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Arithmetic Without Numbers – How LLMs Do Math

alvaro-videla.com

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Re: Arithmetic Without Numbers – How LLMs Do Math

#11

Post by ACCount37 »

iammjm wrote: post #5

Why doesn’t it just call tools such as Mathematica for such operations?

For the same reason you don't run "4+6" on a calculator.

External tool call has an overhead. It requires a round trip into an external tool. It requires an LLM to run in agentic autoregression - it can't be used in prefill.

Which means that having native arithmetic capabilities is useful. Forward pass arithmetics are an LLM version of quick mental math.

An LLM can read "#define SILLY_TIME_CONST (3*20*60*60*1000)" and have "SILLY_TIME_CONST is 60 h expressed as 216000000 ms" already cached by the end of the line, before it even emits its first token.

Re: Arithmetic Without Numbers – How LLMs Do Math

#12

Post by [deleted] »

ACCount37 wrote: post #11
iammjm wrote: post #5

Why doesn’t it just call tools such as Mathematica for such operations?

For the same reason you don't run "4+6" on a calculator. External tool call has an overhead. It requires a round trip into an external tool. It requires an LLM to run in agentic autoregression - it can't be used in prefill. Which means that having native arithmetic capabilities is useful. Forward pass arithmetics are an LLM version of quick mental math. An LLM can read "#define SILLY_TIME_CONST (3*20*60*60*1000)" and…

[deleted]

Re: Arithmetic Without Numbers – How LLMs Do Math

#13

Post by stared »

There is a beautiful MathOverflow thread on how mathematicians imagine concepts, https://mathoverflow.net/questions/38639/thinking-and-explai....

Very often it involves spatial thinking. Vide one example there:

> Once I mentioned this phenomenon to Andy Gleason; he immediately responded that when he taught algebra courses, if he was discussing cyclic subgroups of a group, he had a mental image of group elements breaking into a formation organized into circular groups. He said that 'we' never would say anything like that to the students. His words made a vivid picture in my head, because it fit with how I thought about groups. I was reminded of my long struggle as a student, trying to attach meaning to 'group', rather than just a collection of symbols, words, definitions, theorems and proofs that I read in a textbook.

Re: Arithmetic Without Numbers – How LLMs Do Math

#15

Post by [deleted] »

ACCount37 wrote: post #11
iammjm wrote: post #5

Why doesn’t it just call tools such as Mathematica for such operations?

For the same reason you don't run "4+6" on a calculator. External tool call has an overhead. It requires a round trip into an external tool. It requires an LLM to run in agentic autoregression - it can't be used in prefill. Which means that having native arithmetic capabilities is useful. Forward pass arithmetics are an LLM version of quick mental math. An LLM can read "#define SILLY_TIME_CONST (3*20*60*60*1000)" and…

[deleted]

Re: Arithmetic Without Numbers – How LLMs Do Math

#20

Post by steveBK123 »

jampekka wrote: post #8
iammjm wrote: post #5

Why doesn’t it just call tools such as Mathematica for such operations?

They do. I asked CharGPT for 327 x 48 and it used the "ChatGPT Instruments" calculator. Previously it used to run Python scripts, and may still do for more complex calculations.

What's interesting is that one one hand LLM pumps are claiming a path to AGI.. while on the other hand, they are duct-taping in deterministic plugins for specific prompt types they find it better to offload...

In X years is it just going to be a thin OS-like layer where a majority of work is being handled by other "programs".

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