Arithmetic Without Numbers – How LLMs Do Math
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Arithmetic Without Numbers – How LLMs Do Math
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Re: Arithmetic Without Numbers – How LLMs Do Math
#2What happens inside an LLM when it tries to calculate with nothing but matrices.
Re: Arithmetic Without Numbers – How LLMs Do Math
#3This is a very nice and fresh page layout.
Re: Arithmetic Without Numbers – How LLMs Do Math
#4The spirit of Rube Goldberg is alive and well.
Re: Arithmetic Without Numbers – How LLMs Do Math
#5Why doesn’t it just call tools such as Mathematica for such operations?
Re: Arithmetic Without Numbers – How LLMs Do Math
#6Why doesn’t it just call tools such as Mathematica for such operations?
This is more how an LLM thinks about math internally - an LLM version of drilled tables being used for mental arithmetic "as humans do".
When humans stall on these tasks, they reach for pen and paper, a slide rule, a calculator, etc.
Mathematica is overkill for arithmetic, in addition it's licenced and can cost a bit extra.
If an LLM were to reach for a light cheap arithmetic tool something like bc would be a good first stop - a CLI tool with a language that supports arbitrary precision numbers with interactive execution of statements.
Re: Arithmetic Without Numbers – How LLMs Do Math
#7I assumed it wrote Python or some sort of other code.
Re: Arithmetic Without Numbers – How LLMs Do Math
#8Why 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.
Re: Arithmetic Without Numbers – How LLMs Do Math
#9Turing Award Winner: Thinking Clearly, Paxos vs Raft, Working With Dijkstra | Leslie Lamport
https://www.youtube.com/watch?v=U719vQz-WFs
Leslie Lamport : "I am not smart. I have the gift of abstraction."
Real mathematics isn't about details. Its about concepts and abstractions and how we compose them (LLMs are good at those aspects).
Re: Arithmetic Without Numbers – How LLMs Do Math
#10I assumed it wrote Python or some sort of other code.
writing and calling an entire python setup seems massive overkill, surely just have an internal way of calling a simple calculator function would be millions of times faster