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.
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).
xyzsparetimexyz 5 hours 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!
0x59 7 hours ago [-]
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 4 hours 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?”
zdc1 3 hours ago [-]
You'd think with tool use being as available as it is, the first tool we'd want to give them is a calculator...
iammjm 14 hours ago [-]
Why doesn’t it just call tools such as Mathematica for such operations?
ACCount37 11 hours ago [-]
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.
9 hours ago [-]
10 hours ago [-]
defrost 14 hours ago [-]
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.
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...
jampekka 12 hours ago [-]
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 7 hours ago [-]
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 6 hours 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?
steveBK123 3 hours ago [-]
My point is what makes this terribly different than Alexa skills
grey-area 3 hours ago [-]
For this category of problems, no, very unlike human beings.
steveBK123 3 hours ago [-]
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 6 hours ago [-]
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 7 hours 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 7 hours ago [-]
In which case it’s just a neat extension of search
breezybottom 9 hours ago [-]
ChatGPT does, and has since 2023
euroderf 14 hours ago [-]
The spirit of Rube Goldberg is alive and well.
soupspaces 8 hours ago [-]
We evolved to do incremental fixes, not full refactoring
cwmoore 1 hours ago [-]
Maybe evolutionary, but not ours, as the things we tend to want to refactor have come to exceed our lifespans.
old_sound 2 days ago [-]
What happens inside an LLM when it tries to calculate with nothing but matrices.
silvestrov 15 hours ago [-]
This is a very nice and fresh page layout.
rubyfan 8 hours ago [-]
Why does every exhibit made with AI look the same?
dominotw 9 hours ago [-]
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 7 hours ago [-]
Everything looked the same before too. One of the same 6 Jekyll temples etc. Fads in design come and go
andrewstuart 12 hours ago [-]
I assumed it wrote Python or some sort of other code.
singpolyma3 7 hours ago [-]
Usually yes
mavhc 11 hours ago [-]
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 6 hours ago [-]
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
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.
And obviously Terrence Tao is up there in the response.
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).
What is it with LLM writing where it gives a smaller heading just before the main heading? Its nonsensical!
- color wheel
- oxidation reactions
- interpretive dance
- migratory patterns of curlew sandpipers
Whether one should is another question
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.
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)
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...
Previously it used to run Python scripts, and may still do for more complex calculations.
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".
So, in essence, just like human beings?
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.
That is my hopeful ideal
now everything looks the same and i can no longer read on kindle.