6 ms·
Arithmetic Without Numbers – How LLMs Do Math
- old_sound 4mo agoWhat happens inside an LLM when it tries to calculate with nothing but matrices.
- silvestrov 3mo agoThis is a very nice and fresh page layout.
- euroderf 3mo agoThe spirit of Rube Goldberg is alive and well.
- soupspaces 3mo agoWe evolved to do incremental fixes, not full refactoring
- cwmoore 3mo agoMaybe evolutionary, but not ours, as the things we tend to want to refactor have come to exceed our lifespans.
- iammjm 3mo agoWhy doesn’t it just call tools such as Mathematica for such operations?
- defrost 3mo 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 3mo 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 3mo 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 3mo 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 3mo agoIn which case it’s just a neat extension of search
- beernet 3mo 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?
- BobbyTables2 3mo agoHow creditable would Claude be if it couldn’t answer “1+2=3?” Worse, this is really human beings trying to pretend that their AI is AGI.
- grey-area 3mo agoFor this category of problems, no, very unlike human beings.
- ACCount37 3mo 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.
- deleted 3mo ago[deleted]
- deleted 3mo ago[deleted]
- breezybottom 3mo agoChatGPT does, and has since 2023
- ragebol 3mo 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 3mo agoI assumed it wrote Python or some sort of other code.
- mavhc 3mo 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 3mo 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 3mo agoUsually yes
- Npovview 3mo 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 3mo 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 3mo agoPity Feynman didn’t write a Distributed Systems textbook…
- Chu4eeno 3mo 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 3mo 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 3mo 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 3mo 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 3mo agoEverything looked the same before too. One of the same 6 Jekyll temples etc. Fads in design come and go
- rubyfan 3mo agoWhy does every exhibit made with AI look the same?
- 0x59 3mo 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 3mo 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 3mo 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!
- deleted 3mo ago[deleted]
- zdc1 3mo agoYou'd think with tool use being as available as it is, the first tool we'd want to give them is a calculator...