Understand how transformers work by demystifying the math behind them • Hacker News Board

Re: Understand how transformers work by demystifying the math behind them

#111

Post by ActorNightly » Thu, Jan 04, 2024, 7:22 PM UTC

logicchains wrote: post #79

ActorNightly wrote: post #6

The whole "mystery" of transformer is that instead of a linear sequence of static weights times values in each layer, you now have 3 different matrices that are obtained from the same input through multiplication of learned weights, and then you just multiply the matrices together. I.e more parallelism which works out nice, but very restrictive since the attention formula is static. We arent going to see more progres…

>The whole "mystery" of transformer is that instead of a linear sequence of static weights times values in each layer, you now have 3 different matrices that are obtained from the same input through multiplication of learned weights, and then you just multiply the matrices together. I.e more parallelism which works out nice, but very restrictive since the attention formula is static. That's not it at all. What's spec…

>What's special about transformers is they allow each element in a sequence to decide which parts of data are most important to it from each other element in the sequence, then extract those out and compute on them.

They do that in theory. In practice, its just all matrix multiplication. You could easily structure a transformer as a bunch of fully connected deep layers and it would be mathematically equivalent, just computationally inefficient.

Re: Understand how transformers work by demystifying the math behind them

#112

Post by ActorNightly » Thu, Jan 04, 2024, 7:27 PM UTC

p1esk wrote: post #66

ActorNightly wrote: post #46

Earlier quoted context omitted.

We have made progress in efficiency, not functionality. Instead of searching google or stack overflow or any particular documentation, we just go to Chatgpt. Information compression is cool, but I want actual AI.

Fascinating. What’s “actual AI”?

Something that can reason and figure things out without having ever been exposed to the information during training.

Re: Understand how transformers work by demystifying the math behind them

#113

Post by ActorNightly » Thu, Jan 04, 2024, 7:33 PM UTC

beambot wrote: post #48

ActorNightly wrote: post #33

Earlier quoted context omitted.

The issue is not having access to the cpu, the issue is that the model being able to be trained in such a way that it has representative structures for applicable problem solving. Furthermore, the structures itself should Philosophically, you can start ad hoc-ing functionalities on top of LLMs and expect major progress. Sure, you can make them better, but you will never get to the state where AI is massively useful.…

> Philosophically, you can start ad hoc-ing functionalities on top of LLMs and expect major progress. Sure, you can make them better, but you will never get to the state where AI is massively useful. Evolution created various neural structures in biological brains (visual cortex, medulla, thalamus, etc) rather ad-hoc, and those resulted in "massively useful" systems. Why should AI be different?

I mean, we could definitely run architectures through simulated evolution with genetic algorithms, but then you arrive at the same problem as humans do, which is that you end up with a statistically best solution for given conditions. Sure, that could be a form of AI but there is likely a better (and likely faster) way to build an AI that isn't fundamentally statistical in nature and is adaptable to any and all problems.

Re: Understand how transformers work by demystifying the math behind them

#114

Post by p1esk » Thu, Jan 04, 2024, 8:16 PM UTC

ActorNightly wrote: post #112

p1esk wrote: post #66

Earlier quoted context omitted.

Fascinating. What’s “actual AI”?

Something that can reason and figure things out without having ever been exposed to the information during training.

This either includes GPT-4 or excludes people

Re: Understand how transformers work by demystifying the math behind them

#115

Post by ActorNightly » Thu, Jan 04, 2024, 8:21 PM UTC

knightoffaith wrote: post #108

blackbear_ wrote: post #92

Earlier quoted context omitted.

Perhaps in a way similar to this paper: https://arxiv.org/abs/1806.09055

I wonder why this hasn't taken off.

From brief look at the paper, they are doing a gradient descent of the architecture based on validation loss, which does good for efficiency, but its not ground breaking. The problem is that you are still training towards a target of a correct answer. I don't think this is gonna be applicable in the future, in the sense that we have to train on other things (like logical consistency somehow encoded into the network), as well as correct answers.

Re: Understand how transformers work by demystifying the math behind them

#116

Post by ActorNightly » Thu, Jan 04, 2024, 8:42 PM UTC

danielmarkbruce wrote: post #50

ActorNightly wrote: post #46

Earlier quoted context omitted.

We have made progress in efficiency, not functionality. Instead of searching google or stack overflow or any particular documentation, we just go to Chatgpt. Information compression is cool, but I want actual AI.

The idea that there has been no progress in functionality is silly. Your whole brain might just be doing "information compression" by that analogy. An LLM is sort of learning concepts. Even Word2Vec "learned" than king - male + female = queen and that's a small model that's really just one part (not exact, but similar) of a transformer.

Let me rephrase that.

One level deep information compression is cool, but I want actual AI.

Its true that our brains compress information, but we compress it in a much more complex manner, in the sense that we can not only recall stuff, but also execute a decision tree that often involves physical actions to find the answer we are looking for.

Re: Understand how transformers work by demystifying the math behind them

#117

Post by enriquto » Thu, Jan 04, 2024, 8:44 PM UTC

knightoffaith wrote: post #47

ActorNightly wrote: post #6

The whole "mystery" of transformer is that instead of a linear sequence of static weights times values in each layer, you now have 3 different matrices that are obtained from the same input through multiplication of learned weights, and then you just multiply the matrices together. I.e more parallelism which works out nice, but very restrictive since the attention formula is static. We arent going to see more progres…

How can gradient descent work on compute graphs when the space of compute graphs is discrete?

> How can gradient descent work on compute graphs when the space of compute graphs is discrete?

You can un-discretize the space of compute graphs by interpolating its points by simplices. More precisely, each graph is a subgraph of the complete graph, and the subgraph is identified by the indicator function of its edges whose values are either 0 or 1. By using weighted edges with values between 0 and 1, the space of all graphs (with the same number of vertices) becomes continuous and connected, and you can gradient move around it in small steps.

Of course, "compute graphs" are more general beasts than "graphs", but it is likely that the same idea will apply. At least, for a reasonably large class of compute graphs.

Re: Understand how transformers work by demystifying the math behind them

#118

Post by danielmarkbruce » Thu, Jan 04, 2024, 9:07 PM UTC

ActorNightly wrote: post #116

danielmarkbruce wrote: post #50

Earlier quoted context omitted.

The idea that there has been no progress in functionality is silly. Your whole brain might just be doing "information compression" by that analogy. An LLM is sort of learning concepts. Even Word2Vec "learned" than king - male + female = queen and that's a small model that's really just one part (not exact, but similar) of a transformer.

Let me rephrase that. One level deep information compression is cool, but I want actual AI. Its true that our brains compress information, but we compress it in a much more complex manner, in the sense that we can not only recall stuff, but also execute a decision tree that often involves physical actions to find the answer we are looking for.

An LLM isn't just recalling stuff. Brand new stuff, which it never saw in it's training, can come out.

The minute you take a token and turn it into an embedding, then start changing the numbers in that embedding based on other embeddings and learned weights, you are playing around with concepts.

As for executing a decision tree, ReAct or Tree of Thought or Graph of Thought is doing that. It might not be doing it as well as a human does, on certain tasks, but it's pretty darn amazing.

Re: Understand how transformers work by demystifying the math behind them

#119

Post by godelski » Thu, Jan 04, 2024, 9:18 PM UTC

osanseviero wrote: post #102

godelski wrote: post #38

I love and hate these. I love them because they do give another resource at explaining models such as transformers and I think this one is pretty well done (note: you really need to do something about the equation in 4.2...) First, the critique is coming from love. Great work, so I don't want it to be taken as I'm saying anything it isn't. Why I hate these is that they are labeled as "math behind" but I think this is…

Hey @godelski! Author of the blog post here. I really appreciate you taking the time to provide all this feedback. This feedback + additional resources are extremely useful. I agree that the subtitle is not as accurate as it could be. I'll revisit it! As for content updates, I've been doing some additional updates in the last days based on feedback (e.g. more info about tokenization and the token embeddings). Althoug…

Hey, I'm glad you found it useful. I know it is hard to take critique, but I did enjoy the post. I truly do mean the critique is coming from a place of love. And I hope the comment helps others find more (I guess I'm writing a blog post now). I do feel there is often this gap between nearly no math and way too much math that causes a lot of people to come away with "you don't need math for ML" which is... idk... partially correct but not? haha. I'm a bit mathy of a person so you just caught a pet peeve of mine. I definitely agree what I said is out of scope for how you wrote but I will stand with my subtitle critique ;) I still do like the article though

And I just realized we're in a slack channel together haha (I don't think we've ever talked though). I poked around your website and saw you're at HF. Love you guys to death. You all also have tons of awesome blog posts and you're one of the most useful forces in ML. So I really do appreciate all the work.

Re: Understand how transformers work by demystifying the math behind them

#120

Post by knightoffaith » Thu, Jan 04, 2024, 9:33 PM UTC

ActorNightly wrote: post #115

knightoffaith wrote: post #108

Earlier quoted context omitted.

I wonder why this hasn't taken off.

From brief look at the paper, they are doing a gradient descent of the architecture based on validation loss, which does good for efficiency, but its not ground breaking. The problem is that you are still training towards a target of a correct answer. I don't think this is gonna be applicable in the future, in the sense that we have to train on other things (like logical consistency somehow encoded into the network),…

Your expectations are pretty high. Differentiable architecture search as you mentioned in the original comment is one thing; going beyond empirical risk minimization-based learning is another thing entirely. In fact, they seem mostly orthogonal.

That aside, it seems like AI has had the most empirical success by not imposing hard constraints/structure, but letting models learn completely "organically". The computationalists (the folks who have historically been more into this "AI has to have things like logical consistency embedded into its structure" kind of thinking) seem to have basically lost, empirically. Who even knows what Soar[1] is nowadays? Maybe some marriage of the two paradigms will lead to better results, but I doubt that things will head in that direction anytime soon given how massively far just having parallelizable architectures and adding more parameters has gotten us.

[1] https://en.wikipedia.org/wiki/Soar_(cognitive_architecture)