribution methods by saying, OK, if I take this test example where the test example says what's the capital of France, Paris, and I look at sort of like what the most important examples are for that test example, it should highlight the things that entail that fact.

Yeah, so in practice, what they found in their paper, which came out a while before TRACKT, is that an information retrieval system beat every single data attribution baseline they tried.

In particular, the data attribution

did not work well.