12 条评论
- stared 14小时前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.
- Npovview 16小时前Turing 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).
- 0x59 11小时前One 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 9小时前“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 9小时前> 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!
- iammjm 18小时前Why doesn’t it just call tools such as Mathematica for such operations?
- ACCount37 15小时前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.
- defrost 18小时前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.
- jampekka 17小时前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.
- steveBK123 11小时前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".
- beernet 10小时前> 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?
- steveBK123 7小时前My point is what makes this terribly different than Alexa skills
- grey-area 7小时前For this category of problems, no, very unlike human beings.
- steveBK123 7小时前Right.. 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.
- tzs 10小时前That doesn't seem very persuasive. The one example of a non-A GI we have, humans, does the same thing. We've been offloading arithmetic for at least 4000 years.
- singpolyma3 11小时前> 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 11小时前In which case it’s just a neat extension of search
- ragebol 6小时前I 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...
- breezybottom 14小时前ChatGPT does, and has since 2023
- euroderf 19小时前The spirit of Rube Goldberg is alive and well.
- soupspaces 12小时前We evolved to do incremental fixes, not full refactoring
- cwmoore 6小时前Maybe evolutionary, but not ours, as the things we tend to want to refactor have come to exceed our lifespans.
- zdc1 8小时前You'd think with tool use being as available as it is, the first tool we'd want to give them is a calculator...
- old_sound 2天前What happens inside an LLM when it tries to calculate with nothing but matrices.
- silvestrov 19小时前This is a very nice and fresh page layout.
- rubyfan 12小时前Why does every exhibit made with AI look the same?
- dominotw 13小时前i 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 11小时前Everything looked the same before too. One of the same 6 Jekyll temples etc. Fads in design come and go
- andrewstuart 17小时前I assumed it wrote Python or some sort of other code.
- singpolyma3 11小时前Usually yes
- mavhc 16小时前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
- sebzim4500 11小时前Probably 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
And obviously Terrence Tao is up there in the response.