Theoretical limitations of multi-layer Transformer

https://arxiv.org/abs/2412.02975

by fovc • 1 year ago

107 22 1 year ago

arxiv.org

cs702• 1 year ago

Huh. I just skimmed this and quickly concluded that it's definitely not light reading.

It sure looks and smells like good work, so I've added it to my reading list.

Nowadays I feel like my reading list is growing faster than I can go through it.

Matthyze2• 1 year ago

I'd humbly like to ask people who've read the paper whether it's worth trying to understand it without a great math background. The paper looks intersting but daunting, and I'd hate to sink a lot of time into it and leave defeated.

It sometimes sucks being in ML with 'only' a CS background. Feels like all the math and physics grads are running around having fun with their fancy mathematics, while I stand here, feeling dimwitted.

aketchum• 1 year ago

Most of it is linear algebra and convex optimization. You can learn a lot of it with free resources from MIT, Stanford, Georgia Tech, or YouTube. If you want more of a school style learning environment you can enroll in the Georgia Tech OMSCS program and just take the classes related to the math etc that you are interested in. No reason you have to graduate and it is maybe $800 a course.

szundi• 1 year ago

Would be fun to ask o3

svachalek• 1 year ago

I'm not a math person either, but I'm familiar with some of the terminology. The two things I got out of this paper were:

1. Depth is more important than breadth for making transformers smarter. That is, for a given size of model it will be more powerful with more, smaller layers than it would be with less, bigger ones. Interestingly, Mistral just updated their small model yesterday with a big reduction in layers in order to improve performance. Among the many ways they say it more technically they do say directly "depth plays a more critical role than width in reasoning and composition tasks".

2. As I understand it, they are claiming to be able to prove mathematically that Chain of Thought such as seen in the new DeepSeek R1 and GPT o1/o3 models creates results that wouldn't be possible without it. The thought chains effectively act as additional layers, and per the previous point, the more layers the better. "From a theoretical view, CoT provides Transformer with extra computation space, and previous work ... proved that log-precision Transformer with CoT could simulate any polynomial-time algorithm. Therefore, by further assuming certain complexity conjecture ... their results imply that constant depth Transformer with CoT could simulate poly-time algorithm, while constant depth Transform ... itself can not solve P-complete task."

nighthawk4542• 1 year ago

A nice trick for most papers is to skip the middle (at first). Just don’t read most of the lines of math. Focus on the inputs and outputs.

If the premise and conclusion don’t make sense on fundamentals the math isn’t likely to fix it. Most lines are literally equals signs - just walking you through some equivalencies as proof. A large statement saying “If ABC, then … (and then … and then … and then …) and finally XYZ”

The middle ‘and then’s aren’t really that important if the conclusion XYZ isn’t interesting. Or much more commonly, the ABC premise is false anyway so who cares.

Most readers I’d wager are not sitting here deciphering opaque gradient derivations every single paper. Just skip it unless it proves worthy

DoctorOetker• 1 year ago

It's never too late to study physics or mathematics. I would however recommend studying physics since it will force you to study the slices of mathematics that was motivated by necessity. A lot of mathematics is genuinely interesting in and of itself, or results in mysteriously rich structures, but has not necessarily found many applications. A lot of mathematics was in fact motivated and (often sloppily) invented by physicists, before being put on more rigorous footing by mathematicians...

Studying physics without learning math is impossible, but physics results in a curricular selection of math which is highly relevant to machine learning.

gessha• 1 year ago

Most of the math in ML papers is smoke and mirrors. Some good theoretical papers exist but too many others cover up accidental discovery with vague mathy explanations.

If you really want to go deep on a topic in ML, take a subtopic paper and read related works until you can connect the basics to the paper. This consists of not only writing down the math but also coding the concepts. ML students go through this process when they choose a topic and start working on it. Focus on one topic and learn it. Present it to yourself or others. Find holes in the literature and try exploring them. Science!

cubefox• 1 year ago

Loosely related thought: A year ago, there was a lot of talk about the Mamba SSM architecture replacing transformers. Apparently that didn't happen so far.

thesz2• 1 year ago

Just like with neural networks and Adam [1], LLMs evolve to make transformers their best building block.

[1] https://parameterfree.com/2020/12/06/neural-network-maybe-ev...

thesz2• 1 year ago

  > ...our results give: ... (3) a provable advantage of chain-of-thought, exhibiting a task that becomes exponentially easier with chain-of-thought.

It would be good to also prove that there is no task that becomes exponentially harder with chain-of-thought.

byyoung3• 1 year ago

those lemmas are wild

hochstenbach• 1 year ago

Quanta magazine has an article that explains in plain words what the researchers were trying to do : https://www.quantamagazine.org/chatbot-software-begins-to-fa...

Theoretical limitations of multi-layer Transformer

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