[HN Gopher] ProofOfThought: LLM-based reasoning using Z3 theorem...
       ___________________________________________________________________
        
       ProofOfThought: LLM-based reasoning using Z3 theorem proving
        
       https://arxiv.org/abs/2409.17270
        
       Author : barthelomew
       Score  : 311 points
       Date   : 2025-10-04 18:34 UTC (1 days ago)
        
 (HTM) web link (github.com)
 (TXT) w3m dump (github.com)
        
       | LASR wrote:
       | This is an interesting approach.
       | 
       | My team has been prototyping something very similar with encoding
       | business operations policies with LEAN. We have some internal
       | knowledge bases (google docs / wiki pages) that we first convert
       | to LEAN using LLMs.
       | 
       | Then we run the solver to verify consistency.
       | 
       | When a wiki page is changed, the process is run again and it's
       | essentially a linter for process.
       | 
       | Can't say it moved beyond the prototyping stage though, since the
       | LEAN conversion does require some engineers to look through it at
       | least.
       | 
       | But a promising approach indeed, especially when you have a
       | domain that requires tight legal / financial compliance.
        
         | barthelomew wrote:
         | The autoformalization gap is pretty difficult to bridge indeed.
         | We explored uncertainty quantification of autoformalization on
         | well-defined grammars in our NeurIPS 2025 paper :
         | https://arxiv.org/abs/2505.20047 .
         | 
         | If you ever feel like chatting and discussing more details,
         | happy to chat!
        
         | viraptor wrote:
         | Could you share an example of such policy? I'm struggling to
         | think of something defined well enough in the real world to
         | apply in Lean.
        
         | pbronez wrote:
         | That's pretty cool. It would be super useful to identify
         | contradictory guidance systematically.
        
         | chandureddyvari wrote:
         | For anyone curious about what LEAN is, like me, here's the
         | explanation: Lean Theorem Prover is a Microsoft project. You
         | can find it here: https://www.microsoft.com/en-
         | us/research/project/lean/
        
       | sigmoid10 wrote:
       | I always find it amazing how many people seem to fail to use
       | current LLMs to the fullest, even though they apparently work
       | with them in research settings. This benchmark pipeline simply
       | calls the OpenAI API and then painstakingly tries to parse the
       | raw text output into a structured json format, when in reality
       | the OpenAI API has supported structured outputs for ages now.
       | That already ensures your model generates schema compliant output
       | without hallucinating keys at the inference level. Today all the
       | major providers support this feature either directly or at least
       | indirectly via function calling. And if you run open models, you
       | can literally write arbitrary schema (i.e. not limited to json
       | behind the scenes) adhering inference engines yourself with
       | rather manageable effort. I'm constantly using this in my daily
       | work and I'm always baffled when people tell me about their
       | hallucination problems, because so many of them can be fixed
       | trivially these days.
        
         | atrus wrote:
         | I wouldn't find it amazing, there are so many new models,
         | features, ways to use models that the minute you pause to take
         | a deep dive into something specific, 43 other things have
         | already passed by you.
        
           | sigmoid10 wrote:
           | I would agree if you are a normal dev who doesn't work in the
           | field. But even then reading the documentation once a year
           | would have brought you insane benefits regarding this
           | particular issue. And for ML researchers there is no excuse
           | for stuff like that at this point.
        
         | retinaros wrote:
         | yes this can also improve the said reasoning.
        
           | sigmoid10 wrote:
           | The secret the big companies don't want to tell you is that
           | you can turn all their models into reasoning models that way.
           | You even have full control over the reasoning process and can
           | make it adhere to a specific format, e.g. the ones used in
           | legal settings. I've built stuff like that using plain old
           | gpt-4o and it was even better than the o series.
        
         | jssmith wrote:
         | I see JSON parse errors on occasion when using OpeanAI
         | structured outputs that resolve upon retry. It seems it's
         | giving instructions to the LLM but validation is still up to
         | the caller. Wondering if others see this too.
        
           | barthelomew wrote:
           | Hey, yes! This is because the DSL (Domain Specific Language)
           | is pretty complex, and the LLM finds it hard. We prototype a
           | much more effective version using SMT in our NeurIPS 2025
           | paper (https://arxiv.org/abs/2505.20047). We shall soon open
           | source that code!
        
           | sigmoid10 wrote:
           | Depends on how strictly you define your types. Are you using
           | pydantic to pass the information to the API? There are a few
           | pitfalls with this, because not everything is fully supported
           | and it gets turned into json behind the scenes. But in
           | principle, the autoregressive engine will simply not allow
           | tokens that break the supplied schema.
        
             | striking wrote:
             | Not sure if I've been using it wrong but I've tried using
             | the Zod-to-structured-output helper with GPT-5 and often
             | gotten weird stuff like trailing commas that break a parse
             | or seeing multiple JSON responses in the same response.
             | 
             | Ultimately there are still going to be bugs. For this
             | reason and several others you'll still need it wrapped in a
             | retry.
        
               | sigmoid10 wrote:
               | Yeah that sounds 100% like a user or middleware issue.
               | Don't bother with these wrappers, they are always
               | outdated anyways. Learn how to use the API directly, it
               | will save you a ton of headaches. And it's really not
               | that hard.
        
               | striking wrote:
               | No, we're using the OpenAI vendored version of zod-to-
               | json-schema via https://github.com/transitive-
               | bullshit/openai-zod-to-json-sc..., and applying it
               | directly to the `json_schema` field of the OpenAI API.
               | Maybe we have a subtle bug somewhere but I'd expect a 400
               | response if we were genuinely sending a malformed
               | request.
        
           | eric-burel wrote:
           | Yep from time to time.
        
         | barthelomew wrote:
         | Hey there! I mostly designed and wrote most of the actual
         | interpreter during my internship at Microsoft Research last
         | summer. Constrained decoding for GPT-4 wasn't available when we
         | started designing the DSL, and besides, creating a regex to
         | constrain this specific DSL is quite challenging.
         | 
         | When the grammar of the language is better defined, like SMT
         | (https://arxiv.org/abs/2505.20047) - we are able to do this
         | with open source LLMs.
        
           | sigmoid10 wrote:
           | What are you talking about? OpenAI has supported structured
           | json output in the API since 2023. Only the current
           | structured output API was introduced by OpenAI in summer
           | 2024, but it was primarily a usability improvement that still
           | runs json behind the scenes.
        
             | dang wrote:
             | > _What are you talking about?_
             | 
             | Please edit out swipes like this from your HN comments--
             | this is in the site guidelines:
             | https://news.ycombinator.com/newsguidelines.html. It comes
             | across as aggressive, and we want _curious_ conversation
             | here.
             | 
             | Your comment would be fine without that bit.
        
               | sigmoid10 wrote:
               | This is not meant as snide, I'm literally confused if I
               | might have misunderstood the problem here. Because the
               | solution would be so obvious.
        
               | dang wrote:
               | I believe you! but when an internet reply leads with
               | "what are you talking about?", it's likely to pattern-
               | match this way for many readers. If that's not your
               | intent, it's best to use an alternate wording.
        
               | vasco wrote:
               | Not to be rude, but they clarified it's not a snide, why
               | are you trying to control speech to this degree? If we
               | don't like his tone we can downvote him as well anyway
               | and self regulate.
        
               | dang wrote:
               | They clarified that their intention was good, but intent
               | doesn't communicate itself--it needs to be disambiguated
               | [1]. What matters in terms of moderation is not intent,
               | but effects, i.e. effects on the system in the general
               | case [2].
               | 
               | Arguably your question reduces to: why does HN have
               | moderators at all? The answer to that is that
               | unfortunately, the system of community + software doesn't
               | function well on its own over time--it falls into failure
               | modes and humans (i.e. mods) are needed to jig it out of
               | those [3]. I say "unfortunately" because, of course, it
               | would be so much better if this weren't needed.
               | 
               | You can't assess this at the level of an individual
               | interaction, though, because it's scoped at the whole-
               | system level. That is, we can (and do) make bad
               | individual calls, but what's important is how the overall
               | system functions. If you see the mods making a mistake,
               | you're welcome to point it out (and HN users are not shy
               | about doing so!), and we're happy to correct it. But it
               | doesn't follow that you don't need moderators for the
               | system to work, or even survive.
               | 
               | [1] https://hn.algolia.com/?dateRange=all&page=0&prefix=t
               | rue&que...
               | 
               | [2] https://hn.algolia.com/?dateRange=all&page=0&prefix=t
               | rue&que...
               | 
               | [3] https://hn.algolia.com/?dateRange=all&page=0&prefix=t
               | rue&que...
        
             | barthelomew wrote:
             | You're right about the 2023 JSON mode, but our project
             | required enforcing a much more complex DSL grammar (look in
             | Appendix for details), not just ensuring a *valid JSON
             | object*. The newer structured output APIs are a significant
             | improvement, but the earlier tools weren't a fit for the
             | specific constraints we were working under at the time.
        
         | IanCal wrote:
         | I'd also be surprised if the models are better at writing code
         | in some custom schema (assuming that's not z3s native
         | structure) than writing code in something else. Decent models
         | can write pretty good code and for a lot of mistakes can fix
         | them, plus you get testing/etc setups for free.
        
         | eric-burel wrote:
         | It's a relatively new feature, also people need actual
         | professional training to become true LLM developers using them
         | to their fullest and not just developers that happen to call an
         | LLM API here and there. Takes a lot of time and effort.
        
       | ivanbakel wrote:
       | The repo is sparse on the details unless you go digging, which
       | perhaps makes sense if this is just meant as the artifact for the
       | mentioned paper.
       | 
       | Unless I'm wrong, this is mainly an API for trying to get an LLM
       | to generate a Z3 program which "logically" represents a real
       | query, including known facts, inference rules, and goals. The
       | "oversight" this introduces is in the ability to literally read
       | the logical statement being evaluated to an answer, and running
       | the solver to see if it holds or not.
       | 
       | The natural source of doubt is: who's going to read a bunch of
       | SMT rules manually and be able to accurately double-check them
       | against real-world understanding? Who double checks the
       | constants? What stops the LLM from accidentally (or deliberately,
       | for achieving the goal) adding facts or rules that are unsound
       | (both logically and from a real-world perspective)?
       | 
       | The paper reports a *51%* false positive rate on a logic
       | benchmark! That's shockingly high, and suggests the LLM is either
       | bad at logical models or keeps creating unsoundnesses. Sadly, the
       | evaluation is a bit thin on the ground about how this stacks up,
       | and what causes it to fall short.
        
         | barthelomew wrote:
         | Yep. The paper was written last year with GPT-4o. Things have
         | become a lot better since then with newer models.
         | 
         | E.g. https://arxiv.org/pdf/2505.20047 Tab 1, we compare the
         | performance on text-only vs SMT-only. o3-mini does pretty well
         | at mirroring its text reasoning in its SMT, vs Gemini Flash
         | 2.0.
         | 
         | Illustration of this can be seen in Fig 14, 15 on Page 29.
         | 
         | In commercially available products like AWS Automated Reasoning
         | Checks, you build a model from your domain (e.g. from a PDF
         | policy document), cross verify it for correctness, and during
         | answer generation, you only cross check whether your Q/A pairs
         | from the LLM comply with the policy using a solver with
         | guarantees.
         | 
         | This means that they can give you a 99%+ soundness guarantee,
         | which basically means that if the service says the Q/A pair is
         | valid or guaranteed w.r.t the policy, it is right more than 99%
         | of the time.
         | 
         | https://aws.amazon.com/blogs/aws/minimize-ai-hallucinations-...
        
           | cerved wrote:
           | Who makes the rules?
        
           | bhk wrote:
           | Re: "99% of the time" ... this is an ambiguous sample space.
           | Soundness of results clearly depends on the questions being
           | asked. For what set of questions does the 99% guarantee hold?
        
       | measurablefunc wrote:
       | This is proof of verifiable logic. Computers can not think so
       | calling it proof of thought misrepresents what's actually
       | happening.
        
         | aSanchezStern wrote:
         | I agree that "proof of thought" is a misleading name, but this
         | whole "computers can't think" thing is making LLM skepticism
         | seem very unscientific. There is no universally agreed upon
         | objective definition of what it means to be able to "think" or
         | how you would measure such a thing. The definition that these
         | types of positions seem to rely upon is "a thing that only
         | humans can do", which is obviously a circular one that isn't
         | useful.
        
           | measurablefunc wrote:
           | If you believe computers can think then you must be able to
           | explain why a chain of dominoes is also thinking when I
           | convert an LLM from transistor relay switches into the domino
           | equivalent. If you don't fall for the marketing hype & study
           | both the philosophical & mathematical literature on
           | computation then it is obvious that computers (or any
           | mechanical gadget for that matter) can not qualify for any
           | reasonable definition of "thinking" unless you agree that all
           | functionally equivalent manifestations of arithmetic must be
           | considered "thinking", including cascading dominoes that
           | correspond to the arithmetic operations in an LLM.
        
             | bobxmax wrote:
             | And your definition of thinking is?
        
               | measurablefunc wrote:
               | Not arithmetic or boolean algebra. What's your
               | definition?
        
               | Nevermark wrote:
               | > Not arithmetic or boolean algebra.
               | 
               | That isn't a definition or even a coherent attempt.
               | 
               | For starters, what kind of cognition or computation can't
               | be implemented with either logic or arithmetic?
               | 
               | What is or is not "cognition" is going to be a higher
               | level property than what basic universally capable
               | substrate is used. Given such substrates can easily
               | simulate each other, be substituted for each other.
               | 
               | Even digital and analog systems can be used to implement
               | each other to arbitrary accuracy.
               | 
               | Cognition is a higher level concern.
        
             | supern0va wrote:
             | >If you believe computers can think then you must be able
             | to explain why a chain of dominoes is also thinking when I
             | convert an LLM from transistor relay switches into the
             | domino equivalent.
             | 
             | Sure, but if you assume that physical reality can be
             | simulated by a Turing machine, then (computational
             | practicality aside) one could do the same thing with a
             | human brain.
             | 
             | Unless you buy into some notion of magical thinking as
             | pertains to human consciousness.
        
               | measurablefunc wrote:
               | No magic is necessary to understand that carbon & silicon
               | are not equivalent. The burden of proof is on those who
               | think silicon can be a substitute for carbon & all that
               | it entails. I don't buy into magical thinking like Turing
               | machines being physically realizable b/c I have studied
               | enough math & computer science to not be confused by
               | abstractions & their physical realizations.
        
               | avmich wrote:
               | The proof immediately follows from the ability of silicon
               | systems in principle to model carbon ones with arbitrary
               | precision.
        
               | measurablefunc wrote:
               | I recently wrote a simulation of water molecules & got
               | really confused when the keyboard started getting water
               | condensation on it. I concluded that simulating water was
               | equivalent to manifesting it in reality & immediately
               | stopped the simulation b/c I didn't want to short-circuit
               | the CPU.
        
           | Terr_ wrote:
           | > this whole "computers can't think" thing is making LLM
           | skepticism seem very unscientific.
           | 
           | It's just shorthand for "that's an extraordinary claim and
           | nobody has provided any remotely extraordinary evidence to
           | support it."
        
             | measurablefunc wrote:
             | Lots of people consider company valuations evidence of a
             | singularity right around the corner but it requires a very
             | specific kind of mindset to buy into that as "proof" of
             | anything other than very compelling hype by people who have
             | turned financial scams into an art form.
        
           | encyclopedism wrote:
           | The jury maybe out on how to judge what 'thought' actually
           | is. However what it is not is perhaps easier to perceive. My
           | digital thermometer does not think when it tells me the
           | temperature.
           | 
           | My paper and pen version of the latest LLM (quite a large bit
           | of paper and certainly a lot of ink I might add) also does
           | not think.
           | 
           | I am surprised so many in the HN community have so quickly
           | taken to assuming as fact that LLM's think or reason. Even
           | anthropomorphising LLM's to this end.
           | 
           | For a group inclined to quickly calling out 'God of the gaps'
           | they have quite quickly invented their very own 'emergence'.
        
         | chpatrick wrote:
         | Do you understand human thinking well enough to determine what
         | can think and what can't? We have next to no idea how an
         | organic brain works.
        
           | measurablefunc wrote:
           | I understand computers, software, & the theory of computation
           | well enough to know that there is no algorithm or even a
           | theoretical algorithmic construction that can be considered
           | thought. Unless you are willing to concede that thinking is
           | nothing more than any number of models equivalent to a Turing
           | machine, e.g. lambda calculus, Post systems, context aware
           | grammars, carefully laid out dominoes, permutations of bit
           | strings, etc. then you must admit that computers are not
           | thinking. If you believe computers are thinking then you must
           | also admit dominoes are thinking when falling in a cascading
           | chain.
        
             | chpatrick wrote:
             | Sure, sufficiently advanced dominoes.
             | 
             | https://xkcd.com/505/
             | 
             | We're already at the point where LLMs can beat the Turing
             | test. If we define thinking as something only humans can
             | do, then we can't decide if anyone is thinking at all just
             | by talking to them through text, because we can't tell if
             | they're human any more.
        
               | measurablefunc wrote:
               | Animals can also think. It's not restricted to one
               | specific type of primate physiology. But it seems like
               | you think you're nothing more than falling cascades of
               | dominoes in which case we don't really have much to
               | discuss. Your metaphysical assumptions are fundamentally
               | at odds with what I consider a reasonable stance on
               | computation & reality.
        
               | baq wrote:
               | Hard to argue with religious beliefs.
        
               | measurablefunc wrote:
               | The void created by modernity must be filled somehow so
               | it might as well be the great programmer in the great
               | beyond. Just as childish as religions of pre-modernity
               | but very useful if you're a technocrat building data
               | centers & trying to pump the valuations of companies that
               | can benefit from all that buildout w/ promises of
               | forthcoming utopias approximating the palace of the great
               | programmer in the great beyond. Just a few more nuclear
               | power plants & a few more GPU clusters is all that's
               | needed.
        
               | Nevermark wrote:
               | Ideally it is filled with curiosity and continued
               | exploration.
               | 
               | Not manufactured stop gaps or generic cynicism.
               | 
               | There is no reason more GPUs can't contribute to further
               | understanding, as one of many tools that have already
               | assisted with relevent questions and problems.
               | 
               | Opt out of serious inquiry, no excuse needed, if you
               | wish. Reframing others efforts is not necessary to do
               | that.
        
               | measurablefunc wrote:
               | I recommend taking your own advice on that one,
               | specifically the part about reframing efforts of
               | strangers.
        
               | Nevermark wrote:
               | I take your views to be exactly as you state them.
        
               | measurablefunc wrote:
               | Then there is no need to reframe anything so you might as
               | well get to the actual disagreement you have w/ them.
        
               | QuesnayJr wrote:
               | I think you are misjudging which side of the
               | religion/non-religion divide you are on.
        
               | measurablefunc wrote:
               | The people who think enough nuclear reactors & silicon
               | chips w/ the right incantation of 0s & 1s will deliver
               | them to an abundant utopia don't leave much room in their
               | ideology for any doubt about the eschatological objective
               | of their quest & mission in life. These people are
               | definitely not on some kind of religious side of a
               | religious vs non-religious divide.
               | 
               | Sure thing buddy, I'm the confused one in this entire
               | millenarian frenzy.
        
               | Nevermark wrote:
               | > Animals can also think
               | 
               | What are you saying?
               | 
               | Are you saying you have a clear definition for thinking,
               | and you can demonstrate that animals pass that
               | definituon?
               | 
               | Then share the definition.
               | 
               | Or are you simply defining thinking as a common property
               | of humans and animals, using animals and human behavior
               | as exemplars?
               | 
               | A useful definition for focusing inquiry. But it does not
               | clarify or constrain what else might or might not be
               | enabled to think.
               | 
               | Or are you defining thinking as an inherent property of
               | animals and humans that other things cannot have because
               | they are not animals or humans?
               | 
               | Fine, but that that's an exercise in naming. Something we
               | are all free to do however we want. It has no explanatory
               | power.
        
             | Nevermark wrote:
             | You are confusing primitives with things built with those
             | primitives.
             | 
             | Complex phenomena emerge from interactions of things that
             | don't exhibit that phenomena all the time.
             | 
             | Atoms can't think. In no sense can you find any thinking in
             | an atom.
             | 
             | They are no different from dominos in that respect.
             | 
             | You can pile atoms to the moon without seeing any thinking.
             | 
             | Yet they can still be arranged so they do think.
        
       | nextos wrote:
       | This is a very interesting area of research. I did something
       | similar a couple of years ago using logic and probabilistic logic
       | inference engines to make sure conclusions followed from
       | premises.
       | 
       | I also used agents to synthesize, formalize, and criticize domain
       | knowledge. Obviously, it is not a silver bullet, but it does
       | ensure some degree of correctness.
       | 
       | I think introducing some degree of symbolism and agents-as-a-
       | judge is a promising way ahead, see e.g.:
       | https://arxiv.org/abs/2410.10934
        
         | barthelomew wrote:
         | Yep! I have read your work! Pretty cool! I also worked on a
         | similar deep research agent for autoformalization this summer
         | at AWS ARChecks, building on similar patterns.
         | 
         | Although that work is not public, you can play with the
         | generally available product here!
         | 
         | [1] https://aws.amazon.com/blogs/aws/minimize-ai-
         | hallucinations-...
        
         | CuriouslyC wrote:
         | Agent/LLM as a judge is biased and only good for bootstrapping.
         | As capabilities get better LLM as a judge will artificially cap
         | your performance, you need to graduate to either expert human
         | judges or deterministic oracles.
        
           | jebarker wrote:
           | Why does this have to be true? For example, if you have a
           | different LLM that is judging than the one being judged then
           | their biases could at least be different. Also, as their
           | reasoning abilities improve wouldn't LLM judges approach the
           | abilities of human judges?
        
             | CuriouslyC wrote:
             | LLMs have positional, response length and hedge word biases
             | (and that's just what's rigorously demonstrated in papers)
             | that wash out differences between high performing answers
             | as you approach the limit of your objective. Imagine if you
             | were trying to optimize a function and the measurement
             | function emitted random biased noise, at some point you
             | wouldn't be able to accurately identify the impact of your
             | changes.
        
             | sdenton4 wrote:
             | Indeed - human judges suck on average. And you can prompt
             | an llm judge to look for particular kinds of problems, then
             | throw the ensemble of judges at an output to nitpick.
             | (Essentially, bake in a diversity of biases through a
             | collection of prompts.)
        
           | fnordpiglet wrote:
           | LLMs display a form of abductive reasoning which is not the
           | same as judgement. The only thing in the universe we know
           | that can display judgement is a human. However many tasks we
           | presume to require human judgement do not and abductive
           | reasoning will perform as well as a human. This in theory
           | acts as a filter if used right reducing the tasks of human
           | judgement to those that can't be automated with similar or
           | better precision and recall. The trick then is using LLMs and
           | other techniques to reduce the problem space for the human to
           | the kernel of quandary that requires human judgement and to
           | isolate the salient information to reduce the cognitive load
           | as much as possible. Many many mundane tasks can be automated
           | in this way, and many complex tasks can be facilitated to
           | greatly magnify the effectiveness of the human in the
           | middle's time.
        
       | nakamoto_damacy wrote:
       | LLMs lack logical constraints in the generative process; they
       | only learn probabilistic constraints. If you apply logic
       | verification post-hoc, you're not "ensuring the correctness of
       | your LLMs reasoning" (I went down this path a year ago); you're
       | classifying whether the LLM's statistically driven pattern
       | generation happens to correspond to correct logic or not, where
       | the LLMs output may be wrong 100% of the time, and your theorem
       | prover simply acts as a classifier, ensuring nothing at all.
        
         | barthelomew wrote:
         | Yep, this is a genuine problem, and this is what we term as the
         | autoformalization gap in our follow up paper.
         | (https://arxiv.org/abs/2505.20047)
         | 
         | Some LLMs are more consistent between text and SMT, while
         | others are not. (Tab 1, Fig 14,15)
         | 
         | You can do uncertainty quantification with selective
         | verification to reduce the "risk", for e.g. shown as the Area
         | Under the Risk Coverage Curve in Tab 4.
        
           | YeGoblynQueenne wrote:
           | Well, if you understand that this is a "genuine problem" then
           | what have you done to solve it? A quick look at the abstract
           | of your follow up paper does not reveal an answer.
           | 
           | And let me be clear that this is a major limitation that
           | fundamentally breaks whatever you are trying to achieve. You
           | start with some LLM-generated text that is, by construction,
           | unrelated to any notion of truth or factuality, and you push
           | it through a verifier. Now you are verifying hot air.
           | 
           | It's like research into the efficacy of homeopathic medicine
           | and there's a lot of that indeed, very carefully performed
           | and with great attention to detail. Except all of that
           | research is trying to prove whether doing nothing at all
           | (i.e. homeopathy) has some kind of measurable effect or not.
           | Obviously the answer is not. So what can change that? Only
           | making homeopathy do something instead of nothing. But that's
           | impossible, because homeopathy is, by construction, doing
           | nothing.
           | 
           | It's the same thing with LLMs. Unless you find a way to make
           | an LLM that can generate text that is conditioned on some
           | measure of factuality, then you can verify the output all you
           | like, the whole thing will remain meaningless.
        
         | avmich wrote:
         | Probabilistic constraints are all around us. You learn that the
         | sine function is the ratio of the length of the side of the
         | right triangle opposite to the angle to the length of the side
         | opposite to the right angle, so obviously the sine is always
         | positive. Yet your thinking should be flexible enough to allow
         | changing the definition to the ordinate of the point on the
         | unit circle where the line corresponding to the given angle and
         | drawn from zero intersects that circle. So your knowledge - the
         | symbolic one - can also be probabilistic.
        
           | nakamoto_damacy wrote:
           | You're thinking along the right track but without
           | formalization it goes nowhere fast. By layering of
           | differential geometry on top of probability and then maybe
           | category theoretic logic on top of that, each layer
           | constraining the one below it, and all layers cohering, you
           | get somewhere... There is work that's been done in this area,
           | and I was recently interviewed by a journalist who published
           | a high level article on it on Forbes (Why LLMs are failing)
           | and it links to the actual technical work (at first to my
           | high level presentation then Prof. L. Thorne McCarty's work):
           | https://www.forbes.com/sites/hessiejones/2025/09/30/llms-
           | are...
        
         | nakamoto_damacy wrote:
         | Why is this being down voted? I believe the author acknowledged
         | and responded. Anything wrong?
        
       | zwnow wrote:
       | Reasoning? LLMs can not reason, why is it always assumed they
       | reason? They mimic reasoning.
        
         | elcomet wrote:
         | How can you know?
        
           | measurablefunc wrote:
           | By thinking about what a computer is actually doing &
           | realizing that attributing thought to an arthmetic gadget
           | leads to all sorts of nonsensical consequences like an
           | arrangement of dominoes & their cascade being a thought. The
           | metaphysics of thinking computers is incoherent & if you
           | study computability theory you'll reach the same conclusion.
        
             | elcomet wrote:
             | I'd say that thoughts and reasoning are two different
             | things, you're moving the goalpost.
             | 
             | But what makes the computer hardware fundamentally
             | incompatible with thinking? Compared to a brain
        
               | measurablefunc wrote:
               | I've already explained it in several places. The burden
               | of proof is on those drawing the equivalence to provide
               | actual evidence for why they believe carbon & silicon are
               | interchangeable & why substrate independence is a valid
               | assumption. I have studied this problem for much longer
               | than many people commenting on this issue & I am telling
               | you that your position is metaphysically incoherent.
        
         | moffkalast wrote:
         | It's so funny to me that people are still adamant about this
         | like two years after it's become a completely moot point.
        
           | zwnow wrote:
           | Experts are adamant about this. Just take a look at
           | https://youtu.be/iRqpsCHqLUI
        
             | moffkalast wrote:
             | No such thing as an expert consensus on anything about LLMs
             | these days, just different forms of grift.
             | 
             | My point is, the question if an LLM reasons the same way a
             | human does is about as useful as "does a submarine swim" or
             | "can a telephone talk". The results speak for themselves.
        
               | zwnow wrote:
               | LLMs do not reason. Not hard to understand.
        
               | moffkalast wrote:
               | Idk, before this people from your camp were saying LLMs
               | can't even understand anything. Always moving the
               | goalposts. Then it'll be they can't feel or can't
               | something else just to be pointlessly contrarian. Anyway,
               | wrong idea.
               | 
               | There have been enough cases of models providing novel
               | results that it's clear that whatever human trait they
               | supposedly lack they don't really need. A car does not
               | need legs, it does things differently. Having legs would
               | even be a major detriment and would hold it back from
               | achieving its top performance.
               | 
               | That's what those brain simulating projects are
               | conceptually btw: cars with legs or planes with flapping
               | wings. That's why they all fail, the approach makes no
               | sense.
        
               | raspasov wrote:
               | What is "novel results"? A random UUID generator also
               | gives "novel result", every time.
               | 
               | Even if we're to humor the "novel" part, have they
               | _actually_ come up with anything truly novel? New
               | physics? New proofs of hard math problems that didn 't
               | exist before?
        
               | moffkalast wrote:
               | Yes, exactly. There are other papers, but Google proved
               | it most definitively imo [0], an LLM now holds the state
               | of the art for the lowest bound on a very specific graph
               | problem.
               | 
               | [0] https://research.google/blog/ai-as-a-research-
               | partner-advanc...
        
               | measurablefunc wrote:
               | That's not an LLM. AlphaEvolve is a variant of genetic
               | search for program synthesis. Very different from the
               | chat bot that answers questions about ingrown toenails.
        
               | horacemorace wrote:
               | This will be the exact same argument in 20 years when
               | we've got examples of robots that some fraction of people
               | claim are conscious.
        
               | zwnow wrote:
               | If LLMs could reason, they would flourish in barely
               | understood topics, they dont. They repeat after what
               | humans already said over and over again all across the
               | training data. They are a parrot, its really not that
               | hard to understand.
        
               | kgeist wrote:
               | >They repeat after what humans already said
               | 
               | >They are a parrot
               | 
               | Is it really much different from most people? The average
               | Joe doesn't produce novel theories every day - he just
               | rehashes what he's heard. Now the new goalpost seems to
               | be that we can only say an LLM can "reason" if it matches
               | Fields Medalists.
        
               | encyclopedism wrote:
               | > Is it really much different from most people? The
               | average Joe doesn't produce novel theories every day"
               | 
               | You've presented a false choice.
               | 
               | However the average Joe does indeed produce unique and
               | novel thoughts every day. If it were not the case he
               | would be brain dead. Each decision - wearing blue or red
               | today - every tiny thought, action, feeling, indecision,
               | crisis, or change of heart these are just as important.
               | 
               | The jury maybe out on how to judge what 'thought'
               | actually is. However what it is not is perhaps easier to
               | perceive. My digital thermometer does not think when it
               | tells me the temperature.
               | 
               | My paper and pen version of the latest LLM (quite a large
               | bit of paper and certainly a lot of ink I might add) also
               | does not think.
               | 
               | I am surprised so many in the HN community have so
               | quickly taken to assuming as fact that LLM's think or
               | reason. Even anthropomorphising LLM's to this end.
               | 
               | For a group inclined to quickly calling out 'God of the
               | gaps' they have quite quickly invented their very own
               | 'emergence'.
        
               | NitpickLawyer wrote:
               | > They are a parrot
               | 
               | Those are some mighty parrots there, if they managed to
               | get gold at IMO, IoI, and so on...
        
               | zwnow wrote:
               | Well understood topics... what's so hard to understand?
        
               | Terr_ wrote:
               | > just different forms of grift
               | 
               | That sounds like a false "both sides"-ing.
               | 
               | It's not symmetrical, there's a _lot_ more money (and
               | potential to grift) hyping things up as miracle machines.
               | 
               | In contrast, most of the pessimists don't have a
               | discernible profit motive.
        
               | moffkalast wrote:
               | Well yes the corporate accelerationists are certainly
               | pushing for it the most, shoehorning the tech into things
               | it doesn't belong in to see if they can somehow come up
               | on top, which that in turn makes lots of people resentful
               | towards it in a reactionary way.
               | 
               | You have artists who've lost work due to diffusion
               | models, teachers who can't assign homework essays
               | anymore, people who hate Microsoft Copilot, just anyone
               | not wanting to be replaced by a bot or being forced to
               | use the tech to avoid being outcompeted, people set in
               | their ways who don't want change or imagine it being
               | destructive, etc. It's a large crowd that one can appeal
               | to for personal gain, politics 101. Anyone with half
               | believable credentials can go on a talk show and say the
               | things people want to hear, maybe sell a book or two
               | afterwards.
               | 
               | Are today's models on the brink of some exponential self
               | perpetuating shot towards superintelligence? Obviously
               | not. Are they overhyped glorified lookup tables? Also no.
               | Are there problems? Definitely. But I don't think it's
               | entirely fair to dismiss a tech based on someone
               | misappropriating it in monopolistic endeavours instead of
               | directing dismissal towards those people themselves.
               | 
               | Like, similar to how Elon's douchebaggery has tainted EVs
               | for lots of people for no practical reason, the same has
               | Altman's done for LLMs.
        
           | Terr_ wrote:
           | The normative importance of a fact may _increase_ when more
           | number of people start willfully ignoring it for shorter-term
           | profit.
           | 
           | Imagine somebody in 2007: "It's so funny to me that people
           | are still adamant about _mortgage default risk_ after it 's
           | become a completely moot point because nobody cares in this
           | housing market."
        
             | avmich wrote:
             | Didn't we have economists' consensus then about what's
             | going to happen?
        
               | Terr_ wrote:
               | My point is a fact's _popularity_ is not equal to its
               | _importance_. That was a scenario to highlight how they
               | can even have an _inverse_ relationship.
               | 
               | Diving into how well/badly anybody predicted a certain
               | economic future is a whole different can of worms.
               | 
               | That said: "The market can stay irrational longer than I
               | can stay solvent." :p
        
             | MASNeo wrote:
             | That's nailing it really well: "willfully ignoring" is
             | precisely what's happening all around me. Me talking about
             | small focused AI models, there you have everyone raving
             | about AGI. Energy use and privacy issues of cloud vs local
             | inference discussions end on how awesome the power of GPUs
             | are and the jobs too. GPU backed finance with depreciation
             | schedules past useful life seems OK for anyone chasing some
             | short term gain. Even the job market is troubled, you can
             | hardly tell a relevant candidate from an irrelevant one
             | because everyone is an AI expert these days -
             | hallucinations seem to make lying more casual.
             | 
             | It's pretty clear to me there is a collective desire to
             | ignore the problems to sell more GPU, close the next round,
             | get that high paying AI job.
             | 
             | Part of me wishes humans would show the same dedication to
             | fight climate change...
        
           | emp17344 wrote:
           | Moot point? As far as I know, it's still intensely debated,
           | and there are some excellent papers out there providing
           | evidence that LLMs truly are just statistical prediction
           | machines. It's far from an unreasonable position.
        
       | dehsge wrote:
       | LLMs and its output are bounded by Rices theorem. This is not
       | going to ensure correctness it's just going to validate that the
       | model can produce an undecidable result.
        
         | ogogmad wrote:
         | Errr, checking correctness of proofs is decidable.
        
       | everdrive wrote:
       | I'm honestly confused why we can't determine how LLMs come to
       | their decisions in the general sense. Is it not possible to log
       | every step as the neural network / vector db / magic happens? Is
       | it merely impractical, or is it actually something that's
       | genuinely difficult to do?
        
         | chpatrick wrote:
         | Everything happens in an opaque super-high-dimensional
         | numerical space that was "organically grown" not engineered, so
         | we don't really understand what's going on.
        
         | NotGMan wrote:
         | Chat GPT-4 has alegedly 1.8 trillion parameters.
         | 
         | Imagine having a bunch of 2D matrices with a combined 1.8
         | trillion total numbers, from which you pick out a blocks of
         | numbers in a loop and finally merge them and combine them to
         | form a token.
         | 
         | Good luck figuring out what number represents what.
        
           | everdrive wrote:
           | Wouldn't that mean it's totally impractical for day-to-day
           | usage, but a researcher or team of researchers could solve
           | this?
        
             | typpilol wrote:
             | Anthropic has a tool that lets them do this but apparently
             | doing it for even one prompt can take an entire day of
             | work.
        
               | tymscar wrote:
               | That's so much faster than I expected
        
         | moffkalast wrote:
         | It would be like logging a bunch of random noise from anyone's
         | perspective except the LLM's.
        
           | everdrive wrote:
           | I guess I'm also just confused. I get that this is
           | _difficult_ to do, but I would think that computer scientists
           | would be utterly dissatisfied that AI was "non-deterministic"
           | and would poke at the problem until it could be understood.
        
         | konmok wrote:
         | My understanding is that it's neither impractical nor genuinely
         | difficult, it's just that the "logging every step" approach
         | provides explanations of their "reasoning" that are completely
         | meaningless to us, as humans. It's like trying to understand
         | why a person likes the color red, but not the color blue, using
         | a database recording the position, makeup, and velocity of
         | every atom in their brain. Theoretically, yes, that should be
         | sufficient to explain their color preferences, in that it fully
         | models their brain. But practically, the explanation would be
         | phrased in terms of atomic configurations in a way that makes
         | much less sense to us than "oh, this person likes red because
         | they like roses".
        
           | everdrive wrote:
           | >It's like trying to understand why a person likes the color
           | red, but not the color blue, using a database recording the
           | position, makeup, and velocity of every atom in their brain.
           | 
           | But this is an incredibly interesting problem!
        
             | qcnguy wrote:
             | Anthropic have done some great work on neural
             | interpretability that gets at the core of this problem.
        
         | nickpsecurity wrote:
         | There's people doing both types. Look up survey of mechanistic
         | interpretebility of language models and survey of explainable
         | AI for neural networks. Those will give you many techniques for
         | illustrating what's happening.
         | 
         | You'll also see why their applications are limited compared to
         | what you probably hoped for.
        
       | tonerow wrote:
       | Cool research! I went to the repo to see what the DSL looked like
       | but it was hard to find a clear example. It would be cool if you
       | added a snippet to the README.
        
         | barthelomew wrote:
         | Hey! Thank you for the interest! I shall do that. Meanwhile,
         | check out Page 11 onwards. We describe a lot of situations!
         | (https://arxiv.org/pdf/2409.17270)
        
           | pstoll wrote:
           | Upvoting the comment that the gitrepo would be way more self
           | stand-alone if it had an intro of the DSL.
        
       | tannhaeuser wrote:
       | LLMs are statistical language models (d'uh) not reasoners after
       | all. I found generating logic programs, and Prolog source
       | specifically, to work unreasonably well, though [1], maybe
       | because Prolog was introduced for symbolic natural language
       | processing and there's a wealth of translation examples in the
       | training set. Might be worth checking out Z3's alternative
       | Datalog syntax [2] instead of its Lisp-ish SMTLib syntax.
       | 
       | [1]: https://quantumprolog.sgml.net/llm-demo/part1.html
       | 
       | [2]: https://microsoft.github.io/z3guide/docs/fixedpoints/syntax
        
         | barthelomew wrote:
         | Yep! Datalog syntax for Z3 is pretty neat! We used SMT [1] in
         | our grammars paper because it allowed the most interoperability
         | with solvers, but our technique also works with PROLOG; as
         | tested our at the behest of reviewers at NeurIPS. I would
         | assume that this should also work with datalog [2].
         | 
         | [1] https://arxiv.org/abs/2505.20047 [2]
         | https://github.com/antlr/grammars-v4/blob/master/datalog/dat...
        
         | larodi wrote:
         | Neuralsymbolic systems are very likely the future as so many
         | times mentioned here already.
        
           | a3w wrote:
           | I cannot use wolframalpha most of the time since the syntax
           | is not that natural. WolframAlpha is good AI, it never lies.
           | 
           | Calculators are good AI, they rarely lie (due to floating
           | arithmetics rounding). And yes, Wikipedia says calculators
           | are AI tech, since a Computer was once a person, and not it
           | is a tool that shows the intelligent trait of doing math with
           | numbers or even functions/variables/equations.
           | 
           | Querying a calculator or wolfram alpha like symbolic AI
           | system with LLMs seems like the only use for LLMs except for
           | text refactoring that should be feasible.
           | 
           | Thinking LLMs know anything on their own is a huge fallacy.
        
       | chrchr wrote:
       | I had a surprising interaction with Gemini 2.5 Pro that this
       | project reminds me of. I was asking the LLM for help using an
       | online CAS system to solve a system of equations, and the CAS
       | system wasn't working as I expected. After a couple back and
       | forths with Gemini about the CAS system, Gemini just gave me the
       | solution. I was surprised because it's the kind of thing I don't
       | expect LLMs to be good at. It said it used Python's sympy
       | symbolic computation package to arrive at the solution. So, yes,
       | the marriage of fuzzy LLMs with more rigorous tools can have
       | powerful effects.
        
         | TrainedMonkey wrote:
         | Just like humans... we are not so good at hard number
         | crunching, but we can invent computers that are amazing at it.
         | And with a lot of effort we can make a program that uses a
         | whole lot of number crunching to be ok at predicting text but
         | kind of bad at crunching hard numbers. And then that program
         | can predict how to create and use programs which are good at
         | number crunching.
        
           | jonplackett wrote:
           | Maybe the number crunching program the text generation
           | program creates will, with enough effort become good at
           | generating text, an will in turn make another number
           | crunching computer and then...
        
             | psadri wrote:
             | Watch the movie "The Thirteenth Floor"
        
               | Barbing wrote:
               | This is somewhat unusual: 28% on the Tomatometer, but 7
               | out of 10 on IMDb.
               | 
               | Beyond its relevancy to the parent comment, would you
               | consider it a good movie yourself? (for a random/average
               | HN commenter to watch)
        
               | c-hendricks wrote:
               | It didn't do well critically, but audience scores on many
               | platforms are 60-70%. It came hot on the heels of The
               | Matrix, has similar themes, but nowhere near as ...
               | everything compared to Matrix. I'd bet the only reason it
               | did so poorly critically is due to the timing of the
               | release.
               | 
               | It's a fine movie though.
        
               | bonoboTP wrote:
               | If you like Matrix, Memento, Truman Show, Black Mirror
               | (San Junipero, Bandersnatch), Inception, Interstellar, 12
               | Monkeys etc. you may also like it. These are not
               | necessarily thematically aligned but based on vibes they
               | cluster near it for me.
               | 
               | I definitely enjoyed it many years ago as a younger
               | person.
        
               | self wrote:
               | Three movies with overlapping themes came out in
               | mid-1999: The Matrix, The Thirteenth Floor, and eXistenZ
               | (probably in that order of box office revenue).
        
           | patcon wrote:
           | I love this kind of thought. Thanks.
        
           | idiotsecant wrote:
           | Parent post is talking about symbolic manipulation, not rote
           | number crunching, which is exactly what we're supposed to be
           | good at and machines are supposed to be bad at.
        
           | 29athrowaway wrote:
           | We do plenty of number crunching all the time, just not
           | consciously.
           | 
           | Like the inverse kinematics required for your arm and fingers
           | to move.
        
             | pstoll wrote:
             | I'd argue we aren't solving those inverse kinematics /
             | kinetics via "number crunching" - but rather that our
             | neuromuscular systems are analog. Which I don't usually
             | call that "number crunching" in the sense current computers
             | ... compute.
        
               | tomcloyd wrote:
               | As a psychologist, I completely agree. It absolutely is
               | NOT number crunching. Analog computation is primary and
               | dominant in animals. It has to be, for so many reasons. I
               | continue to be amazed at how much IT people do NOT grasp
               | human and animal IT. And that, I would argue, is why so
               | many IT folks keep talking about our supposedly
               | approaching human intelligence in technology. If they
               | really understood human intelligence the absurdity of
               | that statement would keep them quiet. An elegant, artful
               | puppet is still a puppet, and without the personal
               | history context and consciousness we possess, not to
               | mention a vast complex of analogue computation
               | functionality we rely upon, that puppet will only ever be
               | a clever number-cruncher. We are so much more.
        
               | galaxyLogic wrote:
               | Are our brains "analog"? Or are they in fact "digital"? I
               | would think actually more digital than analog. A synapse
               | triggers or it does not trigger. It either triggers or
               | not, not something in between. In this sense it is 0 or
               | 1.
               | 
               | Similarly transistor-based logic is based on such
               | thresholds, when current or voltage reaches a certain
               | level then a state-transition happens.
        
               | fwip wrote:
               | Well, no, synapses aren't binary in response.
        
               | Flere-Imsaho wrote:
               | Would you say it's more memorization than actual
               | calculations? It certainly feels like it, when say riding
               | a bike.
        
             | HumanOstrich wrote:
             | Neurons aren't crunching numbers for inverse kinematics.
        
           | emporas wrote:
           | Small steps of nondeterministic computation, checked
           | thoroughly with deterministic computation every so often, and
           | the sky is the limit.
           | 
           | That's when A.I. starts advancing itself and needs humans in
           | the loop no more.
        
             | eru wrote:
             | Your checks don't have to be deterministic either.
             | 
             | Eg randomised quicksort works really well.
        
               | emporas wrote:
               | Couldn't disagree more.
               | 
               | Sorting a finite number of elements in a sequence, is a
               | very narrow application of AI, akin to playing chess.
               | Usually very simple approaches like RL work totally fine
               | for problems like these, but auto-regression/diffusion
               | models have to take steps that are not well defined at
               | all, and the next step towards solving the problem is not
               | obvious.
               | 
               | As an example, imagine a robot trying to grab a tomato
               | from a table. It's arm extends across 1 meter maximum,
               | and the tomato is placed 0.98 meters away. Is it able to
               | grab the tomato from the point it stands, or it needs to
               | move closer, and only then try to grab the tomato?
               | 
               | That computation should better be calculated
               | deterministically. Deterministic computation is faster,
               | cheaper and more secure. It has to prove that:
               | $tomato_distance + $tomato_size < $arm_length. If this
               | constraint is not satisfied, then: move_closer();
               | Calculate again:$tomato_distance + $tomato_size <
               | $arm_length.
               | 
               | From the paper:
               | 
               | > Our system employs a custom interpreter that parses
               | "LLM-Thoughts" (represented as DSL code snippets) to
               | generate First Order Logic programs, which are then
               | verified by a Z3 theorem prover.
        
               | eru wrote:
               | > Sorting a finite number of elements in a sequence, is a
               | very narrow application of AI, [...]
               | 
               | Sorry, I did not suggest you should use AI to sort
               | numbers. I was solely replying to this:
               | 
               | > Small steps of nondeterministic computation, checked
               | thoroughly with deterministic computation every so often,
               | and the sky is the limit.
               | 
               | You don't necessarily need your checks to be
               | deterministic.
               | 
               | In fact, it's often better for them to be not
               | deterministic.
               | 
               | See also
               | https://fsharpforfunandprofit.com/series/property-based-
               | test...
               | 
               | I don't understand your claim about 'Deterministic
               | computation is faster, cheaper and more secure.' That's
               | not true at all.
               | 
               | In fact, for many problems the fastest and simplest known
               | solutions are non-deterministic. And in eg cryptography
               | you _need_ non-determinism to get any security at all.
        
             | visarga wrote:
             | > That's when A.I. starts advancing itself and needs humans
             | in the loop no more.
             | 
             | You got to put the environment back in the loop though, it
             | needs a source of discovery and validity feedback for
             | ideas. For math and code is easy, for self driving cars
             | doable but not easy, for business ideas - how would we test
             | them without wasting money? It varies field by field, some
             | allow automated testing, others are slow, expensive and
             | rate limited to test.
        
               | jaggederest wrote:
               | Simulation is the answer. You just need a model that's
               | decent at economics to independently judge the outcome,
               | unless the model itself is smart enough. Then it becomes
               | a self-reinforcing training environment.
               | 
               | Now, depending on how good your simulation is, it may or
               | may not be useful, but still, that's how you do it.
               | Something like https://en.wikipedia.org/wiki/MuZero
        
               | drbojingle wrote:
               | Electric dreams. Simulation of what?
        
               | staplers wrote:
               | doable but not easy, for business ideas
               | 
               | That requires a lot of human psychology and advanced hard
               | economic theory (not the fluffy academic kind). With
               | human controlled monetary supply and most high-level
               | business requiring illegal and immoral exploitation of
               | law and humans in general, it's not a path machines can
               | realistically go down or even want machines treading
               | down.
               | 
               | Think scams and pure resource extraction. They won't
               | consider many impacts outside of bottom line.
        
               | enknee1 wrote:
               | Simulated environment suggests the possibility of
               | alignment during training but real time, real world, data
               | streams are better.
               | 
               | But the larger point stands: you don't need an
               | environment to explore the abstraction landscape
               | prescribed by systems thinking. You only need the
               | environment at the human interface.
        
             | galaxyLogic wrote:
             | The question is where should AI advance itself? Which
             | direction? There are an infinite number of theorems that
             | can be derived from a set of axioms. Infinite. AI can't
             | prove them all. Somebody needs to tell it what it needs to
             | do, and that is us.
        
         | anotherpaulg wrote:
         | I really like LLM+sympy for math. I have the LLM write me a
         | sympy program, so I can trust that the symbolic manipulation is
         | done correctly.
         | 
         | The code is also a useful artifact that can be iteratively
         | edited and improved by both the human and LLM, with git
         | history, etc. Running and passing tests/assertions helps to
         | build and maintain confidence that the math remains correct.
         | 
         | I use helper functions to easily render from the sympy code to
         | latex, etc.
         | 
         | A lot of the math behind this quantum eraser experiment was
         | done this way.
         | 
         | https://github.com/paul-gauthier/entangled-pair-quantum-eras...
        
         | DrewADesign wrote:
         | I get having it walk you through figuring out a problem with a
         | tool: seems like a good idea and it clearly worked even better
         | than expected. But deliberately coaxing an LLM into doing math
         | correctly instead of a CAS because you've got one handy seems
         | like moving apartments with dozens of bus trips rather than
         | taking the bus to a truck rental place, just because you've
         | already got a bus pass.
        
           | afiori wrote:
           | I feel like a better analogy is trying to rent a truck to
           | move to a new apartment and after repeated failures of trucks
           | not working they just hire a moving company for you to get
           | you to leave
        
             | DrewADesign wrote:
             | All of those tools are purpose-built for moving people.
             | LLMs are not at all built for doing math.
        
         | jansan wrote:
         | How die that work? Did Gemini call sympy on your maschine, or
         | is access to sympy built-in and available through normal chat?
        
           | 7734128 wrote:
           | https://cloud.google.com/vertex-ai/generative-
           | ai/docs/multim...
        
       | 0xWTF wrote:
       | Am I reading this right? Statistical LLM outputs pushed through a
       | formal logic model? Wouldn't that be a case of "crap in, crap
       | out"?
        
         | varispeed wrote:
         | That's subjective. One could argue all the things we invented
         | in the past few thousands years were crap. Life would have been
         | much easier in the caves, albeit shorter.
        
         | avmich wrote:
         | Formal logic serves as a useful filter. In other words, "crap
         | in, filtered crap out" - remember, evolution works with
         | absolutely random, "crap" mutations, which then are "filtered"
         | by the environment.
        
         | baq wrote:
         | You assume it's all crap when it clearly isn't often enough to
         | be useful.
        
       | Yoric wrote:
       | That is exactly the kind of things that I hope LLM will help us
       | achieve before the next AI winter.
        
       | Western0 wrote:
       | I need this same with Mizar https://wiki.mizar.org/
        
       | sytse wrote:
       | So the core idea is to use an LLM to draft reasoning as a
       | structured, JSON domain-specific language (DSL), then
       | deterministically translate that into first-order logic and
       | verify it with a theorem prover (Z3).
       | 
       | Interesting that the final answer is provably entailed (or you
       | get a counterexample), instead of being merely persuasive chain-
       | of-thought.
        
       | westurner wrote:
       | ScholarlyArticle: "Proof of thought: Neurosymbolic program
       | synthesis allows robust and interpretable reasoning" (2024)
       | https://arxiv.org/abs/2409.17270 ..
       | https://scholar.google.com/scholar?hl=en&as_sdt=0%2C43&q=%22...
        
       | nakamoto_damacy wrote:
       | I posted about my year long development effort of this very
       | method on reddit 25 days ago. My comment elsewhere in this thread
       | provides a cautionary tale, and the authors response to the basic
       | issue I raised is incomplete in that it leaves out that certain
       | problems simply cannot be solved with LLMs (requires logical
       | constraints in the generative process but LLMs lack that layer)
       | So I've pivoted to something else since (also mentioned in my
       | comment elsewhere in this thread)
       | 
       | https://www.reddit.com/r/healthIT/comments/1n81e8g/comment/n...
        
       | renshijian wrote:
       | This is fascinating! An AI that doesn't just think out loud, but
       | keeps a verifiable diary. It's like a philosopher with a
       | cryptographic notary public living in its brain. Amazing work!
        
       | hamonrye wrote:
       | RHEL knife-edge rolling kernel distribition for the proof of
       | concept.
        
       | derekcheng08 wrote:
       | Interesting. I wonder if you could implement tool calling with
       | this approach so the LLM calls the tool with the formal
       | specification and gets back the result. Just like a coding agent
       | can run a compiler, get back errors and then self-correct.
        
       | maiuki wrote:
       | What industrial problems would this solve?
        
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