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How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell. It's all just passable garbled nonesense that

How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell. It's all just passable garbled nonesense that the reader (goes to lengths) to interept based on their prior knowledge, which is not expressed in the syntax of what these systems output. In the case of mathematics, we're far less willing to "BS away" the interpretive failures. But if we were equally demanding, likewise, all prose generated by these systems isnt AI "getting" anything either. Pass a film reel thru' a shredder and an art student would still call it a film. Pass math thru' and a mathematician wont. This says more about our ability and inclination to make sense out of nonesense when in apparent communicative situations (since, when speaking to a person, this actually improves our mutual understanding). So, how much of AI is just hacking people's cognitive failures: (1) people's willingness to attribute intention; (2) people's willingness to impart sense "at all costs" to apparent communication; and (3) "hopeium".

dimmuborgir 4y ago
AI is bad at music also. Even the state of the art transformer models can't produce more than a few seconds of coherent melodic phrases.
- CactusOnFire 4y ago
  AI is bad at Audio. AI can do MIDI fine.
  - causi 4y ago
    Which is a real shame. AI-powered restoration of poor-quality audio would be highly useful.
    - aaroninsf 4y ago
      That particular niche has had some pretty amazing successes already. It's coming. We can't produce arbitrary media streams with many "stack layers" of meaning and detail yet, but we can do a lot of specific instrumental transformations... Vaguely relevant: https://koe.ai/recast/ https://koe.ai/recast/
  - dwringer 4y ago
    MIDI is extraordinarily expressive and is likely used to sequence a large majority of music produced within the last three decades. A lot of the instruments you hear are synthesizers or samplers running directly from MIDI. There is a lot more to what MIDI can do, and is used for, than the conception most people have from "canyon.mid" or old website background music. If an AI can do MIDI just fine then it's an extremely small leap to doing audio just fine.
    - p1esk 4y ago
      If an AI can do MIDI just fine then it's an extremely small leap to doing audio just fine. Unfortunately this is not true. It takes a huge amount of human effort to make MIDI encoded music sound good. The difference between MIDI and raw audio music generation is the same as the difference between drawing a cartoon and producing a photograph. To clarify, yes MIDI can be expressive, but what's being generated when people say "AI generates MIDI music" is basically a piano roll.
      - NateEag 4y ago
        thank you for clarifying this. As a clasically-trained pianist who then got into electronica and synthesis, it was mind blowing to me that people could wrangle expression and phrasing from a MIDI sequencer.
      - dwringer 4y ago
        I'm not familiar enough with existing implementations of such systems to dispute it, but there's no fundamental reason algorithmic composition systems could not include modulation parameters of all kinds (pitch/breath/effects/synthesizer controls/etc) in their output. I am envisioning a DAW set up with several VST's and samplers with routing and effects in place, then using some combination of genetic algorithms and other methods to "tweak the knobs" in the search for something pleasing. The search space is absolutely enormous, though, so I don't dispute that it's very difficult, but I wouldn't go so far as to say that it can't be done. In such a space there are "no wrong answers" so to speak. I have a python script which creates randomized sequences of notes/rhythm and gives each one a different combination of LP/HP filters and random envelopes - it's not music but it takes on a much less mechanical quality by emulating different attacks and timbres over time, even though it's completely random. I would go so far as to say I'd be genuinely surprised if algorithmic composition and production hasn't been used to some extent significantly greater than "basically a piano roll" in at least some of the past decade's top 40 music on the radio.
- stephencanon 4y ago
  Which is extra funny, because GOFAI models (e.g. David Cope's work) were doing a pretty OK job back in the 1990s!
- mjburgess 4y ago
  I think if we replaced "AI" with "taking averages over subsets of historical examples", then there'd be no mystery for when "AI" will be good or bad at anything. Would we expect a discrete melodic structure to be expressible as averages of prior music? No.
- yeasurebut 4y ago
  That’s what a musician does. They make short loops and loop them. This reads like someone who knows sheet music and theory but does not listen to music. It’s repetition of short phrases over and over. I’m not really sure what people expect of general AI trained on human generated outputs. It can’t make up anything anything “net new” only compose based upon what we feed it. I like to think AI is just showing us how simple minded we really are and how our habit of sharing vain fairy tales about history makes us believe we’re masters of the universe.
  - dimmuborgir 4y ago
    Those models are not trained on short loops. They are trained on whole songs just like image generation models are trained on whole images. And yet they struggle to repeat sections, modulate to a different key, create bridges, intros and outros. After a few seconds of hallucinating a melodic line they simply abandon the idea and migrate to another one. There is no global structure whatsoever.
    - yeasurebut 4y ago
      Musicians don’t spit out an album in one sitting and they’re highly trained in theory. They get bored and tired of a process and take breaks. They come up with an album of loops composed together over time. AIs state will forever be constrained to the limits of human cognition and behavior as that’s what it’s trained on. I read published research all year. Circular reasoning. Tautology. It’s all over PhD thesis. There’s no “global structure” to humanity. Relativity is a bitch. Seeing the world through the vacuum of embedded inner monologue ignores the constraints of the physical one. It’s exhausting dealing with the mentality some clean room idea we imagine in a hammock can actually exist in a universe being ripped asunder by entropy. It’s living in memory of what we were sold; some ideal state. Very akin to religious and nation state idealism.
      - mjburgess 4y ago
        I think it's deeply depressing that AI has been sold as something even capable of modelling anything humans do; and quite depressing that this comment exists. "AI" is just taking `mean()` over our choice of encodings of our choice of measurements of our selection of things we've created. There is as much "alike humans" in patterns in tree bark. AI is an embarrassingly dumb procedure, incapable of the most basic homology with anything any animal has ever done; us especially. We are embedded in our environments, on which we act, and which act on us. In doing so we physically grow, mould our structure and that of our environment, and develop sensory-motor conceptualisations of the world. Everything we do, every act of the imagination or of movement of our limbs, is preconditioned-on and symptomatic-of our profound understanding of the world and how we are in it. The idea that `mean(424,34324,223123,3424,....)` even has any revelance to us at all is quite absurd. The idea that such a thing might sound pleasant thru' a speaker, irrelevant. This is a product of i dont know what. On the optimist side, a cultish desire to see Science produce a new utopia. On the pessimisst side, a likewise delusional desire to see Humans as dumb machines. What a sad state!
- vladf 4y ago
  Have you heard the piano continuations of AudioLM? https://google-research.github.io/seanet/audiolm/examples/ https://google-research.github.io/seanet/audiolm/examples/
  - bloep 4y ago
    Indeed, there is lots of denial or ignorance in this thread (ignorance in the technical sense). AudioLM already produced impressive results and it's a tiny fraction of what is already possible because performance simply improves with scale. One can probably solve music generation today with a ~$1B budget for most purposes like film or game music, or personalized soundtracks. This is not science fiction.
    - p1esk 4y ago
      I don't see a lot of progress in AudioLM compared to results from 2018: https://storage.googleapis.com/magentadata/papers/maestro/index.html https://storage.googleapis.com/magentadata/papers/maestro/in... What's more interesting and concerning - listen carefully to the first piano continuation example from AudioLM, notice the similarity of the last 7 seconds to Moonlight sonata: https://youtu.be/4Tr0otuiQuU?t=516 https://youtu.be/4Tr0otuiQuU?t=516 I'm afraid we will see a lot of this with music generation models in the near future.
      - bloep 4y ago
        There are quite simple tricks to avoid repetition/copying in NNs, e.g. by (1) training a model to predict the "popularity" of the main model's outputs and penalizing popular/copied productions by backpropping through that model so as to decrease the predicted popularity, or (2) by conditioning on random inputs (LLMs can be prompted with imaginary "ID XXX" prefixes before each example to mitigate repetitions), or (3) by increasing temperature or optimizing for higher entropy. LLM outputs are already extremely diverse and verbatim copying is not a huge issue at all. The point being, all evidence points to this not being a show stopper if you massage these evolutionary methods for long enough in one or more of the various right ways.
- deleted 4y ago
  [deleted]
- aaroninsf 4y ago
  AI can be quite good at music, but yes there is not yet at on-demand button rendering from a text prompt of bitstreams encoding composed performed and mastered music.
- denton-scratch 4y ago
  It doesn't surprise me that an AI model for language can't grok maths or music. I can't see how a language model can map to maths. Hell, I don't even know how to describe music in words. It's possible to articulate some maths in words, but that often involves using words with unexpected definitions.
- Der_Einzige 4y ago
  That's wrong, and shows how ignorant you are of SOTA techniques for music generation. They are far ahead of that.
woah 4y ago
Have you ever used Github CoPilot? It does a lot of useful work, automating away rote typing in programming. Have you tried Dall-E or Stable Diffusion? They make good looking images. This comment seems completely unmoored from where the state of the art is right now.
- TuringTest 4y ago
  Math follows a completely different approach with respect to how machine-learning AIs do their thing. Reason derives its strength in having a few primitives and creating new assertions through the transformation of symbols by following precise rules (which is how algorithms work). In ML-based AIs, everything is imprecise and probabilistic, and this kind of generation gets its strength from building recognizable from utterly imprecise inputs and training - quite the opposite of how logic and reason evolve. Now, "classic" AI was a powerful way to derive new knowledge, and automatic theorem proving is a strong discipline; but the recent breakthroughs in AI are not directly applicable to classic techniques. Do you know what machine-learning AIs could be good for? Generating "insight" in problem solvers for guiding the theorem demonstrations through the proof search space, trying to find the best sub-spaces to explore. If there's a way to create human-like general AI, it will likely combine both kinds of generation - the rational methods of symbolic logic and the "irrational" statistical methods of ML.
  - zmgsabst 4y ago
    Automated theorem proving is the same problem as “complete and label the diagram”, which image generation is okay at. Work in progress for sure, though.
    - NateEag 4y ago
      > Automated theorem proving is the same problem as “complete and label the diagram”, which image generation is okay at. How so? I'm no mathematician, but I don't see how these problem types are equivalent. Could you elaborate?
      - 4y ago
planetsprite 4y ago
Language models aren't built for math. Their improvement/training cycles aren't sensitive to the exactness and rule-based nature of mathematical language, plus there are probably a lot of bad/misleading examples of math in the source data. You'd have to be unrealistically pessimistic to call what GPT-3 and other huge language models produce "nonsense".
- visarga 4y ago
  It's not that they were not built for math, but more like verification is hard. But it's hard for humans as well. A large generative model + a fast verifier could do wonders. AlphaGo was built on that - the model can propose moves, but you can verify who won in the end. There are some code generation models that write their own tests as well, or use externally provided tests to verify their solutions. The DeepMind matrix multiplication algorithm was also "learning from verification" of generated solutions, because it's trivial to do that. In general verification remains an open problem.
  - spywaregorilla 4y ago
    I disagree. It is that they were not built for math. While brain analogies are shittier than most people assume, this is like trying to do math in your head without being allowed to think through calculations.
    - visarga 4y ago
      Brains weren't built for math either, just for surviving. And the "trying to do math in your head" is true if you use naive question answering, but if you ask "step by step" or "chain of thought", or "supporting questions", any of them will allow for flexible time steps. There are some solutions called "Language Model Cascades" that compose language models calls to simulate arbitrary complex reasoning chains including recursion. There is no reason to think language models are unfit for math, they are fit for generating possible solutions that need to be verified somehow.
      - 4y ago
saghm 4y ago
> How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell Honestly, even as someone generally pretty dismissive of the AI hype, I'm not sure you can go that far. The whole reason we have specific mathematical notation is that human languages often are not super great at dealing with it, and English in particular is pretty abysmal for being both unambiguous and precise (and I'd be surprised if language models didn't end up suffering from biases analogous to how many image recognition AI models have been found to not deal well with a diverse set of human appearances). We don't teach math the same way we teach English, and we certainly don't expect people to be experts at teaching both, so why would we expect an AI model designed for language to be able to do math?
- mirker 4y ago
  Because there is an algorithm for it. Convert the strings into floating point numbers, add them, convert them back to strings. It’s a leetcode medium question. It should be learnable. The article talks about abstract math questions, but even arithmetic is hard for language models.
  - stevenhuang 4y ago
    That even arithmetic is hard for language models may suggest language models (at least in their current form) are not the most optimum for the task.
edouard-harris 4y ago
This might make sense as a response solely to the title of the article, but I have to admit I find it puzzling as a reaction to its content. Notwithstanding the title, the article mentions a model called Minerva that scored fully 50% on the MATH dataset of high-school/undergrad mathematical problems. For comparison, a human computer science PhD student scored 40%. [1] For context, Minerva came out this July. When it was tested on a national math exam, it scored higher than that year's class of graduating high school seniors. [2] A mere eight months (!) earlier, OpenAI had announced [3] they'd trained a language model that solved math word problems almost as well as an average middle-schooler. So even if you believe — rightly or wrongly — that current capabilities aren't very impressive, it's worth remembering that your understanding of current capabilities might not be entirely accurate, even if it's only a few months out of date. Incidentally, it may be worth looking at some examples of these models' outputs before deciding what they can or can't do. Here's Minerva solving some math problems, for example: https://dl.airtable.com/.attachmentThumbnails/32f10fc59039c7057c095b99338d84f7/bbeaff17 https://dl.airtable.com/.attachmentThumbnails/32f10fc59039c7... https://dl.airtable.com/.attachmentThumbnails/f6f86e0edd14d14f015d76b88a2db8bc/aa14d91a https://dl.airtable.com/.attachmentThumbnails/f6f86e0edd14d1... https://dl.airtable.com/.attachmentThumbnails/d9bc743dca1015ed0e69b93dbe12e5ff/ce8d9c47 https://dl.airtable.com/.attachmentThumbnails/d9bc743dca1015... https://dl.airtable.com/.attachmentThumbnails/51562ef70c2b14542efba987f65deadb/3049873b https://dl.airtable.com/.attachmentThumbnails/51562ef70c2b14... https://dl.airtable.com/.attachmentThumbnails/c081906cc4d23b37dd7fa93f8763e8f9/3602cdd3 https://dl.airtable.com/.attachmentThumbnails/c081906cc4d23b... I'll admit I find it challenging to interpret these results as "passable garbled nonesense [sic]", though perhaps I'm not being demanding enough. At any rate, when these models go from beating 10-year olds at math to beating 18-year olds at math in the span of 8 months, one does start to wonder how much of the hype is really due to over-interpretation — and what the next 8 months have in store. ======================== [1] https://arxiv.org/pdf/1709.04326.pdf https://arxiv.org/pdf/1709.04326.pdf (For comparison, a 3-time Mathematics Olympiad gold-medalist scored 90%.) [2] This was Poland's National Math Exam. Minvera scored 65%; the 2021 national average was 57%. See https://www.aitracker.org/ https://www.aitracker.org/ and Section 3 of the Minerva paper at https://arxiv.org/pdf/2206.14858.pdf https://arxiv.org/pdf/2206.14858.pdf [3] https://openai.com/blog/grade-school-math/ https://openai.com/blog/grade-school-math/
1024core 4y ago
See the "joke explaining" examples on Page 36 of the paper: https://arxiv.org/abs/2204.02311 https://arxiv.org/abs/2204.02311 and tell me if it's just "passable garbled nonsense".
- riskneutral 4y ago
  That's astonishing.
  - stevenhuang 4y ago
    Oo this reminds me. One of my favourite sci-fi novels is The Moon is a Harsh Mistress. In it, it depicts the growth of a nascent AI from its attempts at understanding humor. The AI befriends a technician and gets the human to rate its own crafted jokes. Eventually the AI gets really good at telling jokes, and becomes sentient as a result. It was a very fun take on AI gaining sentience, highly recommended!
- mjburgess 4y ago
  > 500 bn parameter model That solution has a compressed representation of half the internet. NNs are "garabled nonesense" insofar as they try to generalise; insofar as they are search engines, they provide apparent sense by just repeating something in their database (= weights). Google, likewise, returns joke explanations.
  - 1024core 4y ago
    "The Internet" is much, much bigger than 500bn floats. The latest snapshot of archive.org has 505 billion web pages itself.
kazinator 4y ago
> How much of this is just "AI is bad at everything" "AI Language Models" are not touted as some general AI that is smart at everything, like a clever person with multiple intellectual skills integrated into one. AI language models are for modeling language, not for math problem solving, or anything else. People good at language aren't always good at math. DeepL produces very good, correct translations for "Alice has five more balls than Bob, who has two balls after he gives four to Charlie. How many balls does Alice have?" into numerous languages, even though it doesn't offer a solution. I have little doubt that an AI system could be trained to translate word problems like this into systems of equations, which could be dumped into a some decades-old CAS to obtain a solution, which the AI could map back into the verbal domain through the identities between the math variables like x and Alice's apples. "Hey look, that human who is supposedly good at math can't produce a painting of the Grand Canyon in the style of Monet, even if given eight months to do it, and is easily defeated in chess."

dimmuborgir 4y ago

AI is bad at music also. Even the state of the art transformer models can't produce more than a few seconds of coherent melodic phrases.

CactusOnFire 4y ago
AI is bad at Audio. AI can do MIDI fine.
- causi 4y ago
  Which is a real shame. AI-powered restoration of poor-quality audio would be highly useful.
  - aaroninsf 4y ago
    That particular niche has had some pretty amazing successes already. It's coming. We can't produce arbitrary media streams with many "stack layers" of meaning and detail yet, but we can do a lot of specific instrumental transformations... Vaguely relevant: https://koe.ai/recast/ https://koe.ai/recast/
- dwringer 4y ago
  MIDI is extraordinarily expressive and is likely used to sequence a large majority of music produced within the last three decades. A lot of the instruments you hear are synthesizers or samplers running directly from MIDI. There is a lot more to what MIDI can do, and is used for, than the conception most people have from "canyon.mid" or old website background music. If an AI can do MIDI just fine then it's an extremely small leap to doing audio just fine.
  - p1esk 4y ago
    If an AI can do MIDI just fine then it's an extremely small leap to doing audio just fine. Unfortunately this is not true. It takes a huge amount of human effort to make MIDI encoded music sound good. The difference between MIDI and raw audio music generation is the same as the difference between drawing a cartoon and producing a photograph. To clarify, yes MIDI can be expressive, but what's being generated when people say "AI generates MIDI music" is basically a piano roll.
    - NateEag 4y ago
      thank you for clarifying this. As a clasically-trained pianist who then got into electronica and synthesis, it was mind blowing to me that people could wrangle expression and phrasing from a MIDI sequencer.
    - dwringer 4y ago
      I'm not familiar enough with existing implementations of such systems to dispute it, but there's no fundamental reason algorithmic composition systems could not include modulation parameters of all kinds (pitch/breath/effects/synthesizer controls/etc) in their output. I am envisioning a DAW set up with several VST's and samplers with routing and effects in place, then using some combination of genetic algorithms and other methods to "tweak the knobs" in the search for something pleasing. The search space is absolutely enormous, though, so I don't dispute that it's very difficult, but I wouldn't go so far as to say that it can't be done. In such a space there are "no wrong answers" so to speak. I have a python script which creates randomized sequences of notes/rhythm and gives each one a different combination of LP/HP filters and random envelopes - it's not music but it takes on a much less mechanical quality by emulating different attacks and timbres over time, even though it's completely random. I would go so far as to say I'd be genuinely surprised if algorithmic composition and production hasn't been used to some extent significantly greater than "basically a piano roll" in at least some of the past decade's top 40 music on the radio.
stephencanon 4y ago
Which is extra funny, because GOFAI models (e.g. David Cope's work) were doing a pretty OK job back in the 1990s!
mjburgess 4y ago
I think if we replaced "AI" with "taking averages over subsets of historical examples", then there'd be no mystery for when "AI" will be good or bad at anything. Would we expect a discrete melodic structure to be expressible as averages of prior music? No.
yeasurebut 4y ago
That’s what a musician does. They make short loops and loop them. This reads like someone who knows sheet music and theory but does not listen to music. It’s repetition of short phrases over and over. I’m not really sure what people expect of general AI trained on human generated outputs. It can’t make up anything anything “net new” only compose based upon what we feed it. I like to think AI is just showing us how simple minded we really are and how our habit of sharing vain fairy tales about history makes us believe we’re masters of the universe.
- dimmuborgir 4y ago
  Those models are not trained on short loops. They are trained on whole songs just like image generation models are trained on whole images. And yet they struggle to repeat sections, modulate to a different key, create bridges, intros and outros. After a few seconds of hallucinating a melodic line they simply abandon the idea and migrate to another one. There is no global structure whatsoever.
  - yeasurebut 4y ago
    Musicians don’t spit out an album in one sitting and they’re highly trained in theory. They get bored and tired of a process and take breaks. They come up with an album of loops composed together over time. AIs state will forever be constrained to the limits of human cognition and behavior as that’s what it’s trained on. I read published research all year. Circular reasoning. Tautology. It’s all over PhD thesis. There’s no “global structure” to humanity. Relativity is a bitch. Seeing the world through the vacuum of embedded inner monologue ignores the constraints of the physical one. It’s exhausting dealing with the mentality some clean room idea we imagine in a hammock can actually exist in a universe being ripped asunder by entropy. It’s living in memory of what we were sold; some ideal state. Very akin to religious and nation state idealism.
    - mjburgess 4y ago
      I think it's deeply depressing that AI has been sold as something even capable of modelling anything humans do; and quite depressing that this comment exists. "AI" is just taking `mean()` over our choice of encodings of our choice of measurements of our selection of things we've created. There is as much "alike humans" in patterns in tree bark. AI is an embarrassingly dumb procedure, incapable of the most basic homology with anything any animal has ever done; us especially. We are embedded in our environments, on which we act, and which act on us. In doing so we physically grow, mould our structure and that of our environment, and develop sensory-motor conceptualisations of the world. Everything we do, every act of the imagination or of movement of our limbs, is preconditioned-on and symptomatic-of our profound understanding of the world and how we are in it. The idea that `mean(424,34324,223123,3424,....)` even has any revelance to us at all is quite absurd. The idea that such a thing might sound pleasant thru' a speaker, irrelevant. This is a product of i dont know what. On the optimist side, a cultish desire to see Science produce a new utopia. On the pessimisst side, a likewise delusional desire to see Humans as dumb machines. What a sad state!
vladf 4y ago
Have you heard the piano continuations of AudioLM? https://google-research.github.io/seanet/audiolm/examples/ https://google-research.github.io/seanet/audiolm/examples/
- bloep 4y ago
  Indeed, there is lots of denial or ignorance in this thread (ignorance in the technical sense). AudioLM already produced impressive results and it's a tiny fraction of what is already possible because performance simply improves with scale. One can probably solve music generation today with a ~$1B budget for most purposes like film or game music, or personalized soundtracks. This is not science fiction.
  - p1esk 4y ago
    I don't see a lot of progress in AudioLM compared to results from 2018: https://storage.googleapis.com/magentadata/papers/maestro/index.html https://storage.googleapis.com/magentadata/papers/maestro/in... What's more interesting and concerning - listen carefully to the first piano continuation example from AudioLM, notice the similarity of the last 7 seconds to Moonlight sonata: https://youtu.be/4Tr0otuiQuU?t=516 https://youtu.be/4Tr0otuiQuU?t=516 I'm afraid we will see a lot of this with music generation models in the near future.
    - bloep 4y ago
      There are quite simple tricks to avoid repetition/copying in NNs, e.g. by (1) training a model to predict the "popularity" of the main model's outputs and penalizing popular/copied productions by backpropping through that model so as to decrease the predicted popularity, or (2) by conditioning on random inputs (LLMs can be prompted with imaginary "ID XXX" prefixes before each example to mitigate repetitions), or (3) by increasing temperature or optimizing for higher entropy. LLM outputs are already extremely diverse and verbatim copying is not a huge issue at all. The point being, all evidence points to this not being a show stopper if you massage these evolutionary methods for long enough in one or more of the various right ways.
deleted 4y ago
[deleted]
aaroninsf 4y ago
AI can be quite good at music, but yes there is not yet at on-demand button rendering from a text prompt of bitstreams encoding composed performed and mastered music.
denton-scratch 4y ago
It doesn't surprise me that an AI model for language can't grok maths or music. I can't see how a language model can map to maths. Hell, I don't even know how to describe music in words. It's possible to articulate some maths in words, but that often involves using words with unexpected definitions.
Der_Einzige 4y ago
That's wrong, and shows how ignorant you are of SOTA techniques for music generation. They are far ahead of that.

woah 4y ago

Have you ever used Github CoPilot? It does a lot of useful work, automating away rote typing in programming. Have you tried Dall-E or Stable Diffusion? They make good looking images. This comment seems completely unmoored from where the state of the art is right now.

TuringTest 4y ago
Math follows a completely different approach with respect to how machine-learning AIs do their thing. Reason derives its strength in having a few primitives and creating new assertions through the transformation of symbols by following precise rules (which is how algorithms work). In ML-based AIs, everything is imprecise and probabilistic, and this kind of generation gets its strength from building recognizable from utterly imprecise inputs and training - quite the opposite of how logic and reason evolve. Now, "classic" AI was a powerful way to derive new knowledge, and automatic theorem proving is a strong discipline; but the recent breakthroughs in AI are not directly applicable to classic techniques. Do you know what machine-learning AIs could be good for? Generating "insight" in problem solvers for guiding the theorem demonstrations through the proof search space, trying to find the best sub-spaces to explore. If there's a way to create human-like general AI, it will likely combine both kinds of generation - the rational methods of symbolic logic and the "irrational" statistical methods of ML.
- zmgsabst 4y ago
  Automated theorem proving is the same problem as “complete and label the diagram”, which image generation is okay at. Work in progress for sure, though.
  - NateEag 4y ago
    > Automated theorem proving is the same problem as “complete and label the diagram”, which image generation is okay at. How so? I'm no mathematician, but I don't see how these problem types are equivalent. Could you elaborate?
    - 4y ago

planetsprite 4y ago

Language models aren't built for math. Their improvement/training cycles aren't sensitive to the exactness and rule-based nature of mathematical language, plus there are probably a lot of bad/misleading examples of math in the source data. You'd have to be unrealistically pessimistic to call what GPT-3 and other huge language models produce "nonsense".

visarga 4y ago
It's not that they were not built for math, but more like verification is hard. But it's hard for humans as well. A large generative model + a fast verifier could do wonders. AlphaGo was built on that - the model can propose moves, but you can verify who won in the end. There are some code generation models that write their own tests as well, or use externally provided tests to verify their solutions. The DeepMind matrix multiplication algorithm was also "learning from verification" of generated solutions, because it's trivial to do that. In general verification remains an open problem.
- spywaregorilla 4y ago
  I disagree. It is that they were not built for math. While brain analogies are shittier than most people assume, this is like trying to do math in your head without being allowed to think through calculations.
  - visarga 4y ago
    Brains weren't built for math either, just for surviving. And the "trying to do math in your head" is true if you use naive question answering, but if you ask "step by step" or "chain of thought", or "supporting questions", any of them will allow for flexible time steps. There are some solutions called "Language Model Cascades" that compose language models calls to simulate arbitrary complex reasoning chains including recursion. There is no reason to think language models are unfit for math, they are fit for generating possible solutions that need to be verified somehow.
    - 4y ago

saghm 4y ago

> How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell Honestly, even as someone generally pretty dismissive of the AI hype, I'm not sure you can go that far. The whole reason we have specific mathematical notation is that human languages often are not super great at dealing with it, and English in particular is pretty abysmal for being both unambiguous and precise (and I'd be surprised if language models didn't end up suffering from biases analogous to how many image recognition AI models have been found to not deal well with a diverse set of human appearances). We don't teach math the same way we teach English, and we certainly don't expect people to be experts at teaching both, so why would we expect an AI model designed for language to be able to do math?

mirker 4y ago
Because there is an algorithm for it. Convert the strings into floating point numbers, add them, convert them back to strings. It’s a leetcode medium question. It should be learnable. The article talks about abstract math questions, but even arithmetic is hard for language models.
- stevenhuang 4y ago
  That even arithmetic is hard for language models may suggest language models (at least in their current form) are not the most optimum for the task.

edouard-harris 4y ago

This might make sense as a response solely to the title of the article, but I have to admit I find it puzzling as a reaction to its content. Notwithstanding the title, the article mentions a model called Minerva that scored fully 50% on the MATH dataset of high-school/undergrad mathematical problems. For comparison, a human computer science PhD student scored 40%. [1] For context, Minerva came out this July. When it was tested on a national math exam, it scored higher than that year's class of graduating high school seniors. [2] A mere eight months (!) earlier, OpenAI had announced [3] they'd trained a language model that solved math word problems almost as well as an average middle-schooler. So even if you believe — rightly or wrongly — that current capabilities aren't very impressive, it's worth remembering that your understanding of current capabilities might not be entirely accurate, even if it's only a few months out of date. Incidentally, it may be worth looking at some examples of these models' outputs before deciding what they can or can't do. Here's Minerva solving some math problems, for example: https://dl.airtable.com/.attachmentThumbnails/32f10fc59039c7057c095b99338d84f7/bbeaff17 https://dl.airtable.com/.attachmentThumbnails/32f10fc59039c7... https://dl.airtable.com/.attachmentThumbnails/f6f86e0edd14d14f015d76b88a2db8bc/aa14d91a https://dl.airtable.com/.attachmentThumbnails/f6f86e0edd14d1... https://dl.airtable.com/.attachmentThumbnails/d9bc743dca1015ed0e69b93dbe12e5ff/ce8d9c47 https://dl.airtable.com/.attachmentThumbnails/d9bc743dca1015... https://dl.airtable.com/.attachmentThumbnails/51562ef70c2b14542efba987f65deadb/3049873b https://dl.airtable.com/.attachmentThumbnails/51562ef70c2b14... https://dl.airtable.com/.attachmentThumbnails/c081906cc4d23b37dd7fa93f8763e8f9/3602cdd3 https://dl.airtable.com/.attachmentThumbnails/c081906cc4d23b... I'll admit I find it challenging to interpret these results as "passable garbled nonesense [sic]", though perhaps I'm not being demanding enough. At any rate, when these models go from beating 10-year olds at math to beating 18-year olds at math in the span of 8 months, one does start to wonder how much of the hype is really due to over-interpretation — and what the next 8 months have in store. ======================== [1] https://arxiv.org/pdf/1709.04326.pdf https://arxiv.org/pdf/1709.04326.pdf (For comparison, a 3-time Mathematics Olympiad gold-medalist scored 90%.) [2] This was Poland's National Math Exam. Minvera scored 65%; the 2021 national average was 57%. See https://www.aitracker.org/ https://www.aitracker.org/ and Section 3 of the Minerva paper at https://arxiv.org/pdf/2206.14858.pdf https://arxiv.org/pdf/2206.14858.pdf [3] https://openai.com/blog/grade-school-math/ https://openai.com/blog/grade-school-math/

1024core 4y ago

See the "joke explaining" examples on Page 36 of the paper: https://arxiv.org/abs/2204.02311 https://arxiv.org/abs/2204.02311 and tell me if it's just "passable garbled nonsense".

riskneutral 4y ago
That's astonishing.
- stevenhuang 4y ago
  Oo this reminds me. One of my favourite sci-fi novels is The Moon is a Harsh Mistress. In it, it depicts the growth of a nascent AI from its attempts at understanding humor. The AI befriends a technician and gets the human to rate its own crafted jokes. Eventually the AI gets really good at telling jokes, and becomes sentient as a result. It was a very fun take on AI gaining sentience, highly recommended!
mjburgess 4y ago
> 500 bn parameter model That solution has a compressed representation of half the internet. NNs are "garabled nonesense" insofar as they try to generalise; insofar as they are search engines, they provide apparent sense by just repeating something in their database (= weights). Google, likewise, returns joke explanations.
- 1024core 4y ago
  "The Internet" is much, much bigger than 500bn floats. The latest snapshot of archive.org has 505 billion web pages itself.

kazinator 4y ago

> How much of this is just "AI is bad at everything" "AI Language Models" are not touted as some general AI that is smart at everything, like a clever person with multiple intellectual skills integrated into one. AI language models are for modeling language, not for math problem solving, or anything else. People good at language aren't always good at math. DeepL produces very good, correct translations for "Alice has five more balls than Bob, who has two balls after he gives four to Charlie. How many balls does Alice have?" into numerous languages, even though it doesn't offer a solution. I have little doubt that an AI system could be trained to translate word problems like this into systems of equations, which could be dumped into a some decades-old CAS to obtain a solution, which the AI could map back into the verbal domain through the identities between the math variables like x and Alice's apples. "Hey look, that human who is supposedly good at math can't produce a painting of the Grand Canyon in the style of Monet, even if given eight months to do it, and is easily defeated in chess."