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Understand how transformers work by demystifying the math behind them

osanseviero.github.io

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

#41

Post by nomel »

necroforest wrote: post #35
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…

> We arent going to see more progress until we have a way to generalize the compute graph as a learnable parameter That's a bold statement since a ton of progress has been made without learning the compute graph.

From my naive perspective, there seems to be a plateau, that everyone is converging on, somewhere between ChatGPT 3.5 and 4 level of performance, with some suspecting that the implementation of 4 might involve several expert models, which would already be extra sauce, external to the LLM. This, combined with the observation that generative models converge to the same output, given the same training data, regardless of architecture (having trouble finding the link, it was posted here some weeks ago), external secret sauce, outside the model, might be where the near term gains are.

I suppose we'll see in the next year!

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

#43

Post by wardedVibe »

enriquto wrote: post #18

For a dryer, more formal and succinct approach, see "The Transformer Model in Equations" [0], by John Thickstun. The whole thing fits in a single page, using standard mathematical notation. [0] https://johnthickstun.com/docs/transformers.pdf

Thank god, I've had to cobble something like this together for my own notes a couple of times trying to parse papers and was never quite sure if I was missing something.

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

#44

Post by utopcell »

__loam wrote: post #25
brcmthrowaway wrote: post #11

Does the human brain use transformers?

Anyone telling you it does is a fraud.

Here [1] are some "frauds" from Stanford University, Oxford University and University College London telling you exactly that.

From their abstract:

``One of the most exciting and promising novel architectures, the Transformer neural network, was developed without the brain in mind. In this work, we show that transformers, when equipped with recurrent position encodings, replicate the precisely tuned spatial representations of the hippocampal formation; most notably place and grid cells. Furthermore, we show that this result is no surprise since it is closely related to current hippocampal models from neuroscience. We additionally show the transformer version offers dramatic performance gains over the neuroscience version.``

[1] https://arxiv.org/abs/2112.04035

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

#45

Post by wardedVibe »

amelius wrote: post #17
rzzzt wrote: post #13

Earlier quoted context omitted.

Does mystified math lie beyond behind how the ratio of input and output voltages is equal to the ratio of the primary and secondary windings? Can it be derived from Maxwell's equations? Off to a search...

I bet that an LLM (which uses transformers) can explain those aspects of a transformer to you.

Or just read Wikipedia, which I'm sure it will crib from poorly... https://en.wikipedia.org/wiki/Transformer

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

#46

Post by ActorNightly »

necroforest wrote: post #35
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…

> We arent going to see more progress until we have a way to generalize the compute graph as a learnable parameter That's a bold statement since a ton of progress has been made without learning the compute graph.

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.

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

#47

Post by knightoffaith »

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?

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

#48

Post by beambot »

ActorNightly wrote: post #33
exe34 wrote: post #12

Earlier quoted context omitted.

Just give it a computer? Even a virtual machine. It can output assembly code or high level code that gets compiled.

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?

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

#49

Post by itishappy »

ActorNightly wrote: post #33
exe34 wrote: post #12

Earlier quoted context omitted.

Just give it a computer? Even a virtual machine. It can output assembly code or high level code that gets compiled.

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.…

LLMs seem like the least efficient way to accomplish this. NAND gates, for example, are inherently 1-bit operators, but LLMs use more. If weights are all binary, than gradients are restricted to -1, 0, and 1, which doesn't give you much room to make incremental improvements. You can add extra bits back, but that's pure overhead. But all this is besides the real issue, which is that LLMs and NNs in general are inherently fuzzy; they guess. Computers aren't, we have perfect simulators.

Consider how humans design things. We don't talk through every CPU cycle to convince ourself a design works, we use bespoke tooling. Not all problems are language shaped.

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

#50

Post by danielmarkbruce »

ActorNightly wrote: post #46
necroforest wrote: post #35

Earlier quoted context omitted.

> We arent going to see more progress until we have a way to generalize the compute graph as a learnable parameter That's a bold statement since a ton of progress has been made without learning the compute graph.

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.

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