Learning Concepts with Energy Functions 166 points by stablemap 5 months ago | hide | past | web | favorite | 71 comments

 From the abstract of the article they linked:Energy-Based Models (EBMs) capture dependencies between variables by associating a scalar energy to each configuration of the variables. Inference consists in clamping the value of observed variables and finding configurations of the remaining variables that minimize the energy. Learning consists in finding an energy function in which observed configurations of the variables are given lower energies than unobserved ones. The EBM approach provides a common theoretical framework for many learning models, including traditional discriminative and generative approaches, as well as graph-transformer networks, conditional random fields, maximum margin Markov networks, and several manifold learning methods.Probabilistic models must be properly normalized, which sometimes requires evaluating intractable integrals over the space of all possible variable configurations. Since EBMs have no requirement for proper normalization, this problem is naturally circumvented. EBMs can be viewed as a form of non-probabilistic factor graphs, and they provide considerably more flexibility in the design of architectures and training criteria than probabilistic approaches.Seems like a really interesting unification of the wide variety of techniques out there in statistics and machine learning, analogous to the "everything is a computation graph, as long as it's differentiable" revolution. I like it when this kind of thing has its day. Would be interesting to see how well it works non-robotics problems.
 See Yann's tutorial on EBM: http://yann.lecun.com/exdb/publis/pdf/lecun-06.pdfWe actually ran into them when doing research in our startup. It is a really powerful perspective.
 Thank you for this!
 >Probabilistic models must be properly normalized, which sometimes requires evaluating intractable integrals over the space of all possible variable configurations. Since EBMs have no requirement for proper normalization, this problem is naturally circumvented. EBMs can be viewed as a form of non-probabilistic factor graphs, and they provide considerably more flexibility in the design of architectures and training criteria than probabilistic approaches.Can someone explain to me what the major difference is between energy-based models and variational Bayes approximations, which throw out calculating the normalization constant and switch to maximizing the log joint probability of the data and model?
 Setting up some energy function and then finding the lowest energy state sounds a lot like adibatic quantum computing. Assuming this research lives up to the hype, quantum computers might be able to run this algorithm faster. Quantum machine learning is already a thing, but its nice to see it fit so congruently with a classical counterpart.
 Quantum Simulated Annealing?
 I have no idea what's going on in this article. Is there a good resource or video for understanding this stuff?
 Every new technique is able to "quickly learn X." Something most not be so quick, otherwise why aren't these techniques turning into AGI?I think the problem is the goal is not well defined. So, increased velocity has no bearing on increased velocity towards the target.A side question, why is there no research into whether human intelligence is computable? The assumption in AI is that human intelligence is computable, but I've never seen any good argument or evidence that this is true. Seems very unscientific to exert so much energy into this research direction without validating the fundamental assumption.For example, the one instance I know of that defines AGI in a quantitative manner is Solomonoff induction (SI), but it is not computable. If SI is representative of human intelligence, then AGI is impossible.
 > why aren't these techniques turning into AGI?What prompted you to even ask this question? Where in the article does it say that "These results are step N on the path to AGI!"? This is research: the researchers found a problem that had limited solutions before (learning concepts with limited examples) and came up with a better solution. It's not clear why you're questioning this.> [on the computability of human intelligence]This is just silly. Even if human intelligence was beyond the reach of silicon (which I and many real researchers doubt), this work is still useful even if it doesn't result in AGI.You're too fixated on AGI. It's not the end goal.
 From the website:"About OpenAI: OpenAI is a non-profit AI research company, discovering and enacting the path to safe artificial general intelligence."At any rate, the bigger question is whether AGI is even possible. Why does no one even take a stab at answering this question? We have all these well funded research institutes that just assume AGI is possible, and we could just be throwing all the money down a hole.
 People definitely study whether AGI is possible. For example, philpapers.org lists ~2000 on the philosophy of cognitive science [1], and each of these papers is discussing some aspect of the possibility of AGI.
 Every such paper I've seen assumes AGI is possible, and is only concerned with the how question. Alternatively, it talks about 'qualia' and 'consciousness' which are not well defined enough to answer the question whether AGI is possible.If you've seen any papers addressing the more fundamental question in a quantitative manner I'd be interested to see a link.
 > Every such paper I've seen assumes AGI is possible, and is only concerned with the how question.Human brains exist, human brains are AGI, human brains are manufactured on a daily basis, ergo, it is in theory possible to manufacture an AGI.
 How do you know human brains are AGI?
 Define AGI.
 Reducible to a Turing machine.
 That doesn't sound like a complete definition of the term "AGI", unless you mean that anything reducible to a Turing machine is an AGI.In any case, I'm not sure why the term "artificial general intelligence" should be constrained to Turing machines. Nothing about it implies a Turing machine; just that it possesses intelligence and is artificially manufactured.
 Roger Penrose is a pretty famous mathematician who has a side-hobby of arguing that AGI is impossible. I believe his most famous work in this vein is https://en.wikipedia.org/wiki/The_Emperor%27s_New_Mind, but he has a handful of others as well. His arguments are pretty well grounded in both math and physics. I wouldn't describe the work as "quantitative", but it's probably about as quantitative as is possible at this point.
 > Roger Penrose is a pretty famous mathematician who has a side-hobby of arguing that AGI is impossible.If AGI is impossible, natural intelligent is either impossible or non-physical, but Penrose’s argument seems be that computing is insufficient for AGI, not that AGI is impossible.
 Even then, much of his argument is that there must be something "quantum" happening in the human brain, but he apparently fails to notice that a transistor is a quantum device or otherwise articulate why a mechanical object cannot possibly do all the quantum things a neuron can presumably do. Or why a computer model of that process would never be sufficient to emulate it. Half his arguments are misrepresentations of other people's positions and vague pseudo-mathematical conclusions masquerading as indisputable fact.All-in-all, that book is a big nothing.
 I agree with your synopsis. Penrose raises interesting questions, but his answers are not very convincing. But then again, no materialist answer to his question is very convincing. Which gives us two options:1. ignore the question by labeling it nonsensical2. expand our range of hypotheses to include immaterial answers
 (2) has never provided a convincing answer to any question, and there's no reason to believe it will here either.
 Sure it has. Modern physics depends on a number of concepts that were originally considered impossible for materialist explanations, such as any sort of "pulling" force, field effects, wave particle duality, and more recently with the refutation of local realism. Originally, materialists thought everything had to reduce to bumping billiard balls.Math itself is necessarily immaterial, and modern science would completely collapse without mathematics.So, it seems prima facie your claim that immaterial explanations have never been able to adequately answer any question to be incorrect. I see no problem with also proposing an immaterial soul as a scientific hypothesis, if we are able to make the claim quantifiable and empirically testable.
 > Modern physics depends on a number of concepts that were originally considered impossible for materialist explanations,It depends on a lot of things that were considered impossible, but not things that are logically incompatible with materialism.> So, it seems prima facie your claim that immaterial explanations have never been able to adequately answer any question to be incorrect.No, all the things you point to are material explanations.
 Well, that gets to the question of how we define materialism. Broadly enough, then a nonphysical soul can also be a new materialistic cause, so we do not have a disagreement.The fundamental issue is whether the new theory, materialistic or not, can be quantitatively and empirically tested in some way. I propose the notion of the mind as a halting oracle is such a thing. And we can call it a materialistic halting oracle so we don't violate the need for purely materialistic explanations.
 > Math itself is necessarily immaterial, and ...No, that strikes me as false. Geometry is very material and can explain a good bunch of mathematics. Differential geometry, an important aspect of modern AI, is necessarily symbolic, but that does not exclude its materialistic applications.
 If math is material, then we can destroy it. So, for instance, I could destroy the number 1. That doesn't make any sense. Even if the entire universe were destroyed, mathematics would still exist. Recreate the universe again and math would remain unchanged.
 Planet youhaventseenit in the Horse Nebula is material. Can you destroy it? No! Could it be destroyed by an unfortunate event? Perhaps. But if the number 1 is just an abstract thought, then that thought can seize to exist.> Even if the entire universe were destroyed, mathematics would still exist.You presuppose that maths is immaterial to proof that it's immaterial. That stance cannot be argued with, because you cannot show it to be true. If thought seized to exist, there would be nothing left to argue with, so this is reductio ad absurdum either way leading to a false dychotomy. What remains is: "maths" does exist. So my stance holds as much explanatory power as yours, no more, no less, but yours is metaphysical. You idealize things you don't understand, unless you have a concrete plan of action to "Recreate the universe again".
 In philosophy, one opinion is against the notion of the more fundamental question. I see that as institutional philosophy handing off its responsibility, quite paradoxically, because the argument is directed against basal sciences (bio, chem etc.) which give phil a run for its money.
 Considering the commercial benefits of non-AGI machine learning, the money is not really thrown away. And many of the potential negative effects of AI can occur even without AGI, so those are worth researching too.
 I'd be curious to see just how large the commercial benefits of standard ML actually are. The only reason it is hyped right now is because the media is leading people to believe something close to AGI is right around the corner, because we can bruteforce Go and index a million image dataset...Anyways, all the AI/ML hype is generated not by actual commercial value, but implied AGI. So, it would behoove us to question the underlying assumption that AGI is actually possible. After all, it is the scientific thing to do.
 Machine learning is used widely across a huge number of industries and fields from internet search, pharmaceuticals, mining/energy, digital security, entertainment, etc... So the commercial benefits are definitely tangible and not just "media hype".On computability of intelligence. I'm not an expert on this, but many people study the dynamics of biological neural networks and can represent these dynamics as PDEs which can then be mapped to electrical circuits. Granted approximations happen along the way and it has been difficult to scale these methods to large population of neurons. It still points to a solid argument that biological neural networks can be represented on a silicon substrate. This is basically what the entire field of neuromorphic engineering is focused on.
 My understanding is the practical benefit of machine learning and control systems is mostly due to simple models. Not the fancy "deep" models currently in vogue. An added problem is the high dimensional models are essentially black boxes, and are probably significantly overfitting the data, hence all the adversarial type research.Why does the mapping of biological neural networks to silicon substrate imply the human mind is a computer?
 > Why does the mapping of biological neural networks to silicon substrate imply the human mind is a computer?Is this a rhetorical question or something, because it seems to me you've answered yourself there. I mean, if the mapping works, what else should it imply besides the consequent?
 The implication requires a further premise that the mind is reducible to the brain, which we do not know to be true.
 Not just the brain, but the whole body and, even more generally, to phenomena that can be described by physics. Unless you are trying to argue for a non-physical (i.e. magical) soul, the argument is sound.
 Right, why assume the mind reduces to physics? This is usually how people argue for AGI being inevitable, but assuming the mind reduces to physics is a big assumption. Perhaps we have a physical soul.
 Why not? Everything so far had been reduced to physics; sometimes to at-the-time undiscovered physics.
 Deep models on GPUs have made using machine learning on images tractable. Manufacturing is one industry which is expected to benefit a lot from this, using computer vision heavily for automation, quality control and robotics.
 I'd be curious to see the actual ROI on this claim.
 Well, humans are an AGI and they are possible, therefore AGI is possible.
 Solomonoff induction is for just making predictions/models, AIXI is for when it needs to also take actions.Both AIXI and solomonoff induction can be approximated arbitrarily closely, given sufficient computational resources.Human intelligence is generally expected to be computable because physics is generally believed to be computable. However, don't get me wrong: I would be quite excited and probably pleased to learn that it isn't. I just am not convinced enough (or really, convinced much at all) to hang anything important on the idea that it isn't computable.
 Even given infinite resources Solomonoff induction cannot be computed, because we computationally cannot eliminate all non halting programs.Why believe human intelligence is limited by physics?
 Because elan vital and phlogiston turned out to be terrible ideas?Human cognition affects human action which has physical effects. So at the least, intelligence is causally linked with known phycial processes. I'd say that's sufficient to make it amenable to physical inquiry.Pulling out drastic measures like extraphysical magic, just to hand wave at an imprecise problem seems like an act of epistemic violence or something.
 Certainly intelligence is causally linked with the physical world, hence our conversation. But, this does not imply intelligence is itself physical. Additionally, saying intelligence is non physical does not turn it into some kind of inscrutable magic. Could you explain why you think this is the case?For example, I wrote an article explaining how modeling the human mind as a halting oracle results in empirically meaningful results.
 I think it depends on how we delineate physical vs non-physical. In this case, I'm taking a simple definition of "physical" to mean "anything amenable to scientific inquiry" or "any phenomenon that is, in principle, part of consensus reality".Actually, I'm confused what we'd even be claiming by calling intelligence purely non-physical. Perhaps you're thinking of the qualia of intelligence?Regarding the article you wrote, I think the concept of "partial oracle", while coherent, isn't super helpful. Or rather, it's too broad of a characterization. The halting problem doesn't claim that Turing machines can't solve some halting problems, it's that there's no finite class of turing machines which can together solve any halting problem.It's not precisely news that some Turing machines can solve the halting problem for certain (infinite) classes of machines. Case in point, regular languages.Anyway, meta-discussion-wise, I'm super happy to find kindred souls that also enjoy thinking about these things. I recently came across the Complexity Zoo[0] website, and if you're anything like me, I suspect you'll enjoy it too!
 I would disagree with that definition of physical. I believe a better definition of physical is anything that can be reduced to the laws of physics. Since the laws of physics are computable, I would enlarge the definition to be anything that can be reduced to a Turing machine. It's logically possible there are irreducible entities, i.e. partial oracles, so it is logically possible there are non physical, yet physically testable entities.In the article the point is a bit subtle, but partial oracles are still not Turing reducible. The point of the article is that the fact humans cannot solve all problems does not imply they are Turing reducible.At any rate, from my cursory analysis, it appears the notion of a non Turing reducible human mind is empirically tractable, so I still don't understand why it is not a viable scientific hypothesis and why AGI is assumed to be necessarily true. The mind as a partial oracle would imply AGI is impossible.Thanks for the link, I'll be checking it out!
 How do you know the laws of physics are computable (for a particular sense of "computable")? Perhaps the known physical laws are, but physics is still not a solved problem. In any case, if any new irreducible, physically-interacting elements of reality were to be discovered, there would be no reason not to consider them as irreducible elements of physics.
 Yes, as far as we know they are computable. And sure, without a well defined concept of "physical" we can call anything we want physical.The main point is the brain, as far as we know, is reducible to the known laws of physics, which, as far as we know, are entirely computable. Therefore, if human beings exhibit non computable phenomena, such as functioning as halting oracles, then that is a good reason to believe the mind does not reduce to the brain. And we could call this 'mind' a new form of matter or something, so that people don't get alarmed by non-physical phenomena.
 > The main point is the brain, as far as we know, is reducible to the known laws of physics, which, as far as we know, are entirely computable. Therefore, if human beings exhibit non computable phenomena, such as functioning as halting oracles, then that is a good reason to believe the mind does not reduce to the brain.This is where I disagree. It would, to me, seem to be a good reason to believe we've missed something about the way the body (not specifically the brain) works.> And we could call this 'mind' a new form of matter or something, so that people don't get alarmed by non-physical phenomena.This just sounds like you are eager to label any new phenomena "non-physical". There is no reason to pull the extraphysical gun just because you are stumbling upon new physics.
 Solomonoff induction can be computed in the limit. During round i, simulate your chosen UTM on each valid input string (note: assuming that the valid input strings are prefix free, which iirc is the standard for solomonoff induction) of length at most i, until you have simulated it for i steps total, or until it halts (whichever comes first).When doing so, for any string, the proportion of the inputs (with respect to the coin flip measure thing) to the UTM that eventually halt with whatever particular output, which will have been found to halt , will approach "all of them".Now, you can't quite say "run as long as you need to in order to get answer within this epsilon of correct answer", because you don't have a way of determining whether something hasn't halted yet but will, or if it never will, but, it is still computable in the limit. If you use absurdly (possibly quite absurdly) large but finite amounts of computational resources, it should give you a good enough approximation.Humans make mental errors often enough. I don't see why one would think that, because solomonoff induction is only approximable, that that suggests human intelligence is uncomputable. Why not suppose that humans just have a very close approximation to the uncomputable thing, rather than the noncomputable thing itself?Why believe that human intelligence is computable? Well, for me it is more of a "choosing not to believe that it is uncomputable". If I believed it uncomputable, I might hang too much of my philosophy/worldview on that assumption, and then if I turned out to be incorrect on that, too much might come crashing down.Edit: note: I mean "not believing", not "disbelieving". Not(believe(p)) rather than believe(not(p)) .
 Ah, right. That's true. Since the elegant program is guaranteed to halt, then we'll get to it eventually. My mistake. That being said, even with infinite resources we will never know when that actually happens, so we still will never known when Solomonoff induction has succeeded.I don't see what will come "crashing down." Science is about being able to quantify and empirically test our hypotheses. Nothing about uncomputable intelligence seems to undermine this idea, but perhaps I am missing something. Instead, it broadens the range of hypotheses we can use to explain the world, which seems to be a good thing.
 When I said crashing down, I meant in my own beliefs personally, not anything about the impact on science as a whole.Like, for example, if I built a justification for my believing in the existence of souls on top of the belief that the human mind is uncomputable, then if I turned out to be incorrect about the human mind, it might lead me to believe that souls don't exist (though that wouldn't really be a logical result, but I am not always rational). So, in order to have better foundations for my personal beliefs, I prefer not to rely on the assumption of uncomputability of the mind (nor on its negation).Basically, I want to avoid being too optimistic and believing too much because of it being convenient for my other beliefs.
 If your beliefs are consistent with a computable mind, then what stops you from also investigating the uncomputable mind? If true, then your beliefs are broadened, and if false nothing is threatened.
 Ah, I don't mean to reject the possibility that minds are uncomputable. Perhaps they are!It does seem likely that ideal minds would be (for reasons like those you describe).I just think I should require a rather strong argument to conclude that they are, instead of remaining non-commital.
 Solomonoff induction is not representative of human intelligence.At least, speaking for myself, I do not exhaustively search literally every hypothesis and match it against my data. Your mileage may vary. Dunno. It's a diverse world out there, right?
 > I do not exhaustively search literally every hypothesis and match it against my dataHaha. My problem is that my brain attempts to do this but can’t, which just leads to analysis paralysis instead.
 >> I do not exhaustively search literally every hypothesis and match it against my dataAre you implying you're a prodigy who's never fallen while learning to walk as a kid?
 Solomonoff induction is a way to quantify the human ability to induce general principles from limited observations. All the computable methods are unable to achieve this ability.
 With respect, no, that is not what it is. My summary is glib and phrased in non-mathematical terms, but closer.A true Solomonoff Inductor would be wildly, wildly smarter than a human being, if it could get over the problem that such a machine would also consume super-exponentially more resources than the universe has.
 It's not a matter of resources. Solomonoff induction is not computable, since it needs to calculate the Kolmogorov complexity of the data.If that is what is required for induction, it is surprising that humans are able to do so well at identifying concise descriptions of the data we observe. This seems inexplicable with a computational view of human cognition.
 Disregard, I realized my error is that the elegant program is guaranteed to halt at some point, which gives us the Kolmogorov complexity. We just will never know when that happens, even with infinite resources.
 That's just marketing.Also that assumes that the goal is some general AI. We're just getting started here
 I assume the goal is to achieve something useful. If AGI is impossible, then much more useful than these incremental steps is to figure out how to most effectively combine human cognition and computational systems.
 > then much more useful than these incremental steps is to figure out how to most effectively combine human cognition and computational systems.You don't know that
 And you don't know AGI is possible. Both are options, and we should first do some kind of basic research to determine which is a better route before dumping billions of dollars in one direction. Or, at very least we should dump money in both directions, and tune towards which is getting better real world gains.
 Obviously it's possible, we're having this conversation aren't we?
 In the sense that the "Artificial" part of AGI means: created by humans, we do not know if it is possible.
 I mean... what's so special about biology? How about I flip a few base pairs here and there, artificial enough yet? We already routinely genetically engineer mice and other model animals such that particular bits of their brain will either glow or fire in response to laser light, we have the technology today to put make little mice helmets that we can use to steer mice around - just need to do a bit more research to find out what particular bit of the (probably) hippocampus to stimulate. Is that artificial enough?OK and how about just simulating the universe? There is a legitimate question about computability there - it does seem plausible that aspects of simulating the universe could be uncomputable.Suppose that this is case - well it's still an open question as to whether or not this spells doom for the simulation route. The uncomputable bits are going to be some quantum this or that, and it's not at all clear that such low-level bits are fundamentally required for human-level intelligence; that the high-level process of intelligence is inseparable from the underlying processes which give rise to human intelligence.Personally, I find it a highly unlikely that intelligence is inseparable/has no reduced model, for whatever my prognostication is worth.BUT even if it is inseparable, there's still a strong argument to be made that you could construct AGI through means of so-called 'embodied computation', just like biology does.
 Embodied computation is not AGI. For example, if it is an immaterial soul that is doing the non reducible processing, and we take the bit of matter that the soul communicates with the world through, we have not created AGI. We've only managed to entrap a beings soul in a machine.If we can empirically quantify the behavior of an irreducible entity, which seems plausible, then the hypothesis is scientific.
 I don't understand what you mean. We are having this conversation about AGI so AGI is possible? We can talk about 1 + 1 = 3, but that's not possible...Or are you saying only AGIs can have conversations? That's begging the question.

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