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Transformers Can Do Arithmetic with the Right Embeddings

arxiv.org

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Re: Transformers Can Do Arithmetic with the Right Embeddings

#161

Post by ckemere »

PartiallyTyped wrote: post #144
neves wrote: post #109

Earlier quoted context omitted.

but it makes sense to have a different encoding. Mathematics is a completely different language. Maybe we should have more than one class of encodings.

There were some recent posts (either here or reddit) supporting the claim that different regions activate when reading programs vs when reading text. If we take that to be true; and squint just enough, one could claim that arithmetic and mathematics should be treated differently to language.

Numeracy is definitely associated with different brain regions than just reading. See, e.g. https://www.sciencedirect.com/science/article/pii/S105381191...

(Dehaene also has a book, “The Numbet Sense”)

Re: Transformers Can Do Arithmetic with the Right Embeddings

#163

Post by ckemere »

anon291 wrote: post #89
short_sells_poo wrote: post #37

Earlier quoted context omitted.

I suppose it's a question whether what we call "reasoning" is an emergent phenomenon from having enough connections in a graph, or whether it's some other special sauce which we simply don't have in our current models yet. E.g. humans follow a deductive process to answer questions which they haven't encountered yet. Do we gain this ability purely from a denser/larger graph of knowledge, or from a completely different…

I must be in the minority here, but I don't think most people exercise any reason. I'd even venture that the vast majority of people haven't reasoned recently at all. In my mind, reasoning is an ability... a willful act to engage in thinking through an abstract problem. Most people don't do this and just use rationalization and learned behavior, which our brains are good at.

People do inference all the time. “Is that driver about to turn?” “Where is the water next to the faucet coming from?” “Does this person like me?”

Re: Transformers Can Do Arithmetic with the Right Embeddings

#164

Post by ckemere »

golol wrote: post #35
msoad wrote: post #4

It seems like a hack to be honest. Problem at hand is not to make transformers do addition of 100 digit numbers. Problem is the current systems can’t reason about things, math included. Optimizing for a certain use case is not gonna take us where we wanna be. We want to have a system that can learn to reason.

As I understand, conceptually they just changed 346 + 23 = ? to (1: 3, 2: 4, 3: 6) + (1: 2, 2: 3) = ? So it is not that much of a specific hack. There could be a broader principle here where something is holding transformers back in a general fashion, and we might be able to improve on the architecture!

Hopefully 3:3, 2:4, 1:6 and 2:2, 1:3?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#165

Post by EVa5I7bHFq9mnYK »

jhanschoo wrote: post #127
nprateem wrote: post #92

Earlier quoted context omitted.

But I don't want tricks. I want to know that it knows so I don't have to continually guess whether it's right or not.

A basic transformer architecture performs only a bounded amount of computation per generated token, so it can never emulate a machine computing sufficiently hard problems.

Yes, because it's feed forward. It must have loops to be a Turing machine.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#166

Post by CamperBob2 »

andoando wrote: post #132
short_sells_poo wrote: post #79

Earlier quoted context omitted.

Of course there are cases like this, nobody is perfect. But we are talking about mathematics here, not everyday subconscious decision making. I agree that 99% of daily life is trivial pattern recognition. That's not what distinguishes humans though is it? Because animals, down to single celled organisms do just fine without higher order mental capabilities. But we are talking about reasoning here - and specifically a…

I disagree that daily life is "trivial pattern recognition". Just our visual object recognition is immensely powerful and far beyond and current AI. A simple task like walking to the fridge requires a ton of pattern recognition and spatial reasoning. Recognizing people's moods/predicting behaviors is also incredibly involved imo. Ive said this many times but perhaps we should focus on achieving dog level intelligence…

Just our visual object recognition is immensely powerful and far beyond and current AI.

That's a point you'll likely have to revisit pretty soon. Radiology, for instance, probably won't exist as a profession 20-30 years from now. Captchas are already pretty much done for.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#167

Post by TeMPOraL »

badrunaway wrote: post #157
vessenes wrote: post #57

Wow, a lot of grumpiness in here. If it's true that adding like 20 or so tokens to encode column location / decimal spot triples math performance in out of band tasks, that's a big deal. It's a simple fix, it improves performance A LOT, and they even indicate it's not just a party trick, in that the LLM can use the information to do better on related tasks like sorting and list making. This is basically free to add,…

engineering vs. science -> scientist-types find such hacks ugly whereas engineers have to pay bills and get things moving fast.

And when engineers accumulate enough related hacks, scientist-types may discover a pattern and find a proper, general solution. But they wouldn't get there without the pile of hacks that are effectively meta-level empirical evidence.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#168

Post by TeMPOraL »

jayd16 wrote: post #151
shepherdjerred wrote: post #126

Earlier quoted context omitted.

Your calculator is deterministic. Humans and AI are not.

LLMs are deterministic. We just sample the results, no? Also, no reason AI needs not be deterministic.

> LLMs are deterministic.

In theory, yes. In practice, parallelism combined with floating point math make current implementations fundamentally non-deterministic.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#169

Post by phkahler »

EVa5I7bHFq9mnYK wrote: post #165
jhanschoo wrote: post #127

Earlier quoted context omitted.

A basic transformer architecture performs only a bounded amount of computation per generated token, so it can never emulate a machine computing sufficiently hard problems.

Yes, because it's feed forward. It must have loops to be a Turing machine.

It does. The output is fed back in.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#170

Post by simianparrot »

jhanschoo wrote: post #128
sshine wrote: post #19

Earlier quoted context omitted.

> Problem is the current systems can’t reason about things Sounds like the AGI argument trap: They're not able to reason, but we can't succintly define what it is. I don't come with a reasoning chip. Whatever I call reasoning happens as a byproduct of my neural process. I do think that the combination of a transformer network and calls to customized reasoning chips (systems that search and deduce answers, like Wolfra…

> They're not able to reason, but we can't succintly define what it is. For transformer-based LLMs, and most LLMs there's an obvious class of problems that they cannot solve. LLMs generally perform bounded computation per token, so they cannot reason about computational problems that are more than linearly complex, for a sufficiently large input instance. If you have a back-and-forth (many shot) your LLM can possibly…

Humans can realise they don’t understand something and seek more knowledge to learn to understand it. But also humans can build complex structures out of simple fundamentals: The same logic of counting up beans on a table can be extrapolated to multiplying that table of beans. And then counting horses the same way you count beans but give them a value of multiple beans. And then simplify that by trading in promises of beans in trade of horses.

The fact that so many people can’t see the fundamental differences of an LLM and human intelligence reminds me of back when the very early computer scientists thought they could model the entirety of nature by reducing every “component” to a numeric value and compute it as “transfer of energy”.

Quite literally they did the same thing: They had a new toy (very advanced computation machines) and forced all of nature to “fit” within it. It also ended in failure, obviously. Not because nature or ecosystems (as it was coined) are “magic” but because grossly oversimplifying reality to fit desired models is a fool’s errand.

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