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Arithmetic Without Numbers – How LLMs Do Math
- old_sound 5mo agoWhat happens inside an LLM when it tries to calculate with nothing but matrices.
- silvestrov 5mo agoThis is a very nice and fresh page layout.
- euroderf 5mo agoThe spirit of Rube Goldberg is alive and well.
- soupspaces 5mo agoWe evolved to do incremental fixes, not full refactoring
- cwmoore 5mo agoMaybe evolutionary, but not ours, as the things we tend to want to refactor have come to exceed our lifespans.
- iammjm 5mo agoWhy doesn’t it just call tools such as Mathematica for such operations?
- defrost 5mo agoThis 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. https://en.wikipedia.org/wiki/Bc_(programming_language) https://en.wikipedia.org/wiki/Bc_(programming_language)
- jampekka 5mo agoThey 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.
- steveBK123 5mo agoWhat'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".
- singpolyma3 5mo ago> 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" That is my hopeful ideal
- steveBK123 5mo agoIn which case it’s just a neat extension of search
- beernet 5mo ago> while on the other hand, they are duct-taping in deterministic plugins for specific prompt types they find it better to offload So, in essence, just like human beings?
- grey-area 5mo agoFor this category of problems, no, very unlike human beings.
- steveBK123 5mo agoRight.. plumbing in specific plugins for specific prompt forms feels like an expert system, rather than some general purpose intelligence. Also big picture its hard to see it as some sort of self-improving intelligence if humans are hand crafting these paths and tools for it.
- ACCount37 5mo agoFor 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.
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- breezybottom 5mo agoChatGPT does, and has since 2023
- ragebol 5mo agoI was thinking the same thing. Why not call into a dedicated math tool? But I don't as well, and I have some intuition about numbers that I would probably not have if I always relied on calculators. Would the same sort of thing apply to LLMs? I'm probably anthropomorphising here...
- andrewstuart 5mo agoI assumed it wrote Python or some sort of other code.
- mavhc 5mo agowriting 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
- sebzim4500 5mo agoProbably but the cost of running a short lived python interpreter to run "print (100 + 200)" is likely negligable compared to the cost of running the language model itself
- singpolyma3 5mo agoUsually yes
- Npovview 5mo agoTuring Award Winner: Thinking Clearly, Paxos vs Raft, Working With Dijkstra | Leslie Lamport https://www.youtube.com/watch?v=U719vQz-WFs 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).
- helterskelter 5mo agoThat's an interesting quote, because Feynman's superpower seemed to be his ability to visualize a difficult problem and make it parsable by mere mortals. I think he only scored ~135 on an IQ test (whatever that's worth).
- BobbyTables2 5mo agoPity Feynman didn’t write a Distributed Systems textbook…
- Chu4eeno 5mo agoIt wouldn't have been that out of left field, he did work on massively parallel machines at Connection Machine. Though I guess that was more AI than distributed systems, iirc.
- stared 5mo agoThere is a beautiful MathOverflow thread on how mathematicians imagine concepts, https://mathoverflow.net/questions/38639/thinking-and-explaining 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.
- stymaar 5mo ago> There is a beautiful MathOverflow thread on how mathematicians imagine concepts, https://mathoverflow.net/questions/38639/thinking-and-explai https://mathoverflow.net/questions/38639/thinking-and-explai.... And obviously Terrence Tao is up there in the response.
- dominotw 5mo agoi dont like this new trend of generating html with ai to say something. i think some guy from anthropic started this trend . now everything looks the same and i can no longer read on kindle.
- singpolyma3 5mo agoEverything looked the same before too. One of the same 6 Jekyll temples etc. Fads in design come and go
- rubyfan 5mo agoWhy does every exhibit made with AI look the same?
- 0x59 5mo agoOne could use many things to do arithmetic: - color wheel - oxidation reactions - interpretive dance - migratory patterns of curlew sandpipers Whether one should is another question
- throw1234567891 5mo ago“You know how when you see prime numbers, they appear red, but when they're twin primes, they're pink and smell like gasoline?”
- xyzsparetimexyz 5mo ago> The original dream > A just-in-time compiler for arithmetic What is it with LLM writing where it gives a smaller heading just before the main heading? Its nonsensical!
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- zdc1 5mo agoYou'd think with tool use being as available as it is, the first tool we'd want to give them is a calculator...