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Smallest transformer that can add two 10-digit numbers

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Re: Smallest transformer that can add two 10-digit numbers

#81

Post by xg15 »

> Self-attention is required. The model must contain at least one self-attention layer. This is the defining feature of a transformer — without it, you have an MLP or RNN, not a transformer.

I think it would be interesting to see challenges where two networks are trained and evaluated on the exact same datasets and the architecture is the same except for the presence of self-attention layers in one network.

So far it seems to me that self-attention really brought new capabilities to a network - essentially change the network's functionality in response to the input. It would be interesting to see if there are problems (i.e. datasets) that a "traditional" feedforward network fails to solve, but a transformer network of the same size can solve.

My guess would be: yes there are, and they are the kinds of "variable task" datasets that we see with LLMs, i.e. where part of the input indicates the task itself and part indicates the data for the task.

Re: Smallest transformer that can add two 10-digit numbers

#83

Post by base76 »

wmf wrote: post #51
prng2021 wrote: post #46

How is anyone predicting timelines for AGI when these systems can’t do basic addition of 2 arbitrary numbers with 100% accuracy?

LLMs should use tool calling (which is 100% reliable) instead of doing math internally. But in general it would be nice to be able to teach a process and have the AI execute it deterministically. In some sense, reliability between 99% and 100% is the worst because you still can't trust the output but the verification feels like wasted effort. Maybe code gen and execution will get us there.

"reliability between 99% and 100% is the worst because you still can't trust the output"

Re: Smallest transformer that can add two 10-digit numbers

#84

Post by Lerc »

qsera wrote: post #75
Lerc wrote: post #71

Earlier quoted context omitted.

You are going to have to be more specific, because that reads like nonsense. By what mechanism do you propose the model observed the test set?

>By what mechanism do you propose the model observed the test set.. By explicitly setting the model parameters. What happens when a model is trained? We tweak the model parameters by some feed back. In both cases, you affect the model parameters. Only the method is different. So both are eqvialent to "model observing the test set".

I still do no see any causal link from the test set. When was this observed, how and by whom?

Are you trying to say that the person who entered the parameters had access to the test set? I find it more likely that they encoded the generalising rule than observed every instance of its use.

Re: Smallest transformer that can add two 10-digit numbers

#86

Post by base76 »

wmf wrote: post #51
prng2021 wrote: post #46

How is anyone predicting timelines for AGI when these systems can’t do basic addition of 2 arbitrary numbers with 100% accuracy?

LLMs should use tool calling (which is 100% reliable) instead of doing math internally. But in general it would be nice to be able to teach a process and have the AI execute it deterministically. In some sense, reliability between 99% and 100% is the worst because you still can't trust the output but the verification feels like wasted effort. Maybe code gen and execution will get us there.

This is the exact problem CognOS was built to solve.

  99% reliable means you still can't remove the human from the loop — because you never know which 1% you're in. The only way to actually trust output is to attach a verifiable confidence   
  signal to each response, not just hope the aggregate accuracy holds.                                                                                                                        
                                                                                                                                                                                            
  We built a local gateway that wraps every LLM output with a trust envelope: decision trace, risk score, and an explicit PASS/REFINE/ESCALATE/BLOCK classification. The point isn't to make 
  LLMs more accurate — it's to make their uncertainty legible so the human knows when to step in.

  Open source if you want to look at the architecture: github.com/base76-research-lab/operational-cognos

Re: Smallest transformer that can add two 10-digit numbers

#87

Post by qsera »

Lerc wrote: post #84
qsera wrote: post #75

Earlier quoted context omitted.

>By what mechanism do you propose the model observed the test set.. By explicitly setting the model parameters. What happens when a model is trained? We tweak the model parameters by some feed back. In both cases, you affect the model parameters. Only the method is different. So both are eqvialent to "model observing the test set".

I still do no see any causal link from the test set. When was this observed, how and by whom? Are you trying to say that the person who entered the parameters had access to the test set? I find it more likely that they encoded the generalising rule than observed every instance of its use.

>I find it more likely that they encoded the generalising rule..

Look, I am saying that during training the model ends up "learning" the generalising rule from training data, but here it was explicitly entered into it, with out any training.

Re: Smallest transformer that can add two 10-digit numbers

#89

Post by getnormality »

xg15 wrote: post #81

> Self-attention is required. The model must contain at least one self-attention layer. This is the defining feature of a transformer — without it, you have an MLP or RNN, not a transformer. I think it would be interesting to see challenges where two networks are trained and evaluated on the exact same datasets and the architecture is the same except for the presence of self-attention layers in one network. So far it…

> So far it seems to me that self-attention really brought new capabilities to a network

Do we have a layman explanation for what makes self-attention so uniquely powerful? Something more than "it lets you do self-attention".

Re: Smallest transformer that can add two 10-digit numbers

#90

Post by varispeed »

SlinkyOnStairs wrote: post #79
kstrauser wrote: post #56

So, what happens when you test it on 11 digit numbers? I don’t mean that as a gotcha or “LOL dumb transformer” snark. More like, does the accuracy start to drop as you add digits? Or instead, maybe it’s the transformer equivalent of a stack overflow and it outputs a picture of a burning spoon or something? And for that matter, what’s it do with 9 digit numbers? Like, is it more accurate with them, or are these little…

One major limitation of the LLM architecture is that even the failure mode varies unpredictably between inputs. The set of 11-digit numbers with any given failure mode (or even successful output) has no discernable pattern, merely whatever randomness the training process baked into the model. You can't predict ahead of time when they will fail spectacularly, nor draw a clear boundary around the failure cases. And ear…

Most humans struggle to compute 10 digit stuff. They use tools instead. Can LLM learn to use calculator? Sorry if that is a stupid question. Maybe brains are not well suited for calculations natively.
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