[HN Gopher] AI language models are struggling to "get" math
___________________________________________________________________
AI language models are struggling to "get" math
Author : rbanffy
Score : 61 points
Date : 2022-10-12 13:53 UTC (9 hours ago)
(HTM) web link (spectrum.ieee.org)
(TXT) w3m dump (spectrum.ieee.org)
| blueprint wrote:
| Maybe because it's not actual AI.
| PaulHoule wrote:
| Ashby strikes again.
|
| Current sequence models don't have the right structures to
| represent math. Even if they use floating point internally, they
| can't really float the point because the nonlinearity in the
| model has a certain scale.
|
| A system that processes language can take advantage of the human
| desire for closure
|
| https://www.eurogamer.net/blood-in-the-gutter
|
| to fool people into thinking it is more capable than it really
| is. Math isn't like that.
| hey_over_here wrote:
| Mwell, the article claims, and points to work that also claims,
| that large language models can actually be made to perform
| arithmetic well. They need fine-tuning, verification, chain of
| thought prompting and majority voting to be combined but the
| linked Google blog says that Minerva hit 78.5% accuracy (on the
| GSM8K benchmark).
|
| For me the problem is that we can look at the output and say if
| it's right or wrong, but we know what language models do,
| internally: they predict the next token in a sequence. And we
| know that this is no way to do arithmetic, in the long run,
| even though it might well work over finite domains.
|
| Which is to say, I'm just as skeptical as you are, and probably
| even more, but I think it's useful to separate the claim from
| what has actually been demonstrated. Google claims its Minerva
| model is "solving maths problems" but what it's really doing is
| predicting solutions to problems like the ones it's been fine-
| tuned on, and those problems are problems stated at least
| partly in natural language, not "naked" arithmetic operations.
| In the latter, language models are still crap because they
| can't use the context of the natural language problem statement
| to help them predict the solution.
|
| Btw, "chain of thought prompting" if I remember correctly is a
| process by which an experimenter prompts the language model
| with a sequence of intermediary problems. So it's not so much
| the model's chain of thought, as the experimenter's chain of
| thought and the experimenter is asking the model to help him or
| her complete their chain of thought. I have a fuzzy
| recollection of that though.
| sharemywin wrote:
| computers already do math. language models just need to
| translate problems into code of some kind that can be run to
| get the answer.
|
| executive function/planning is probably the biggest problem at
| this point for ai.
| sharemywin wrote:
| The point I'm trying to make is LLMs don't need to do
| everything just be the glue to other systems.
| enord wrote:
| Wait what? Glue as in extract high level semantic
| representations from _syntatic probabilities_ and pass on
| to appropriate domain specific tools?
|
| This is the glaring hole in LLMs, a paradoxical semantic
| incoherence despite impressive sentenial and gramatical
| coherence.
|
| As glue it is so thin as to be potable.
| zackmorris wrote:
| That's interesting, I hadn't made the connection between
| executive function and intelligence.
|
| I went through a burnout in 2019 that felt like having a
| stroke. My brain finally reached such a level of negative
| reinforcement after years of failure that it wouldn't let me
| work anymore. I'd go to do very simple tasks, everything from
| brushing my teath to writing a TODO list, and it was like the
| part of my brain that performed those tasks wasn't there
| anymore. Or at least, it no longer obeyed if it perceived a
| potential reward involved. It was like my motivation got
| reversed. I had to relearn how to do everything, despite
| knowing that no reward might come for a very long time, which
| took at least 6 months before I began recovering. The closest
| answer I have is that my brain healed through faith.
|
| I only bring it up because executive function may be
| associated with a subjective experience of meaning. If
| there's truly no point to anything, then it's hard to summon
| the motivation to string together a sequence of AI tasks into
| something more like AGI.
|
| I guess that's another way of saying that nihilism could be
| the final hurdle for AGI to overcome. It's like the human
| philosophical question of why there's something instead of
| nothing. Or why angels would choose to be incarnate on Earth
| to experience a life of suffering when it's so much easier to
| remain dissociated.
| the_af wrote:
| > _language models just need to translate problems into code
| of some kind that can be run to get the answer_
|
| A huge "just"! Isn't this the magic step? Translating
| ambiguous symbols to meaning and combining them in meaningful
| ways is a big deal which, apparently, these AI models cannot
| do. They can just parrot things.
| gamegoblin wrote:
| It's already being done and will only get better: https://t
| witter.com/sergeykarayev/status/1569377881440276481
| the_af wrote:
| I suspect it's not solved, because solving this (beyond
| some trick/toy examples) is essentially solving General
| AI.
| JacobiX wrote:
| I'm not so sure about that. Of course computers can do
| arithmetic operations, but this is not the same as solving
| math problems, proving theorems, etc. Even mathematical
| objects are approximated up to an approximation error in a
| computer (like a differentiable manifold or a real number).
| PaulHoule wrote:
| There has been big progress in automated theorem proving
| lately
|
| https://en.wikipedia.org/wiki/Automated_theorem_proving
|
| you just don't hear about it much because the technology is
| not so fashionable today. Also it is more clear what the
| limits are, I mean, Turing, Godel, Tarski and all of those
| apply to neural networks as well any other formal system
| but people mostly forget it.
|
| Knuth wrote a really fun volume of _The Art of Computer
| Programming_ about advances in SAT solvers which are the
| foundation for theorem provers
|
| https://www.amazon.com/Art-Computer-Programming-Fascicle-
| Sat...
|
| Everybody is aware that neural network techniques have
| improved drastically in performance, it's much more obscure
| that the toolbox of symbolic A.I. has improved greatly.
| Back in the 1980s production rules engines struggled to
| handle 10,000 rules, now Drools can handle 1,000,000+ rules
| with no problems.
| sva_ wrote:
| > There has been big progress in automated theorem
| proving lately
|
| It doesn't seem like there has been much progress for
| anything but FOL?
| thwayunion wrote:
| The wiki article on automated theorem proving is quite
| bad as an overview of the active field; it's more a
| historical article about the mid to late 20th century.
| Most of the interesting things in automated reasoning
| have happened since the naughts, and that article kind of
| stops in the 90s
|
| SMT solvers have gotten quite good over the past couple
| decades, there are tons of domain-specific tools (eg in
| software and hardware verification), tons of niche
| applied decidable or semi-decidable theories (eg various
| modal and description logics), a lot of progress on the
| proof assistant ("non-fully-automated theorem proving")
| paradigm, and so on.
| PaulHoule wrote:
| It's clear that commonsense reasoning needs to deal with
| modals, counterfactuals, defaults, temporal logic, etc.
|
| It's not hard to add some extensions to logic for a
| particular application but a very hard problem to develop
| a general purpose extended logic.
|
| I look at the logic-adjacent production rules systems
| which never really standardized some of the commonly
| necessary things such as agendas, priorities, defaults,
| etc.
| IshKebab wrote:
| Computers are much much better at all that stuff than
| almost everyone too. Try asking Wolfram Alpha to solve
| something. Computers have gotten really good at proving
| things in the last couple of decades and formal
| verification methods are becoming increasingly popular.
|
| I think sharemywin is probably on to something. It's going
| to be _really_ hard for an AI to prove that e.g. x >0 &&
| x+y <= 1 && y>1 is unsatisfiable, but it's trivial for an
| SMT solver. On the other hand it probably isn't that much
| of a leap to make an AI that can feed that problem _into_
| an SMT solver.
| thwayunion wrote:
| _> Of course computers can do arithmetic operations, but
| this is not the same as solving math problems, proving
| theorems, etc. _
|
| Computers can solve math problems and prove theorems; this
| remains a significant subfield of Computer Science with
| lots of industrial use cases. However, pure machine
| learning based approaches toward these problems remain
| subpar.
|
| _> Even mathematical objects are approximated up to an
| approximation error in a computer (like a differentiable
| manifold or a real number)._
|
| Only because it caught on (and in the case of non-
| computationally-intensive applications, for purely
| historical reasons). For example, Mathematica has Reals and
| even functionality for Reals that is literally impossible
| to implement for integers [1,2]. There are also precise
| characterizations of objects in differential geometry [3].
| You could imagine applying LLMs to these types of programs
| a la Copilot, but when you do this you will find yourself
| agreeing with Paul Houle's observation that math is harder
| to fake than eg art, language, or even glue code for web
| apps.
|
| [1] https://reference.wolfram.com/language/ref/Reduce.html
|
| [2] https://en.wikipedia.org/wiki/G%C3%B6del%27s_incomplete
| ness_...
|
| [3] https://github.com/bollu/diffgeo
| the_af wrote:
| > _Computers can solve math problems and prove theorems_
|
| But the specification of the problem must be done by a
| human, translating to a formalized system that the
| software can understand. And if there's a problem in the
| formal specification, it's mostly up to the human to
| notice and fix; the computer will happily output garbage
| or crash or enter an infinite loop.
|
| So it seems this translation, going from an exploration
| of the problem statement, usually in ambiguous terms, to
| a formal specification, _and the awareness to possibly
| detect whether the answers make sense and the specs were
| right_ , is uniquely human.
| casey2 wrote:
| Counterexample: Shalosh B. Ekhad is a computer who is also
| a mathematician.
| Sharlin wrote:
| Well, you don't _need_ anything else than basic arithmetic
| to encode the entirety of, say, ZFC, enumerate every
| proposition in it, and halt iff you find a proof of
| whatever theorem you 're after. It just might take a
| while...
| sharemywin wrote:
| Online Integral Calculator Solve integrals with
| Wolfram|Alpha
|
| https://www.wolframalpha.com/calculators/integral-
| calculator...
| sva_ wrote:
| Now try to make a computer prove that there are no
| natural numbers a,b,c; so that a^n + b^n = c^n for any n
| > 2.
| Sharlin wrote:
| Shifting the goal posts a bit, aren't we?
| sharemywin wrote:
| I guess it depends on the outcome your worried about.
| Super intelligence or machines that replace the average
| office worker.
| PaulHoule wrote:
| That's not a bad approach, necessarily.
|
| There is a fairly simple program in
|
| https://www.amazon.com/Paradigms-Artificial-Intelligence-
| Pro...
|
| that solves word problems using the methods of the old AI.
| The point is that is is efficient and effective to use real
| math operators and not expect to fit numbers through the
| mysterious bottleneck of neural encoding.
| lupire wrote:
| Floating point isn't relevant here.
|
| The problem is that human language is approximate and correct
| math is not, so pattern matching on prose text is doomed. AI
| trained on exact math does a lot better. But that's not fully
| generic so fails the weird GPT goal of modeling all of human
| intelligence through prose. That's not how people solve math at
| all.
|
| GPT's "Superficially plausible but wrong" math is actually
| pretty good match for non-expert bad-at-math average human
| behavior.
| zozbot234 wrote:
| > GPT's "Superficially plausible but wrong" math is actually
| pretty good match for non-expert bad-at-math average human
| behavior.
|
| Relevant blog post: https://www.greaterwrong.com/posts/YhgjmC
| xcQXixStWMC/artific... "The best experts in the field
| estimate it will be at least a hundred years before
| calculators can add as well as a human twelve-year-old."
| PaulHoule wrote:
| I like Yudkovsky parodying himself there although I still
| don't know if he has a sense of humor or not.
| CommieBobDole wrote:
| Also Excel is terrible at encoding MP3s.
|
| It's a language model; why would we expect it do math or try to
| somehow shoehorn math into the model? Do the language centers of
| our brain do math?
|
| If something approximating AGI is going to happen, it's going to
| be a lot of models tied together with an executive function to
| recognize and send things to the area that's good at working with
| them.
| dr_dshiv wrote:
| Well, because we want rational language models. Something with
| a sense of truth.
|
| Math is not irrelevant--and I'm sure it's a solvable problem
| with language models.
| CommieBobDole wrote:
| But if it's rational and has a sense of truth, then it's AGI.
| Which I don't think is impossible or even unattainable within
| a reasonable amount of time, but we're .001% of the way
| there, not 50% or 75%.
|
| These models are fascinating, but the problem 'a lot of the
| things this model generates lack any semantic meaning' is
| inherent and likely insurmountable without connecting the
| model to other, far more complex models that haven't been
| built yet.
|
| We are at the level where our models can consistently
| generate blocks of text with full sentences in them that make
| grammatical sense. Which is pretty cool.
|
| But the next step is being able to consistently generate full
| sentences that make grammatical sense and usefully convey
| information. And while the current models do that a lot of
| the time, they don't do that all of the time because they
| don't and can't know the difference without essentially being
| a different thing. Because to do that consistently, we need
| an "understanding what things mean" model. Which is many
| orders of magnitude larger and more difficult than a text
| generator.
| [deleted]
| thwayunion wrote:
| What are some (non-nefarious) applications of generative
| language models that produce language which isn't constrained
| by some sort of rationality or directed by some sort of high-
| level goal?
|
| The point isn't the math. The point is that, in math and
| similar disciplines, it's harder to get away with producing
| mostly undirected gibberish that happens to have some imputed
| meaning. The point is "use language to do something where it's
| easy to verify correctness and generating infinite amounts of
| synthetic data is trivial"
|
| If a language model can't even do high school algebra, then I
| have a lot less confidence that it will ever be useful for
| customer service applications or any other number of potential
| applications outside of propaganda, advertising, and spam.
| hey_over_here wrote:
| > It's a language model; why would we expect it do math or try
| to somehow shoehorn math into the model?
|
| Language models can do math, or anyway arithmetic. That's
| because language models are trained to predict the next token
| in a sequence and an arithmetic operation can be represented as
| a sequence of tokens.
|
| For example, see Figure 3.10 on page 22, here:
|
| https://arxiv.org/abs/2005.14165
|
| The only problem is that language models are crap at arithmetic
| because they can only predict the next token in a sequence.
| That's enough to guess at the answer of an arithmetic problem
| some of the time but not enough to solve any arithmetic problem
| all of the time.
|
| More generally, the answer to your question is in the same
| Figure 3.10 I've referenced above. OpenAI (and others) have
| claimed that their large language models can do arithmetic. So
| then people tested the claim and found it to be a bag of old
| cobblers.
|
| Hence the article above. Nobody's trying to "shoehorn" anything
| anywhere. It's just something that language models can do,
| albeit badly.
| CommieBobDole wrote:
| Right, but what you're describing is 'not being able to do
| math'. Like, if I've memorized a multiplication table and can
| give you any result that's on the table but can't multiply
| anything that wasn't on the table, I can't do multiplication.
| hey_over_here wrote:
| It depends on how you see it. I agree with you, generally,
| but in the limit, if you memorised all possible instances
| of multiplication, then yes, you could certainly be said to
| know multiplication.
|
| I've not just come up with that off the top of my head,
| either. In PAC-Learning (what we have in terms of theory,
| in machine learning) a "concept" (e.g. multiplication) is a
| set of instances and a learning system is said to learn a
| concept if it can correctly label each of a set of testing
| instances by membership to the target concept with
| arbitrary probability of error. Trivially, a learner that
| has memorised every instance of a target concept can be
| said to have learned the concept. All this is playing fast
| and loose with PAC-Learning terminology for the sake of
| simplification.
|
| The problem of course is that some concepts have infinite
| sets of instances, and that is the case with arithmetic. On
| the other hand, it's maybe a little disingenuous to require
| a machine learning system to be able to represent infinite
| arithmetic since there is no physical computer that can do
| that, either.
|
| Anyway that's how the debate goes on these things. I'm on
| the side that says that if you want to claim your system
| can do arithmetic, you have to demonstrate that it has
| something that we can all agree is a recognisable
| representation of the rules of arithmetic, as we understand
| them. For instance, the axioms of Peano arithmetic. Which
| though is a bit unfair for deep learning systems that can't
| "show their work" in this way.
| abrax3141 wrote:
| The situation is actually much worse for science, or any moving
| field. This models are by design and necessity historical. So
| that if, for example, the FDA issues a drug approval overnight,
| The model camp follow sudden changes in a "reasoned" why.
| make3 wrote:
| The article is actually about how they are getting good at it :)
| mavu wrote:
| Talking about this stuff would be so much easier if we stopped
| calling those software "AI".
|
| It is a machine learning algorithm. It is an electronic Parrot.
|
| thats it. And suddenly no one will wonder "OH MY WHY CANN IT NOT
| DO MATH< IT SMART?!?!"
| mjburgess wrote:
| 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".
| woah wrote:
| 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.
| civilized wrote:
| I agree. It's possible to point out the clear limitations of
| current AI without being oblivious to the huge, indisputable
| advances that have occurred.
|
| People thought it might take centuries for a computer to
| defeat a top human in Go. Then deep learning showed up and a
| few years later it's the opposite.
|
| A lot of the things deep learning methods are doing now are
| things no one had any idea how long research would take to
| achieve, or if they were even possible.
|
| Personally, I think we are currently hitting some walls that
| might take a while to climb before we get to AGI, but I am
| _very_ impressed at the recent progress.
| TuringTest wrote:
| 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 wrote:
| 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.
| mjburgess wrote:
| sure, but co-pilot is mostly just copying code (see, for
| example, the issue with it producing quake source code).
|
| If you think of AI as a dial from sample(data) to mean(data),
| then as the dial is turned towards the mean() you get more
| "generic" results, but also more garbled ones.
|
| Copilot is more like a search engine, having turned the dial
| more towards sample().
|
| The real invention of the NN is simply to provide that dial
| in a trainable way.
|
| The only change to the "state of the art" is the size of the
| weights, and how long they take to train. This "advancement"
| is no more impressive than google indexing more webpages.
|
| There has been no step-change advancement in AI in, perhaps,
| 50 years. All we see today is a product of hardware, in
| GPU/CPUs able to compress TBs of data into c. 300GB of
| weights. And likewise, the internet to provide it and SSDs to
| hold it.
|
| The "magic" of AI is no more the magic of wikipida, here:
| copilot is good only because million+ programmers made github
| good.
|
| It's still little more than a fancy search.
| woah wrote:
| > 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.
|
| > It's still little more than a fancy search.
|
| I feel like the goalposts have been moved between your two
| comments. CoPilot is obviously not producing garbled
| nonsense, and it's also not just printing the top result
| from StackOverflow. It is producing code that references my
| variables, does the right thing 50% of the time, and
| usually compiles.
|
| One of the nice little things is error messages- when I
| type `if (!foo) { throw ... ` CoPilot is able to complete a
| nicely formatted and descriptive error message from its
| understanding of my code. It's not garbled nonsense, and
| it's not just a search engine.
|
| Does AI deserve the hype it sometimes gets? Not yet. But I
| think you're going to have to start digging a little deeper
| for your commentary.
| planetsprite wrote:
| Even if AI got to the point of perfectly passing every
| expert-level Turing test your degree of rigor as to what
| "thinking" is would never truly permit any belief of AI
| having struck the golden nugget of intelligence.
|
| Imagine if we were all self-replicating computers, and
| certain members of this silicon race began experimenting
| with making creatures with carbon macro-molecules to create
| organic intelligence, you could make the same claim in the
| other direction:
|
| "There has been no step-change advancement in Organic
| Intelligence in, perhaps, 50 years. All we see today is a
| product of cell count, in neurotransmitter chemistry able
| to compress TBs of experiences into c. 300B neurons."
| Marazan wrote:
| Dall-E produces good looking images within certain
| parameters.
|
| When you are in its bounds it seems magical, once you go
| outside it seems like a weak joke.
|
| And many of the reasons it is bad outside its sweet spot are
| fundamental to how it works not a flaw that can be iterated
| away.
| dimmuborgir wrote:
| 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.
| [deleted]
| vladf wrote:
| Have you heard the piano continuations of AudioLM?
|
| https://google-research.github.io/seanet/audiolm/examples/
| bloep wrote:
| 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 wrote:
| I don't see a lot of progress in AudioLM compared to
| results from 2018: https://storage.googleapis.com/magenta
| data/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
|
| I'm afraid we will see a lot of this with music
| generation models in the near future.
| bloep wrote:
| 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.
| p1esk wrote:
| I'm not sure what you mean by "backpropping through that
| model so as to decrease the predicted popularity". During
| training, we train a model to literally reproduce famous
| chunks of music exactly as they are in the training set.
| We can also learn to predict popularity at the same time,
| but we can't backpropagate anything that will reduce
| popularity, because this would directly contradict to the
| main loss objective of exact reproduction.
|
| Having said that, I think the idea of predicting
| popularity is good - we can use it for filtering already
| generated chunks during post-training evaluation phase.
|
| I don't think the other two methods you suggest would
| help here, we want to generate while conditioning on
| famous pieces, and we don't want to increase temperature
| if we want to generate conservative, but still high
| quality pieces.
|
| It's true that we (humans) are less sensitive to
| plagiarism in the text output, but even for LLMs it is a
| problem when it tries to generate something highly
| creative, such as poetry. I personally noticed multiple
| times a particular beautiful poetry phrases generated by
| GPT-2 only to google it and find out they were copied
| verbatim from a human poem.
| phillipharr1s wrote:
| Pretty sure the first continuation is a famous piece with a
| few notes messed up. Can't remember the name. Honestly it
| only sounds marginally better than the old markov chain
| continuations.
| macrolocal wrote:
| Yep, Moonlight Sonata (mov. 3) no less. Talk about over-
| fitting!
| vladf wrote:
| Isn't that as good as it gets? The whole point of the
| continuations is that given a short leading prompt from a
| real piece that it should continue it realistically.
|
| It didn't get to train on the test set, if that's what
| you're implying, and I find it hard to believe the
| assertion that continuations are copies of the train set
| (if that's your claim).
| p1esk wrote:
| It definitely copied a piece of Moonlight sonata in the
| last 7 seconds of the first continuation sample:
| https://youtu.be/4Tr0otuiQuU?t=516
| holub008 wrote:
| Interestingly, the original piece is a later Beethoven
| Sonata, Op. 31 No. 3. The model has its styles down!
| https://youtu.be/P-Q5aBAw-T4?t=78
| Der_Einzige wrote:
| That's wrong, and shows how ignorant you are of SOTA
| techniques for music generation. They are far ahead of that.
| denton-scratch wrote:
| 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.
| aaroninsf wrote:
| 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.
| CactusOnFire wrote:
| AI is bad at Audio. AI can do MIDI fine.
| dwringer wrote:
| 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 wrote:
| _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.
| causi wrote:
| Which is a real shame. AI-powered restoration of poor-
| quality audio would be highly useful.
| aaroninsf wrote:
| 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/
| stephencanon wrote:
| Which is extra funny, because GOFAI models (e.g. David Cope's
| work) were doing a pretty OK job back in the 1990s!
| mjburgess wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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!
| pessimizer wrote:
| I lack your confidence, and find it a bit religious.
|
| > The idea that `mean(424,34324,223123,3424,....)` even
| has any revelance to us at all is quite absurd.
|
| Most of what I say to anyone is exactly this.
|
| When I'm about to give anyone any information, I look
| back at all of the relevant past information that I can
| recall (through word and sensory association, not by
| logic, unless I have a recollection of an associated
| internal or external dialog that also used logical
| rules.) I multiply those by strength of recollection and
| similarity of situation (e.g. can I create a metaphor for
| the current situation from the recalled one?). I take the
| mean, then I share it, along with caveats about the
| aforementioned strength of recollection and similarity of
| situation.
|
| This is what it feels like I actually do. Any of these
| steps can be either taken consciously or by reflex. It's
| not hidden.
|
| > I think it's deeply depressing that AI has been sold as
| something even capable of modelling anything humans do
|
| This is a bizarre position. All computers ever do is
| model things that humans do. All a computer consists of
| is a receptacle for placing human will that will continue
| to apply that will after the human is removed. They are a
| way of crystallizing will in a way that you can sustain
| it with things (like electricity) other than the
| particular combination of air, water, food, space,
| pressure, temperature, etc. that is a person. An overflow
| drain is a computer that models the human will. An
| automatic switch/regulator is the basic electrical model
| of human will, and a computer is just a bunch of those
| stitched together in a complementary way.
| mjburgess wrote:
| You're an animal. You've no idea what you do, and you're
| using machines as a model. Likewise, in the 16th C. it
| was brass cogs; and in anchient greece, air/fire/etc.
|
| You're no more made of clay & god's breath, as you are
| sand and electricy.
|
| You're an oozing, growing, malluable organic organism
| being physiologically dynamically shaped by your sensory-
| motor oozing. You're a mystery to yourself, and these
| self-reports, heavily coloured by the in-vogue tech _are
| not science_ , they're pseudoscience.
|
| If you want to study how animals work, you'd need to
| study _that_. Not these impoverished metaphors that
| mystify both machines and men. No machine has ever
| acquired a concept through sensory-motor action, nor used
| one to imagine, nor thereby planned its actions. No
| machine is ever at play, nor has grown its muscles to be
| better at-play. No machine has, therefore, learned to
| play the piano. No machine has thought about food,
| because no machine has been hungry; no machine has cared,
| nor been motivated to care by a harsh environment.
|
| An inorganic mechanism is nothing at all like an animal,
| and an algorithm over a discrete sequence of numbers with
| electronic semantics, is nothing like tissue development.
|
| What you are doing is not something you can introspect.
| And you arent really doing that. Rather, you've learned a
| "way of speaking" about machine action and are back-
| projecting that onto yourself. In this way, you're
| obliterating 95% of the things you are.
| saghm wrote:
| > 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?
| planetsprite wrote:
| 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 wrote:
| 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 wrote:
| 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.
| burlesona wrote:
| I genuinely wonder if we will find there are some inherent
| tradeoffs to knowledge and understanding such that if we ever
| have machines that can "think like humans" they would in practice
| run into human-like cognition limits: ie such machines would be
| "bad at math" in the same way humans are "bat at math" compared
| to conventional computers.
| ryandvm wrote:
| Indeed. I posit that as we get closer and closer to simulating
| how the human brain works in the pursuit of artificial
| intelligence, we're going to start seeing more and more of the
| same "bugs" that humans have (logical fallacies, susceptibility
| to illusions, mental illness, etc.)
|
| You think your job sucks now, just wait until you're dealing
| with the general AI over on the UX team that's trying to get
| your ass fired because it's fostering a 3 year old grudge over
| that time you said Chappie was stupid.
| Der_Einzige wrote:
| At first, I thought it was surprising that a language model
| with a restricted vocabulary (e.g. banning the letter "E")
| acts significantly more "mentally ill", and then I thought
| about how I would come across if forced to use that
| constraint all the time, and I realized that maybe I'd appear
| mentally ill too!
|
| You can play with LMs with constrained vocabularies here:
| https://huggingface.co/spaces/Hellisotherpeople/Gadsby
| blackbear_ wrote:
| That's an interesting thought. However it's not cognitive
| limits that make humans bad at math, it's just a "hardware"
| issue: a human with a piece of paper is much better at math.
| aaaaaaaaaaab wrote:
| Even if neural networks were fundamentally incompatible with
| conventional computation, I don't see why you couldn't augment
| a neural network with a conventional ALU to do the numerical
| computations. This is exactly what humans do with pencil and
| paper - it's just a bit too slow.
| auganov wrote:
| Either the language model would need to know what it's doing
| or the host program would have to know what the AI is doing.
| Both seem out of reach. The latter seems more doable since
| you could hack something up for simple scenarios, but you'd
| effectively have to match the capabilities of the neural
| network in a classical way to handle every case (which would
| render using a neural net moot).
| WalterBright wrote:
| People struggle to get math, too.
| _0ffh wrote:
| And no wonder, as they correspond much closer to a Kahneman
| system 1 than system 2, where _we_ do most of our math.
| [deleted]
| bionhoward wrote:
| I bet vision transformers understand math better because it's
| somewhat artistic
| abrax3141 wrote:
| More generally, they struggle to get thing right. They're great
| at grammatical confabulation, but when you need a correct answer,
| or a correct drug recommendation, ask an expert.
| pessimizer wrote:
| That's because they're not modelling anything. The shocking thing
| about current AI models is that just sort of repeating and
| copying from memory what you've heard and seen gets you 97% of
| the way to imitating a person.* They still need to generate
| actual models somewhere to create consistency; so many generated
| images with one eye completely different from the other, or three
| arms, or fingers that grow into their cellphones.
|
| If you solve this, you've probably solved almost anything in the
| simulation field. I have no confidence that the solution will
| even be complicated. Information consumed needs to be used to add
| to some sort of model, and that model always needs to be used as
| part of input. The complicated part would be to make that base
| model able to modify itself reasonably based on input, to
| tolerate constant inconsistency, and to constantly refine itself
| towards consistency i.e. ruminate.
|
| I think a huge difference (which I think was approached through
| theories of embodied cognition) is that people start with a model
| (or the ability to create a model) of themselves. We can apply
| that model to other things and use it both to change how we
| ourselves behave, and how we speculate about the invisible states
| of other things. It's not for nothing that we can (and must)
| anthropomorphize anything.
|
| -----
|
| * Which was huge towards the confirmation of my belief that this
| is all people do 97% of the time.
| mgraczyk wrote:
| This is factually wrong, both in terms of quantity and quality.
|
| Current AI models are not "just sort of repeating and copying
| from memory". This is just an incorrect characterization of how
| they work and how they perform.
|
| AI skeptics often say things like this then backpedal with
| something like "Well they aren't really repeating what they
| heard, but their generative model is just a slightly more
| sophisticated version of repeating what they've heard." But
| this weaker claim is also true of humans. It's certainly the
| case that >97% percent of what humans say is "just repeating
| and copying" in the same sense.
| pessimizer wrote:
| > Current AI models are not "just sort of repeating and
| copying from memory". This is just an incorrect
| characterization of how they work and how they perform.
|
| You say this, but don't explain how. Because this is exactly
| what they are doing.
|
| > AI skeptics often say things like this
|
| I'm not really an AI skeptic. I think that we're very close
| to AI being indistinguishable from people. There are clearly
| problems that need to be solved, but I think the hardest
| problem was _accepting the fact that humans are largely just
| copying_ and realizing that would be enough to get you 97% of
| the way there, especially if you gave a machine far more to
| copy than a human could consume.
|
| > then backpedal with something like "Well they aren't really
| repeating what they heard, but their generative model is just
| a slightly more sophisticated version of repeating what
| they've heard." But this weaker claim is also true of humans.
| It's certainly the case that >97% percent of what humans say
| is "just repeating and copying" in the same sense.
|
| Maybe I'm not expressing myself clearly, but it seems that
| you're just repeating my comment with a sneer. Agreeing
| angrily?
| mgraczyk wrote:
| I'm disagreeing with the language you are using to
| characterize models. "copying from memory" implies that
| there is something being copied, and a memory that you are
| copying it from. I am pointing out that LLMs do not do
| this. It's not how they work.
|
| If you polled 1M random English speakers randomly and asked
| them whether or not a system that "just sort of repeating
| and copying from memory" could produce completely novel
| answers in response to completely novel questions, I
| suspect that the overwhelming majority would respond by
| saying no.
|
| Similarly if you asked 1000 people working on LLMs whether
| they work by "copying from memory", I suspect nearly all
| would say no. It would be accurate to say they are
| "generating text via a probabilistic model of language,
| which is encoded in the weights of a neural network", but
| there really is just no sense in which the models are
| "copying" anything.
|
| That being said, these models do "copy" some text in the
| sense that they can reconstruct some strings from their
| training input. For example every LLM I have played with
| can recite the first few paragraphs of A Tale of Two Cities
| verbatim. But that's a capability they have _in spite of_
| their actual design, not because of it.
| pessimizer wrote:
| > I'm disagreeing with the language you are using to
| characterize models. "copying from memory" implies that
| there is something being copied, and a memory that you
| are copying it from. I am pointing out that LLMs do not
| do this. It's not how they work.
|
| Then we're arguing about the semantics of the word
| "copy." That is not an interesting argument when you know
| exactly what I mean and can express it clearly.
|
| edit: If it helps, either substitute your description in
| whenever I say 'pretty much copy' or change the word
| "copy" to whatever word you want to use. But even though
| I can't reproduce the opening paragraph to A Tale of Two
| Cities verbatim, I can certainly write something that is
| "copying" it without doing that, and anyone who was
| familiar with the book and read my paragraph would agree
| with me.
| mgraczyk wrote:
| It is semantics, but that was your whole point no?
|
| > That's because they're not modelling anything
|
| If we agree on "how LLMs work", then how can you claim
| that they aren't modeling anything? They are modeling
| language, and while it's unlikely current paradigms will
| be proving new mathematical truths, it's completely
| plausible to me that bigger models will be able to handle
| simple math word problems like those in the article,
| precisely because LLMs can model the "Alice", "Apple",
| and "Bob" entities.
| sebastialonso wrote:
| can you actually share what "current AI models" are then? Not
| trying to be rude, but you just said "na ah" and then refused
| to argument any position.
| mgraczyk wrote:
| Current LLMs are "modeling" something according to pretty
| much any sense of the word "model".
|
| In the technical, computational linguistics sense, LLMs are
| language models that give a conditional posterior
| distribution over sentences. Given some (constrained)
| context, the model tells you the posterior distribution
| over sentences in or around that context.
|
| In the nontechnical, layman sense of the word, they are a
| system that is used as an example of language. LLMs imitate
| language by generating new sentences. They are a "model" in
| the same way that an architectural model is a model, or in
| the same way that a statue is a model of a human.
|
| The other point I disagreed with is the characterization
| that LLMs "just sort of repeat and copy from memory". I
| went into more detail about that in other replies.
| [deleted]
| jxy wrote:
| > "When multiplying really large numbers together ... they'll
| forget to carry somewhere and be off by one," says Vineet
| Kosaraju, a machine learning expert at OpenAI. Other mistakes
| made by language models are less human, such as misinterpreting
| 10 as 1 and 0, not ten.
|
| So the expert has never seen a seven year old struggling in
| adding two single digit numbers together? Did the expert learn 1
| and 0 being 10 first and learn to speak second?
|
| > The MATH group found just how challenging quantitative
| reasoning is for top-of-the-line language models, which scored
| less than 7 percent. (A human grad student scored 40 percent,
| while a math olympiad champ scored 90 percent.)
|
| Is this that surprising? How would our ieee editor score on the
| same problem set?
| Buttons840 wrote:
| Are there any general purpose models that are good at learning
| math? I mainly know basic feed-forward neural nets, but I don't
| think they do well outside their training region. Math, of
| course, has an infinite training region.
| alan-crowe wrote:
| I attempted to create a general purpose model for the exact
| version of the "what comes next problem." It enumerated
| primitive recursive functions, trying them out as it went. The
| limitation to primitive recursive functions was convenient
| because they always terminate. I didn't have to filter out the
| functions that ran for too long. (or do I?)
|
| The enumeration inherently includes functions of several
| variables, so I wasn't restricted to examples such as 1->1,
| 2->4, 3->9, 4->16 etc.
|
| I could try it out on examples such as (1,2)->3 (2,1)->3
| (0,2)->2, etc. Perhaps with enough it would "learn to add" =
| find a primitive recursive function that did addition.
|
| I got as far as finding the first problem. The enumeration
| technique that I used was effectively doing a tree recursion,
| like that function for computing Fibonacci numbers that bogs
| down because Fib(10) is computing Fib(5) lots of times. I had a
| lot of numbers that coded for the identity function, lots of
| numbers that coded for the first few functions, making the
| whole thing bog down, trying the same few functions over and
| over under different numerical disguises.
|
| I thought that I could see my way to fixing this first problem.
| Have some way of recognizing numbers that give forms that give
| the same function. I guessed that I could approximate this by
| saying that if two functions give the same value on a variety
| of arguments they are probably the same. Then I parameterise
| this criterion and tune. That opens the way to creating a
| consolidated enumeration, analogous to fixing the tree
| recursive fibonacci function by memoization, except trickier.
|
| But my health is poor and I ran out of energy.
|
| Also, I have a guess for the second problem. What happens if I
| fix the first problem and my enumeration reaches decently
| complicated primitive recursive functions. While they will all
| terminate, some might run for far too long, causing the process
| to bog down. Rejecting them on the basis of limiting the run
| time might work well. We are happy to only learn reasonably
| effect functions for doing maths.
|
| It is a fun idea and I encourage others to have a go.
| geoduck14 wrote:
| From my (limited) experience with the advanced ML models, they
| can "do basic math", but they make amateur mistakes with basic
| things - which indicates they _don 't actually know addition_,
| but they are good at looking at patterns in existing language.
|
| I would assume that state-of-the-art ML models could "convert a
| word problem into an equation", then feed _that_ equation into
| a 30 year-old graphing calculator to "do the math"
|
| The fact that no one has done this is an indicator that "there
| are more important things to work on", and it is just a matter
| of time that someone connects the two together
| MarkPNeyer wrote:
| This seems so much like humans that it makes me think lots of
| people are learning math with an ML-like approach instead
| of... whatever the heck people like engineers and
| mathematicians are doing.
| vidarh wrote:
| I wonder how these language models would do if we tried to
| teach them maths the way schools do: Feed them explanations
| first, then endless sequences of toy problems, see which
| they got wrong and feed them corrected examples back in.
|
| I'm not at all surprised they don't do well at maths,
| because while there are maths texts online, I doubt there
| is _enough_ material to give these models the same
| experience of repetition and reinforcement to help
| sufficiently generalise an understanding of the underlying
| rules.
| lupire wrote:
| Generating solved math problems is trivial, like making
| AlphaZero play itself in chess. Sparse Data is not the
| problem. Refusing to use it is.
| vidarh wrote:
| I don't think it's so much a refusal, as that it's not
| been a sufficient priority for anyone before. As the
| article points out there are now a few training sets
| which includes math problems, and models which do well on
| them. But the remaining problems seems to be with basics
| which humans tends to learn to do consistently with a lot
| of repetition, and it'd be interesting to see those
| datasets extended to the very simple.
| idealmedtech wrote:
| Anyone can do higher level math, the problem is that math
| education is generally done by people who see math as a
| tool for computation, rather than a study of deep
| connections bordering on philosophy, and beautiful insights
| resembling poetry. I've been in arguments before where
| someone didn't believe me that the underpinnings of modern
| philosophy are essentially the same as math!
|
| If the teachers don't love math, how can we expect students
| to?
| lupire wrote:
| What you describe is exactly what state of the art has done.
| They even lied and said it was "solving math problems" by
| calling numpy methods.
| the_af wrote:
| > _" convert a word problem into an equation"_
|
| Isn't this a huge step? It's not a minor detail remaining to
| be solved, but possibly the largest step!
| neoneye2 wrote:
| There is "LODA", which uses genetic algorithms, that
| continuously mutates existing math programs until discovering
| something new. It uses OEIS as training data, around 350k known
| integer sequences, such as primes/fibonacci. Around 100k
| programs have been mined so far.
|
| https://loda-lang.org/
|
| I'm a contributer to LODA.
|
| LODA runs on CPU. It doesn't use GPU. If you have spare
| computer, then please consider contributing with the mining.
| Your contribution helps.
|
| https://boinc.loda-lang.org/loda/
| xiphias2 wrote:
| It is a great sign that we are building AI in the right
| direction. Before building artificial human intelligence, it
| makes sense to get to the intelligence level of a mosquito or
| fly, then go to more intelligent animals in later iterations.
|
| As most of the human knowledge is encoded in videos, getting
| better at understanding / generating videos will clearly get us
| closer to make computers understand the world.
| yshrestha wrote:
| Language models can generate a Python function that does the math
| perfectly.
|
| I bet you would get better results if you tweaked the prompt to
| say "Generate a Python program that solves X math problem" and
| then just ran the resulting Python script.
|
| It does not need to be AGI to be useful.
| lupire wrote:
| You mean "generate a Python function that _calls a library_
| that does math perfectly, right?
| hgomersall wrote:
| In the limit, it's going to design an AI to write some python
| to call a library that does the math perfectly.
| thwayunion wrote:
| Unlike 99.99% of human programmers, who can and often do
| implement everything in sympy/numpy from scratch ;-)
| yshrestha wrote:
| Exactly! Hey it gets the job done :)
|
| Software is just a tall wedding cake of abstractions built on
| top of abstractions.
| swyx wrote:
| you can also tell the model that it doesnt know how to do math,
| and _it respects that_
|
| https://twitter.com/goodside/status/1568448128495534081
| Kim_Bruning wrote:
| That is also a very valid and interesting thing to do.
|
| But it's also quite interesting to see how the model would do
| "by itself". All kinds of interesting lessons to be learned!
| yshrestha wrote:
| Yeah! It is interesting to try and figure out "what" the
| model is actually learning. It is a valid thread of
| scientific inquiry.
| mlajtos wrote:
| Exactly, we need computer-equipped neural nets. Models need to
| use traditional UIs (including programming languages) and then
| we can talk about how to stop them. :)
| lairv wrote:
| That could only generate constructivist [0] proofs, and there
| are many things done in modern maths which are not
| constructivist. Maybe a better approach would be to use Curry-
| Howard [1] correspondence to directly get proofs from generated
| programs
|
| [0]
| https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...
|
| [1]
| https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
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