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"why do neural networks work better than other models?" That sounds really interesting - any references (for a non specialist)?

Do neural networks work better than other models? They can definitely model a wider class of problems than traditional ML models (images being the canonical example). However, I thought where a like for like comparison was possible they tend to worse than gradient boosting.

We’re in a strange era where the Information-Theoretic foundations of deep learning are solidifying. The 'Why' is largely solved: it’s the efficient minimization of irreversible information loss relative to the noise floor. There is so much waste scaling models bigger and bigger when the math points to how to do it much more efficiently. One can take a great 70B model and have it run in only ~16GB with no loss in capability and the ability to keep training, but the last few years funding only went for "bigger".

As you noted, the industry has moved the goalposts to Agency and Long-horizon Persistence. The transition from building 'calculators that predict' to 'systems that endure' is a non-equilibrium thermodynamics problem. There is math/formulas and basic laws at play here that apply to AI just as much as it applies to other systems. Ironically it is the same math. The same thing that results in a signal persisting in a model will result in agents persisting.

This is my specific niche. I study how things persist. It’s honestly a bit painful watching the AI field struggle to re-learn first principles that other disciplines have already learned. I have a doc I use to help teach folks how the math works and how to apply it to their domain and it is fun giving it folks who then stop guessing and know exactly how to improve the persistence of what they are working on. Like the idea of "How many hours we can have a model work" is so cute compared to the right questions.

In my opinion current research should focus on revisiting older concepts to figure out if they can be applied to transformers.

Transformers are superior "database" encodings as the hype about LLMs points out, but there have been promising ML models that were focusing on memory parts for their niche use cases, which could be promising concepts if we could make them work with attention matrixes and/or use the frequency projection idea on their neuron weights.

The way RNNs evolved to LSTMs, GRUs, and eventually DNCs was pretty interesting to me. In my own implementations and use cases I wasn't able to reproduce Deepmind's claims in the DNC memory related parts. Back at the time the "seeking heads" idea of attention matrixes wasn't there yet, maybe there's a way to build better read/write/access/etc gates now.

[1] a fairly good implementation I found: https://github.com/joergfranke/ADNC

> why do neural networks work better than other models

The only people for whom this is an open question are the academics - everyone else understands it's entirely because of the bagillions of parameters.

The inflection point was 2012, when AlexNet [0], a deep convolutional neural net, achieved a step-change improvement in the ImageNet classification competition.

After seeing AlexNet’s results, all of the major ML imaging labs switched to deep CNNs, and other approaches almost completely disappeared from SOTA imaging competitions. Over the next few years, deep neural networks took over in other ML domains as well.

The conventional wisdom is that it was the combination of (1) exponentially more compute than in earlier eras with (2) exponentially larger, high-quality datasets (e.g., the curated and hand-labeled ImageNet set) that finally allowed deep neural networks to shine.

The development of “attention” was particularly valuable in learning complex relationships among somewhat freely ordered sequential data like text, but I think most ML people now think of neural-network architectures as being, essentially, choices of tradeoffs that facilitate learning in one context or another when data and compute are in short supply, but not as being fundamental to learning. The “bitter lesson” [1] is that more compute and more data eventually beats better models that don’t scale.

Consider this: humans have on the order of 10^11 neurons in their body, dogs have 10^9, and mice have 10^7. What jumps out at me about those numbers is that they’re all big. Even a mouse needs hundreds of millions of neurons to do what a mouse does.

Intelligence, even of a limited sort, seems to emerge only after crossing a high threshold of compute capacity. Probably this has to do with the need for a lot of parameters to deal with the intrinsic complexity of a complex learning environment. (Mice and men both exist in the same physical reality.)

On the other hand, we know many simple techniques with low parameter counts that work well (or are even proved to be optimal) on simple or stylized problems. “Learning” and “intelligence”, in the way we use the words, tends to imply a complex environment, and complexity by its nature requires a large number of parameters to model.

0. https://en.wikipedia.org/wiki/AlexNet

1. https://en.wikipedia.org/wiki/Bitter_lesson

A much earlier major win for deep learning was AlexNet for image recognition in 2012. It dominated the competition and within a couple years it was effectively the only way to do image tasks. I think it was Jeremy Howard who wrote a paper around 2017 wondering when we’d get a transfer learning approach that worked as well for NLP as convnets did for images. The attention paper that year didn’t immediately dominate. The hardware wasn’t good enough and there wasn’t consensus on belief that scale would solve everything. It took like five more years before GPT3 took off and started this current wave.

I also think you might be discounting exactly how much compute is used to train these monsters. A single 1ghz processor would take about 100,000,000 years to train something in this class. Even with on the order of 25k GPUs training GPT3 size models takes a couple months. The anemic RAM on GPUs a decade ago (I think we had k80 GPUs with 12GB vs 100’s of GBs on H100/H200 today) and it was actually completely impossible to train a large transformer model prior to the early 2020s.

I’m even reminded how much gamers complained in the late 2010s about GPU prices skyrocketing because of ML use.

As others pointed out, the explosion of interest started with the deep convolutional networks that were applied in image problems. What I always thought was interesting was that prior to that, NNs were largely dismissed as interesting. When I took a course on them around the year 2000 that was the attitude most people took. It seems like what it took to spark renewed interest was ImageNet and seeing what you get when you have a ton of training data to throw at the problem and fast processors to help. After that the ball kept rolling with the subsequent developments around specific network architectures. In the broader community AlexNet is viewed as the big inflection point, but in the academic community you saw interest simmering a couple years earlier - I began to see more talks at workshops about NNs that weren’t being dismissed anymore, probably starting around 2008/09.

The same thing happened with matrices. We had matrices for 400 years, but the field of linear algebra and especially numerical linear algebra exploded only with advent of computers.

In olden days, the correct way to solve a linear system of equations was to use theory of minors. With advent of computers, you suddenly had a huge theory of gaussian elimination, or Krylov spaces and what not.

> I understand that deep learning is accelerated by GPUs but the concept of a transformer could have been used on much slower hardware much earlier

But they don't give the same results at those smaller scales. People imagined, but no one could have put into practice because the hardware wasn't there yet. Simplified, LLMs is basically Transformers with the additional idea of "and a shitton of data to learn from", and for making training feasible with that amount of data, you do need some capable hardware.

This video gives a great overview of the history of the acceleration:

https://youtu.be/glWvwvhZkQ8?si=-HGtfd_KHYfatEQ

Although it’s focused on Ilya, some great history is covered.

Without fast parallel hardware there would neither have been the incentive to design the Transformer, or much benefit even if someone had come up with the design all the same!

The incentive to design something new - which became the Transformer - came from language model researchers who had been working with recurrent models such as LSTMs, whose recurrent nature made them inefficient to train (needing BPPT), and wanted to come up with a new seq-2-seq/language model that could take advantage of the parallel hardware that now existed and (since AlexNet) was now being used to good effect for other types of model.

As I understand it, the inspiration for the concept of what would become the Transformer came from Attention paper co-author Jakob Uzkoreit who realized that language, while superficially appearing sequential (hence a good match for RNNs) was in fact really parallel + hierarchical as can be seen by linguist's sentence parse trees where different branches of the tree reflect parallel analysis of different parts of the sentence, which are then combined at higher levels of the hierarchical parse tree. This insight gave rise to the idea of a language model that mirrored this analytical structure with hierarchical layers of parallel processing, with the parallel processing being the whole point since this could be accelerated by GPUs. While the concept was Uzkoreit's, it took another researcher, Noam Shazeer, to take the concept and realize it as a performant architecture - the Transformer.

Without the fast parallel hardware already pre-existing, there would not have been any incentive to design a new type of language model to take advantage of it!

The other point is that while the Transformer is a very powerful general purpose and scalable type of model, it only really comes into it's own at scale. If a Transformer had somehow been designed in the pre-GPU-compute era, before the compute power to scale it up to massive size existed it, then it would likely not have appeared so promising/interesting.

The other aspect to the history is that neural networks, of various types, have evolved in complexity and sophistication over time. RNNs and LSTMs came first, then Bahdanau attention as a way to improve their context focus and performance. Attention was now seen to be a valuable part of language and seq-2-seq modelling, so when GPUs motivated the Transformer, attention was retained, recurrence ditched, and hence "Attention is all you need".

The time was right for the Transformer to appear when it did, designed to take advantage of recent GPU advances, building on top of this new attention architecture, and now with the compute power and dataset size available that it started to really shine when scaled from GPT-1 to GPT-2 size, and beyond.

The modern neural net revival got kicked off long before 2017.

Agreed, there is probably a theoretical world where we got enough money/compute together and had this explosion happen earlier.

Or perhaps a world where it happened later. I think a big part of what enabled the AI boom was the concentration of money and compute around the crypto boom.

Deep-learning hinges on highly redundant solution space (highly redundant weights), along with normalized weights (optimization methodology is commoditized). The original neural network work had no such concepts.

If you are in the radiology field it started “exploding” much earlier, with CNNs.

the concept of a transformer could have been used on much slower hardware much earlier.

It could have been done in the early 1970s -- see "Paper tape is all you need" at https://github.com/dbrll/ATTN-11 and the various C-64 projects that have been posted on HN -- but the problem was that Marvin Minsky "proved" that there was no way a perceptron-based network could do anything interesting. Funding dried up in a hurry after that.

Don't understimate the massive data you need to make those networks tick. Also, impracticable in slow training algorithms, beyond if they were in GPUs or CPUs.

> measure when a deep learning system is making stuff up or hallucinating

That's a great problem to solve! (Maybe biased, because this is my primary research direction). One popular approach is OOD detection, but this always seemed ill-posed to me. My colleagues and I have been approaching this from a more fundamental direction using measures of model misspecification, but this is admittedly niche because it is very computationally expensive. Could still be a while before a breakthrough comes from any direction.

There is an analogy with statistical mechanics. It's not crazy.

No

"Yeah, about that" - Gödel

tbf, we've learned (ha!) more from smashing teeny tiny particles and "looking" at what comes out than from say 40 years of string theory. Sometimes doing stuff works, and the theory (hopefully) follows.

This is the field of information geometry: https://en.wikipedia.org/wiki/Information_geometry

As I understand, Rice's theorem does not apply because neural networks are not Turing-complete.

It's actually really fascinating that there isn't a scientific theory of deep learning, especially as it's a product of human engineering as opposed to e.g. biology or particle physics.

This one is impressive too: https://arxiv.org/abs/2501.12948

The whole point about theory, though, is that simple rules can define complex phenomena. I don’t think anything you wrote fundamentally rules out the idea that we could find a theory of deep learning.