4 ms·

I'd hope most functional adults understand that the Fields Medal and basically every other annual "prize" out there is awarded to both "recombinant" innovations

I'd hope most functional adults understand that the Fields Medal and basically every other annual "prize" out there is awarded to both "recombinant" innovations and "new-dimensional thinking" innovations. Humans aren't going to come up with "new-dimensional" innovations in every field, every single year. I'd say yes, LLMs "just" recombine things. I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. (I'm open to being proven wrong.) But stuff like this is exactly the type of innovation LLMs are great at, and that doesn't discount the need for humans to also be good at "recombinant" innovation. We still seem to be able to do a lot that they cannot in terms of synthesizing new ideas.

bbor 4mo ago
To keep my usual rant short: I think you’re assuming a categorical distinction between those two types of innovations that just doesn’t exist. Calculus certainly required some fundamental paradigm shifts, but there’s a reason that they didn’t have to make up many words wholesale to explain it! Also we shouldn’t be thinking about what LLMs are good at, but rather what any computer ever might be good at. LLMs are already only one (essential!) part of the system that produced this result, and we’ve only had them for 3 years. Also also this is a tiny nitpick but: the fields medal is every 4 years, AFAIR. For that exact reason, probably!
- symfrog 4mo ago
  We have had LLMs for much longer than 3 years.
  - danielmarkbruce 4mo ago
    No, we haven't, for any reasonable definition of L.
    - wavemode 4mo ago
      OpenAI themselves must not have a "reasonable definition of L", then. Their own papers and press releases refer to GPT-2 (from 2019) as a "large language model". https://openai.com/index/better-language-models/ https://openai.com/index/better-language-models/
      - danielmarkbruce 4mo ago
        Yes, and 1.5 billion parameters meets no reasonable current definition of large. It would be considered a tiny language model. OpenAI themselves refer to their small/fast models as small models all over their documentation.
        wavemode 4mo ago
        The term doesn't change its meaning because something new comes along. The point of the term "large" is to highlight the massive parameter count (compared to traditional statistical models, where having 1.5 billion parameters was basically unheard of). It leads to the "double decent" phenomenon that allows them to generalize in ways traditional statistical models can't. The idea that the "large" descriptor was just a subjective exclamation, like "oh wow this model is pretty large ain't it", is revisionism.
        danielmarkbruce 4mo ago
        yes, it does. That's why OpenAI refers to it's small models as small. They are just so different. The capabilities have changed dramatically. The use cases are wildly different. The architectures are quite different. Even the core idea of attention is different. Training them is materially different. Serving them is materially different. A 1.5 bill parameter model from 2019 is so different from today's LLMs that they really don't have much in common. What we have now is quite similar to what we had a couple years ago though.
        bbor 4mo ago
        The term doesn't change its meaning because something new comes along. ...you're gonna flip when you hear about how language works :)
    - Yizahi 4mo ago
      Sure we do, since Fei-Fei Li and team created that annotated dataset, which allowed to train first LLMs. So LLMs are here for more than a decade already.
      - danielmarkbruce 4mo ago
        You are confused by what the L and L mean in LLM, or which data set she created, or both, or in general.
        Yizahi 4mo ago
        Or it is you who are confused. And I want to remind you that you can't retcon historical word use.
        danielmarkbruce 4mo ago
        Fei Fei was annotating images... the second L in LLM is for "language". The first language models named LLM at the time were trained on language data, with an objective function of predicting the next token. It had nothing to do with the imagenet data. Imagenet data was used in... vision models. The attention is all you need paper didn't ever use the term LLM or large language model because the phrase didn't exist in industry. Why comment on a field you know nothing about?
  - Nevermark 4mo ago
    I took humans thousands of years, then hundreds of years, to come to terms with very basic concepts about numbers. Its amazing to me when people talk about recombining things, or following up on things as somehow lesser work. People can't separate the perspective they were given when they learned the concepts, that those who developed the concepts didn't have because they didn't exist. Simple things are hard, or everything simple would have been done hundreds of years ago, and that is certainly not the case. Seeing something others have not noticed is very hard, when we don't have the concepts that the "invisible" things right in front of us will teach us.
    - adi_kurian 4mo ago
      Anyone in the arts is aware that creativity is not the new, it is the repackaging of what already exists into something that is itself new.
      - RajT88 4mo ago
        Except for "Being John Malkovich". That movie was way out there on its own.
        fragmede 4mo ago
        It's "just" a Man-vs-Self story, of the ~7 story archetypes out there.
        RajT88 4mo ago
        You need to rewatch that movie.
    - godelski 4mo ago
      It's why the invention of teaching has been so important. Took a long time for humans to develop calculus. A long time to then refine it and make it much more useful. But then in a year or two an average person can learn what took hundreds of years to invent. It's crazy to equate these tasks as being the same. Even incremental innovation is difficult. You have to see something billions of people haven't. But there's also paradigm shifts and well... if you're not considered crazy at first then did you really shift a paradigm?
  - nextaccountic 4mo ago
    Fine, 8 years? That's not a long time
  - asdfasgasdgasdg 4mo ago
    When people say this what they mean is that we've had plausibly useful LLMs for around three years, and I would say that is basically true.
  - asdfasgasdgasdg 4mo ago
    When people say this what they mean is that we've had plausibly useful LLMs for around three years, and I would say that is basically true. The stuff before 2023 could barely be classified above the level of an interesting toy.
- pegasus 4mo ago
  The fundamental paradigm shift is the categorical distinction. And what would constitute many new words for you? It introduced a bunch of concepts and terms which we take for granted today, including "derivative", "integral", "infinitesimal", "limit" and even "function", the latter two not a new words, but what does it matter? – the associated meanings were new.
  - azakai 4mo ago
    There was a lot new in calculus, but it also didn't come out of nowhere. That Newton and Leibniz came up with similar ideas in parallel, independently, around the same time (what are the odds?), supports that. https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculu...
- m4x 4mo ago
  I think your comment about inventing new words is an interesting one. One of the things that I believe limits our ability to discover new ideas is our ability to describe related concepts. For example, the reason we still can't have clear discussions on consciousness is probably partly due to the fact that the necessary concepts haven't been cemented in language. We need new language before we can describe consciousness. I would guess LLMs are limited in their ability to be genuinely novel because they are trained on a fixed language. It makes research into the internal languages developed by LLMs during training all the more interesting.
oncallthrow 4mo ago
[flagged]
kelseyfrog 4mo ago
> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. (I'm open to being proven wrong.) The experiment is feasible. If it were performed and produced a positive result, what would it imply/change about how you see LLMs?
- sumeno 4mo ago
  How are you going to train a frontier level llm with no references to post 1700 mathematics?
  - bjt 4mo ago
    "frontier level" is doing a lot of work there, but the idea would be to only feed it earlier sources. There are people working on this. e.g. https://github.com/haykgrigo3/TimeCapsuleLLM https://github.com/haykgrigo3/TimeCapsuleLLM
    - lovecg 4mo ago
      The problem is the amount of data with that cutoff is really minuscule to produce anything powerful. You might be able to generate a lot of 1700s sounding data, you’d have to be careful not to introduce newer concepts or ways of thinking in that synthetic data though. A lot of modern texts talk about rates of change and the like in ways that are probably influenced by preexisting knowledge of calculus.
      - NewJazz 4mo ago
        Doesn't it prove GP's point then, that LLMs themselves simply aren't capable of creating/proving new theories and axioms?
        codebje 4mo ago
        Without passing opinion on GP's point, I think that just proves it's hard to establish a data set that doesn't bias toward the result you're hoping to find.
amelius 4mo ago
> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. Yes but that is because there was not enough text available to create an intelligent LLM to begin with.
JonathanMerklin 4mo ago
I agree with almost all of what you have stated, save for a minor nitpick: I frankly don't think most functional adults think about the Fields Medal, similar annual prizes, or the qualities of the innovations of their candidate pools. I also think that that's totally okay. I think among a certain learned cohort of adults it's okay to hope that, and I think it's okay to imagine an idealized world where having an opinion on this sort of matter is a baseline, but I don't think it's realistic or fair to imply that (what I believe handwavily to be a majority of) adults are nonfunctional for not sharing this understanding.
hgoel 4mo ago
I think an LLM trained on pre-calculus material would easily stumble into reinventing at least early calculus. It's already pretty easy for students to stumble into calculus from solid enough fundamentals. We even think that the Babylonian astronomers figured out they could integrate over velocity to predict the position of Jupiter.
- bananaflag 4mo ago
  Something like this would be interesting: https://en.wikipedia.org/wiki/Adequality https://en.wikipedia.org/wiki/Adequality
godelski 4mo ago
> Humans aren't going to come up with "new-dimensional" innovations in every field, every single year. In fact, they are more rare. Specifically because they harder to produce. This is also why it is much harder to get LLMs to be really innovative. Human intelligence is a lot of things, it is deeply multifaceted. Also, I'm not sure why CS people act like axioms are where you start. Finding them is very very difficult. It can take some real innovation because you're trying to get rid of things, not build on top of. True for a lot of science too. You don't just build up. You tear down. You translate. You go sideways. You zoom in. You zoom out. There are so many tools at your disposal. There's so much math that has no algorithmic process to it. If you think it all is, your image is too ideal (pun(s) intended). But at the same time I get it, it is a level of math (and science) people never even come into contact with. People think they're good at math because they can do calculus. You're leagues ahead of most others around you, yes, and be proud of that. But don't let that distance deceive you into believing you're anywhere near the experts. There's true for much more than just math, but it's easy to demonstrate to people that they don't understand math. Granted, most people don't want to learn, which is perfectly okay too

bbor 4mo ago

To keep my usual rant short: I think you’re assuming a categorical distinction between those two types of innovations that just doesn’t exist. Calculus certainly required some fundamental paradigm shifts, but there’s a reason that they didn’t have to make up many words wholesale to explain it! Also we shouldn’t be thinking about what LLMs are good at, but rather what any computer ever might be good at. LLMs are already only one (essential!) part of the system that produced this result, and we’ve only had them for 3 years. Also also this is a tiny nitpick but: the fields medal is every 4 years, AFAIR. For that exact reason, probably!

symfrog 4mo ago
We have had LLMs for much longer than 3 years.
- danielmarkbruce 4mo ago
  No, we haven't, for any reasonable definition of L.
  - wavemode 4mo ago
    OpenAI themselves must not have a "reasonable definition of L", then. Their own papers and press releases refer to GPT-2 (from 2019) as a "large language model". https://openai.com/index/better-language-models/ https://openai.com/index/better-language-models/
    - danielmarkbruce 4mo ago
      Yes, and 1.5 billion parameters meets no reasonable current definition of large. It would be considered a tiny language model. OpenAI themselves refer to their small/fast models as small models all over their documentation.
      - wavemode 4mo ago
        The term doesn't change its meaning because something new comes along. The point of the term "large" is to highlight the massive parameter count (compared to traditional statistical models, where having 1.5 billion parameters was basically unheard of). It leads to the "double decent" phenomenon that allows them to generalize in ways traditional statistical models can't. The idea that the "large" descriptor was just a subjective exclamation, like "oh wow this model is pretty large ain't it", is revisionism.
        danielmarkbruce 4mo ago
        yes, it does. That's why OpenAI refers to it's small models as small. They are just so different. The capabilities have changed dramatically. The use cases are wildly different. The architectures are quite different. Even the core idea of attention is different. Training them is materially different. Serving them is materially different. A 1.5 bill parameter model from 2019 is so different from today's LLMs that they really don't have much in common. What we have now is quite similar to what we had a couple years ago though.
        bbor 4mo ago
        The term doesn't change its meaning because something new comes along. ...you're gonna flip when you hear about how language works :)
  - Yizahi 4mo ago
    Sure we do, since Fei-Fei Li and team created that annotated dataset, which allowed to train first LLMs. So LLMs are here for more than a decade already.
    - danielmarkbruce 4mo ago
      You are confused by what the L and L mean in LLM, or which data set she created, or both, or in general.
      - Yizahi 4mo ago
        Or it is you who are confused. And I want to remind you that you can't retcon historical word use.
        danielmarkbruce 4mo ago
        Fei Fei was annotating images... the second L in LLM is for "language". The first language models named LLM at the time were trained on language data, with an objective function of predicting the next token. It had nothing to do with the imagenet data. Imagenet data was used in... vision models. The attention is all you need paper didn't ever use the term LLM or large language model because the phrase didn't exist in industry. Why comment on a field you know nothing about?
- Nevermark 4mo ago
  I took humans thousands of years, then hundreds of years, to come to terms with very basic concepts about numbers. Its amazing to me when people talk about recombining things, or following up on things as somehow lesser work. People can't separate the perspective they were given when they learned the concepts, that those who developed the concepts didn't have because they didn't exist. Simple things are hard, or everything simple would have been done hundreds of years ago, and that is certainly not the case. Seeing something others have not noticed is very hard, when we don't have the concepts that the "invisible" things right in front of us will teach us.
  - adi_kurian 4mo ago
    Anyone in the arts is aware that creativity is not the new, it is the repackaging of what already exists into something that is itself new.
    - RajT88 4mo ago
      Except for "Being John Malkovich". That movie was way out there on its own.
      - fragmede 4mo ago
        It's "just" a Man-vs-Self story, of the ~7 story archetypes out there.
        RajT88 4mo ago
        You need to rewatch that movie.
  - godelski 4mo ago
    It's why the invention of teaching has been so important. Took a long time for humans to develop calculus. A long time to then refine it and make it much more useful. But then in a year or two an average person can learn what took hundreds of years to invent. It's crazy to equate these tasks as being the same. Even incremental innovation is difficult. You have to see something billions of people haven't. But there's also paradigm shifts and well... if you're not considered crazy at first then did you really shift a paradigm?
- nextaccountic 4mo ago
  Fine, 8 years? That's not a long time
- asdfasgasdgasdg 4mo ago
  When people say this what they mean is that we've had plausibly useful LLMs for around three years, and I would say that is basically true.
- asdfasgasdgasdg 4mo ago
  When people say this what they mean is that we've had plausibly useful LLMs for around three years, and I would say that is basically true. The stuff before 2023 could barely be classified above the level of an interesting toy.
pegasus 4mo ago
The fundamental paradigm shift is the categorical distinction. And what would constitute many new words for you? It introduced a bunch of concepts and terms which we take for granted today, including "derivative", "integral", "infinitesimal", "limit" and even "function", the latter two not a new words, but what does it matter? – the associated meanings were new.
- azakai 4mo ago
  There was a lot new in calculus, but it also didn't come out of nowhere. That Newton and Leibniz came up with similar ideas in parallel, independently, around the same time (what are the odds?), supports that. https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculu...
m4x 4mo ago
I think your comment about inventing new words is an interesting one. One of the things that I believe limits our ability to discover new ideas is our ability to describe related concepts. For example, the reason we still can't have clear discussions on consciousness is probably partly due to the fact that the necessary concepts haven't been cemented in language. We need new language before we can describe consciousness. I would guess LLMs are limited in their ability to be genuinely novel because they are trained on a fixed language. It makes research into the internal languages developed by LLMs during training all the more interesting.

oncallthrow 4mo ago

[flagged]

kelseyfrog 4mo ago

> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. (I'm open to being proven wrong.) The experiment is feasible. If it were performed and produced a positive result, what would it imply/change about how you see LLMs?

sumeno 4mo ago
How are you going to train a frontier level llm with no references to post 1700 mathematics?
- bjt 4mo ago
  "frontier level" is doing a lot of work there, but the idea would be to only feed it earlier sources. There are people working on this. e.g. https://github.com/haykgrigo3/TimeCapsuleLLM https://github.com/haykgrigo3/TimeCapsuleLLM
  - lovecg 4mo ago
    The problem is the amount of data with that cutoff is really minuscule to produce anything powerful. You might be able to generate a lot of 1700s sounding data, you’d have to be careful not to introduce newer concepts or ways of thinking in that synthetic data though. A lot of modern texts talk about rates of change and the like in ways that are probably influenced by preexisting knowledge of calculus.
    - NewJazz 4mo ago
      Doesn't it prove GP's point then, that LLMs themselves simply aren't capable of creating/proving new theories and axioms?
      - codebje 4mo ago
        Without passing opinion on GP's point, I think that just proves it's hard to establish a data set that doesn't bias toward the result you're hoping to find.

amelius 4mo ago

> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. Yes but that is because there was not enough text available to create an intelligent LLM to begin with.

JonathanMerklin 4mo ago

I agree with almost all of what you have stated, save for a minor nitpick: I frankly don't think most functional adults think about the Fields Medal, similar annual prizes, or the qualities of the innovations of their candidate pools. I also think that that's totally okay. I think among a certain learned cohort of adults it's okay to hope that, and I think it's okay to imagine an idealized world where having an opinion on this sort of matter is a baseline, but I don't think it's realistic or fair to imply that (what I believe handwavily to be a majority of) adults are nonfunctional for not sharing this understanding.

hgoel 4mo ago

I think an LLM trained on pre-calculus material would easily stumble into reinventing at least early calculus. It's already pretty easy for students to stumble into calculus from solid enough fundamentals. We even think that the Babylonian astronomers figured out they could integrate over velocity to predict the position of Jupiter.

bananaflag 4mo ago
Something like this would be interesting: https://en.wikipedia.org/wiki/Adequality https://en.wikipedia.org/wiki/Adequality

godelski 4mo ago

> Humans aren't going to come up with "new-dimensional" innovations in every field, every single year. In fact, they are more rare. Specifically because they harder to produce. This is also why it is much harder to get LLMs to be really innovative. Human intelligence is a lot of things, it is deeply multifaceted. Also, I'm not sure why CS people act like axioms are where you start. Finding them is very very difficult. It can take some real innovation because you're trying to get rid of things, not build on top of. True for a lot of science too. You don't just build up. You tear down. You translate. You go sideways. You zoom in. You zoom out. There are so many tools at your disposal. There's so much math that has no algorithmic process to it. If you think it all is, your image is too ideal (pun(s) intended). But at the same time I get it, it is a level of math (and science) people never even come into contact with. People think they're good at math because they can do calculus. You're leagues ahead of most others around you, yes, and be proud of that. But don't let that distance deceive you into believing you're anywhere near the experts. There's true for much more than just math, but it's easy to demonstrate to people that they don't understand math. Granted, most people don't want to learn, which is perfectly okay too