Carl Allen

How do tokens evolve as they are processed by a deep Transformer?

With José A. Carrillo, @gabrielpeyre.bsky.social and @pierreablin.bsky.social, we tackle this in our new preprint: A Unified Perspective on the Dynamics of Deep Transformers arxiv.org/abs/2501.18322

ML and PDE lovers, check it out!

Softmax is also the exact formula for a label distribution p(y|x) under Bayes rule if class distributions p(x|y) have exponential family form (equivariant if Gaussian), so it can have a deeper rationale in a probabilistic model of the data (than a one-hot relaxation).

Sorry, more a question re the OP. Just looking to understand the context.

Can you give some examples of the kind of papers you’re referring to?

And of course this all builds on the seminal work of @wellingmax.bsky.social, @dpkingma.bsky.social, Irina Higgins, Chris Burgess et al.

sorry, @benmpoole.bsky.social (fat fingers..)

Any constructive feedback, discussion or future collaboration more than welcome!

Full paper: arxiv.org/pdf/2410.22559

Building on this, we clarify the connection between diagonal covariance and Jacobian orthogonality and explain how disentanglement follows, ultimately defining disentanglement as factorising the data distribution into statistically independent components

We focus on VAEs, used as building blocks of SOTA diffusion models. Recent works by Rolinek et al. and Kumar & @benmpoole.bsy.social suggest that disentanglement arises because diagonal posterior covariance matrices promote column-orthogonality in the decoder’s Jacobian matrix.

While disentanglement is often linked to different models whose popularity may ebb & flow, we show that the phenomenon itself relates to the data’s latent structure and is more fundamental than any model that may expose it.

Machine learning has made incredible breakthroughs, but our theoretical understanding lags behind.

We take a step towards unravelling its mystery by explaining why the phenomenon of disentanglement arises in generative latent variable models.

Blog post: carl-allen.github.io/theory/2024/...

Maybe give it time. Rome, a day, etc..

Yup sure, the curve has to kick in at some point. I guess “law” sounds cooler than linear-ish graph. Maybe it started out as an acronym “Linear for A While”.. 🤷‍♂️

I guess as complexity increases math->phys->chem->bio->… It’s inevitable that “theory-driven” tends to “theory-inspired”. ML seems a bit tangential tho since experimenting is relatively consequence free and you don’t need to deeply theorise, more iterate. So theory is deprioritised and lags for now

But doesn’t theory follow empirics in all of science.. until it doesn’t? Except that in most sciences you can’t endlessly experiment for cost/risk/melting your face off reasons. But ML keeps going, making it a tricky moving/expanding target to try to explain/get ahead of.. I think it’ll happen tho.

The last KL is nice as it’s clear that the objective is optimised when the model and posteriors match as well as possible. The earlier KL is nice as it contains the data distribution and all explicitly modelled distributions, so maximising ELBO can be seen intuitively as bringing them all “in line”.

I think an intuitive view is that:
- max likelihood minimises
KL[p(x)||p’(x)] (p’(x)=model)

- max ELBO minimises
KL[p(x)q(z|x) || p’(x|z)p’(z)]
So brings together 2 models of the joint. (where p’(x)=\int p’(x|z)p’(z))

Can rearrange in diff ways, eg as
KL[p(x)q(z|x) || p’(x)p’(z|x)]
(or as in VAE)

Ha me too, exactly that..

(and here it comes.. ;) ). The latter view of classification is the motivation behind this work: scholar.google.co.uk/citations?vi...

In the binary case, both look the same: sigmoid might be a good model of how y becomes more likely (in future) as x increases. But sigmoid is also 2-case softmax so models Bayes rule for 2 classes of (exp-fam) x|y. The causality between x and y are very different, which "p(y|x)" doesn't capture.

I think this comes down to the model behind p(x,y). If features of x cause y, e.g. aspects of a website (x) -> clicks (y); age/health -> disease, then p(y|x) is a (regression) fn of x. But if x|y is a distrib'n of different y's (e.g. cats) then p(y|x) is given by Bayes rule (squint at softmax).

Pls add me thanks!

If few-shot transfer is ur thing!

Could you pls add me? Thanks!

Yep, could maybe work. The accepted-to-RR bar would need to be high to maintain value, but “shininess” test cld be deferred. Think there’s still a separate issue of “highly irresponsible” reviews that needs addressing either way (as at #CVPR2025). We can’t just whinge & doing absolutely nothing!

Definitely something to be said for RR, as main confs are effectively a lumpy version. But if acceptance to main confs is still the metric for recruiters etc, RR acceptance may not mean so much and the issue of the subjective criteria for what gets accepted to confs remains…?

You’d think that just the threat of it (& the occasional AC pointed reminder) would be enough to rarely, if ever, need to enforce it. If so, how much it’s used wouldn’t reflect success.
You’d maybe need a survey of review quality from authors/ACs… or an analysis of the anger on here! 🤬🤣

go.bsky.app/PFpnqeM

Some conferences already give free entry to top reviewers. But this prob just rewards those who would anyway give good reviews.

This is happening at #CVPR2025:
“If a reviewer is flagged by an AC as “highly irresponsible”, their paper submissions will be desk rejected per discretion of the PCs”.

Can’t see why all confs don’t do this, especially if making all authors review.

(pt 2) cvpr.thecvf.com/Conferences/...