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Why can't transformers learn multiplication?

arxiv.org

91–100 of 111 posts

Re: Why can't transformers learn multiplication?

#91

Earlier quoted context omitted.

People are probabilistic, and I've been informed that people are able to perform multiplication.

Are you sure? I bet you if you pull 10 people off the street and ask them to multiply 5 digit by 5 digit numbers by hand, you won't have a 100% success rate.

I bet with a little training, practically anyone could multiply 5 digit numbers reliably.

Re: Why can't transformers learn multiplication?

#92
post #39
post #4

The chains-of-thought here are artificially constructed, very information-dense partial sums formatted in a specific way that guides the fine tuning. A potential next step would be to look at real-world chains-of-thought and see whether some process could start with those and achieve the same result. Then you could really have a self-improving system! Also I wonder if the LLM "knows" that it has this capability after…

But it's very hard to define "real-world CoT" -- think about human, we learn multiplications by vertical calculation and we learn division in a similar way -- all these learning process requires an "information dense" tools (calculation process) with intrinsic math rules in it. Isn't that an adapted way of CoT?

Oh, by "real world" I meant "chains of thought generated by existing reasoning LLMs" (as opposed to injecting predefined CoT like was done in the experiment), not human thoughts.

Re: Why can't transformers learn multiplication?

#93
post #81

There are two kinds of computing - precision computing and probabilistic computing. For example, cryptography falls into precision computing. There is no room for being incorrect even by a single bit. Where as machine learning is about getting a range of answers, with tolerance for error. I like to visualize them as cuts and spans in a continuum, such as a number line. They make up the full picture. One exists only b…

> For example, cryptography falls into precision computing. There is no room for being incorrect even by a single bit. Where as machine learning is about getting a range of answers, with tolerance for error. Doesn't both of them rely on randomness in real use cases/usage? And it's only once you have fixed seeds that cryptography becomes deterministic, and then you can make the same claim for most of ML, when the seed…

Fixing the seed wouldn't necessarily make LLMs deterministic. LLMs do lots of computation in parallel and the order in which these computations are performed is often indeterministic and can lead to different final results.

Re: Why can't transformers learn multiplication?

#94
post #81

There are two kinds of computing - precision computing and probabilistic computing. For example, cryptography falls into precision computing. There is no room for being incorrect even by a single bit. Where as machine learning is about getting a range of answers, with tolerance for error. I like to visualize them as cuts and spans in a continuum, such as a number line. They make up the full picture. One exists only b…

> Banks wouldn't use AI to compute the account balance after a transaction or for authenticating a customer. Network software wouldn't use AI for encryption and decryption of the TLS traffic.

Not directly, no. But they might use AI to write the code that computes account balance, or authenticates a user, or encrypts/decrypts TLS.

Re: Why can't transformers learn multiplication?

#95
post #59

Earlier quoted context omitted.

You don't need general intelligence to make good memes to keep people scrolling through Instagram. You don't need general intelligence to make a decent coding tool like Cursor. You don't need general intelligence to improve SERPs. You don't need general intelligence to sell a subscription for a decent AI assistant. There's tons of value already added without anything general.

Yes but $500B and counting for memes wasn’t what was sold

$500B is future projections for total spending (a lot of that decently far into the future).

The revenues are already in the high tens of billions per year.

Models will get better from here, especially on the low end.

Costs will eventually approach peanuts for current capabilities.

Given enough time, this will pay for existing investments. If growth slows, future spending will slow as well.

Re: Why can't transformers learn multiplication?

#97
post #93

Earlier quoted context omitted.

> For example, cryptography falls into precision computing. There is no room for being incorrect even by a single bit. Where as machine learning is about getting a range of answers, with tolerance for error. Doesn't both of them rely on randomness in real use cases/usage? And it's only once you have fixed seeds that cryptography becomes deterministic, and then you can make the same claim for most of ML, when the seed…

Fixing the seed wouldn't necessarily make LLMs deterministic. LLMs do lots of computation in parallel and the order in which these computations are performed is often indeterministic and can lead to different final results.

Yep. And to answer the question about randomness - it's absolutely vital to have a good source of noise to obscure the underlying pattern to prevent the secret information leaking - but the mathematical part that manipulates that noise into the encrypted output has to be precise. That's the distinction made here relating to probability.

Disclaimer: Not a crypto expert. Just like reading about it. Check actual sources for a better insight. Very interesting technology and much smarter people working in this field who deserve a lot of praise.

Re: Why can't transformers learn multiplication?

#98
post #81

There are two kinds of computing - precision computing and probabilistic computing. For example, cryptography falls into precision computing. There is no room for being incorrect even by a single bit. Where as machine learning is about getting a range of answers, with tolerance for error. I like to visualize them as cuts and spans in a continuum, such as a number line. They make up the full picture. One exists only b…

> Banks wouldn't use AI to compute the account balance after a transaction or for authenticating a customer. Network software wouldn't use AI for encryption and decryption of the TLS traffic. Not directly, no. But they might use AI to write the code that computes account balance, or authenticates a user, or encrypts/decrypts TLS.

I would argue that there are already quite a few slow-moving corporate procedures in place for the exact reason of ensuring correctness.

Especially when financials are on the line, it's not like they don't have the money to ensure excruciatingly painful amounts of scrutiny here.

I did note that you said "might". So, I would hope not but I've seen things so maybe you're upsettingly right haha

Re: Why can't transformers learn multiplication?

#99
post #63

Computers are already fast and efficient at multiplication - optimized long ago. Transformers are fast and efficient at working with sequences of tokens. Tools are not universal. A hammer is not a good violin bow. A MRI machine is not a good relational database. This extends to the natural world too. A zebra is not a good dairy animal. And a human poet may or may not be a good surgeon. It’s good to explore what thing…

Well. I don't like your limits... I'm looking forward to my zebra farm utopia. :D

Re: Why can't transformers learn multiplication?

#100

Earlier quoted context omitted.

This field of study is known as "Curriculum Learning" for your Googling pleasure (or I guess ChatGPT Deep Research now).

Probably don’t need the name of the field for ChatGPT to get it.

I get why this comment was downvoted but I also get where you're coming from - yes, these models are becoming increasingly intelligent at understanding the nuance and where to look without knowing what to begin searching for.

But the downside is, you end up digging in the wrong direction if you leave it to a generalist system instead of a professional community in some cases which is counter productive.

Getting burnt is a good way to learn not to sometimes though...

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