neverix

1mo30

From a conversation on Discord:

Do you have in mind a way to weigh sequential learning into the actual prior?

Dmitry:

good question! We haven't thought about an explicit complexity measure that would give this prior, but a very loose approximation that we've been keeping in the back of our minds could be a Turing machine/Boolean circuit version of the "BIMT" weight penalty from this paper https://arxiv.org/abs/2305.08746 (which they show encourages modularity at least in toy models)

Response:

Hmm, BIMT seems to only be about intra-layer locality. It would certainly encourage learning an ensemble of features, but I'm not sure if it would capture the interesting bit, which I think is the fact that features are built up sequentially from earlier to later layers and changes are only accepted if they improve local loss.

I'm thinking about something like an existence of a relatively smooth scaling law (?) as the criterion.

So, just some smoothness constraint that would basically integrate over paths SGD could take.

2mo10

You could literally go through some giant corpus with an LLM and see which samples have gradients similar to those from training on a spelling task.

4mo10

There are also somewhat principled reasons for using a "fuzzy ellipsoid", which I won't explain here.

If you view as 2x learning rate, the ellipsoid contains parameters which will jump straight into the basin under the quadratic approximation, and we assume for points outside the basin the approximation breaks entirely. If you account for gradient noise ~~in the form of a Gaussian with sigma equal to gradient, the PDF of the resulting point at the basin is equal to the probability a Gaussian parametrized by the ellipsoid at the preceding point.~~ This is wrong, but there is an interpretation of the noise as a Gaussian with variance increasing away from the basin origin.

Seems like quoting doesn't work for LaTeX, it was definitions 2/3. Reading again I saw D2 was indeed applicable to sets.

5moΩ020

A0>A1

How is orbit comparison for sets defined?

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7mo21

This is the whole point of goal misgeneralization. They have experiments (albeit on toy environments that can be explained by the network finding the wrong algorithm), so I'd say quite plausible.

Also related is https://arxiv.org/abs/2210.10960. They use a small neural network to generate steering vectors for the UNet bottleneck in diffusion to edit images using CLIP.