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[-]Alexander Gietelink Oldenziel6mo4110

Why don't animals have guns?

Or why didn't evolution evolve the Hydralisk?

Evolution has found (sometimes multiple times) the camera, general intelligence, nanotech, electronavigation, aerial endurance better than any drone, robots more flexible than any human-made drone, highly efficient photosynthesis, etc.

First of all let's answer another question: why didn't evolution evolve the wheel like the alien wheeled elephants in His Dark Materials?

Is it biologically impossible to evolve?

Well, technically, the flagella of various bacteria is a proper wheel.

No the likely answer is that wheels are great when you have roads and suck when you don't. Roads are build by ants to some degree but on the whole probably don't make sense for an animal-intelligence species.

Aren't there animals that use projectiles?

Hold up. Is it actually true that there is not a single animal with a gun, harpoon or other projectile weapon?

Porcupines have quils, some snakes spit venom, a type of fish spits water as a projectile to kick insects of leaves than eats insects. Bombadier beetles can produce an explosive chemical mixture. Skunks use some other chemicals. Some snails shoot harpoons from very c... (read more)

6Daniel Murfet5mo

Please develop this question as a documentary special, for lapsed-Starcraft player homeschooling dads everywhere.

5Garrett Baker6mo

My naive hypothesis: Once you're able to launch a projectile at a predator or prey such that it breaks skin or shell, if you want it to die, its vastly cheaper to make venom at the ends of the projectiles than to make the projectiles launch fast enough that there's a good increase in probability the adversary dies quickly.

4Alexander Gietelink Oldenziel6mo

Why don't lions, tigers, wolves, crocodiles, etc have venom-tipped claws and teeth? (Actually, apparently many ancestral mammal species like did have venom spurs, similar to the male platypus)

7JBlack6mo

My completely naive guess would be that venom is mostly too slow for creatures of this size compared with gross physical damage and blood loss, and that getting close enough to set claws on the target is the hard part anyway. Venom seems more useful as a defensive or retributive mechanism than a hunting one.

4Nathan Helm-Burger6mo

Most uses of projected venom or other unpleasant substance seem to be defensive rather than offensive. One reason for this is that it's expensive to make the dangerous substance, and throwing it away wastes it. This cost is affordable if it is used to save your own life, but not easily affordable to acquire a single meal. This life vs meal distinction plays into a lot of offense/defense strategy expenses. For the hunting options, usually they are also useful for defense. The hunting options all seem cheaper to deploy: punching mantis shrimp, electric eel, fish spitting water... My guess it that it's mostly a question of whether the intermediate steps to the evolved behavior are themselves advantageous. Having a path of consistently advantageous steps makes it much easier for something to evolve. Having to go through a trough of worse-in-the-short-term makes things much less likely to evolve. A projectile fired weakly is a cost (energy to fire, energy to producing firing mechanism, energy to produce the projectile, energy to maintain the complexity of the whole system despite it not being useful yet). Where's the payoff of a weakly fired projectile? Humans can jump that gap by intuiting that a faster projectile would be more effective. Evolution doesn't get to extrapolate and plan like that.

5Carl Feynman2mo

Jellyfish have nematocysts, which is a spear on a rope, with poison on the tip. The spear has barbs, so when it goes in, it sticks. Then the jellyfish pulls in its prey. The spears are microscopic, but very abundant.

2Nathan Helm-Burger2mo

Yes, but I think snake fangs and jellyfish nematocysts are a slightly different type of weapon. Much more targeted application of venom. If the jellyfish squirted their venom as a cloud into the water around them when a fish came near, I expect it would not be nearly as effective per unit of venom. As a case where both are present, the spitting cobra uses its fangs to inject venom into its prey. However, when threatened, it can instead (wastefully) spray out its venom towards the eyes of an attacker. (the venom has little effect on unbroken mammal skin, but can easily blind if it gets into their eyes).

2Alexander Gietelink Oldenziel6mo

Fair argument I guess where I'm lost is that I feel I can make the same 'no competitive intermediate forms' for all kinds of wondrous biological forms and functions that have evolved, e.g. the nervous system. Indeed, this kind of argument used to be a favorite for ID advocates.

3Carl Feynman2mo

There are lots of excellent applications for even very simple nervous systems. The simplest surviving nervous systems are those of jellyfish. They form a ring of coupled oscillators around the periphery of the organism. Their goal is to synchronize muscular contraction so the bell of the jellyfish contracts as one, to propel the jellyfish efficiently. If the muscles contracted independently, it wouldn’t be nearly as good. Any organism with eyes will profit from having a nervous system to connect the eyes to the muscles. There’s a fungus with eyes and no nervous system, but as far as I know, every animal with eyes also has a nervous system. (The fungus in question is Pilobolus, which uses its eye to aim a gun. No kidding!)

2Tao Lin6mo

Another huge missed opportunity is thermal vision. Thermal infrared vision is a gigantic boon for hunting at night, and you might expect eg owls and hawks to use it to spot prey hundreds of meters away in pitch darkness, but no animals do (some have thermal sensing, but only extremely short range)

4Carl Feynman2mo

Snakes have thermal vision, using pits on their cheeks to form pinhole cameras. It pays to be cold-blooded when you’re looking for nice hot mice to eat.

3quetzal_rainbow6mo

Thermal vision for warm-blooded animals has obvious problems with noise.

2Alexander Gietelink Oldenziel6mo

Care to explain? Noise?

1quetzal_rainbow6mo

If you are warm, any warm-detectors inside your body will detect mostly you. Imagine if blood vessels in your own eye radiated in visible spectrum with the same intensity as daylight environment.

4Alexander Gietelink Oldenziel6mo

Can't you filter that out? . How do fighter planes do it?

6Carl Feynman2mo

It‘s possible to filter out a constant high value, but not possible to filter out a high level of noise. Unfortunately warmth = random vibration = noise. If you want a low noise thermal camera, you have to cool the detector, or only look for hot things, like engine flares. Fighter planes do both.

2Alexander Gietelink Oldenziel6mo

Woah great example didn't know bout that. Thanks Tao

1nim6mo

Animals do have guns. Humans are animals. Humans have guns. Evolution made us, we made guns, therefore guns indirectly exist because of evolution. Or do you mean "why don't animals have something like guns but permanently attached to them instead of regular guns?" There, I'd start with wondering why humans prefer to have our guns separate from our bodies, compared to affixing them permanently or semi-permanently to ourselves. All the drawbacks of choosing a permanently attached gun would also disadvantage a hypothetical creature that got the accessory through a longer, slower selection process.

[-]Alexander Gietelink Oldenziel24d3923

Novel Science is Inherently Illegible

Legibility, transparency, and open science are generally considered positive attributes, while opacity, elitism, and obscurantism are viewed as negative. However, increased legibility in science is not always beneficial and can often be detrimental.

Scientific management, with some exceptions, likely underperforms compared to simpler heuristics such as giving money to smart people or implementing grant lotteries. Scientific legibility suffers from the classic "Seeing like a State" problems. It constrains endeavors to the least informed stakeholder, hinders exploration, inevitably biases research to be simple and myopic, and exposes researchers to constant political tug-of-war between different interest groups poisoning objectivity.

I think the above would be considered relatively uncontroversial in EA circles. But I posit there is something deeper going on:

Novel research is inherently illegible. If it were legible, someone else would have already pursued it. As science advances her concepts become increasingly counterintuitive and further from common sense. Most of the legible low-hanging fruit has already been picked, and novel research requires venturing higher into the tree, pursuing illegible paths with indirect and hard-to-foresee impacts.

[-]Thomas Kwa24d11-1

Novel research is inherently illegible.

I'm pretty skeptical of this and think we need data to back up such a claim. However there might be bias: when anyone makes a serendipitous discovery it's a better story, so it gets more attention. Has anyone gone through, say, the list of all Nobel laureates and looked at whether their research would have seemed promising before it produced results?

[-]Alexander Gietelink Oldenziel23d115

Thanks for your skepticism, Thomas. Before we get into this, I'd like to make sure actually disagree. My position is not that scientific progress is mostly due to plucky outsiders who are ignored for decades. (I feel something like this is a popular view on LW). Indeed, I think most scientific progress is made through pretty conventional (academic) routes.

I think one can predict that future scientific progress will likely be made by young smart people at prestigious universities and research labs specializing in fields that have good feedback loops and/or have historically made a lot of progress: physics, chemistry, medicine, etc

My contention is that beyond very broad predictive factors like this, judging whether a research direction is fruitful is hard & requires inside knowledge. Much of this knowledge is illegible, difficult to attain because it takes a lot of specialized knowledge etc.

Do you disagree with this ?

I do think that novel research is inherently illegible. Here are some thoughts on your comment :

1.Before getting into your Nobel prize proposal I'd like to caution for Hindsight bias (obvious reasons).

And perhaps to some degree I'd like to argue the burden of proo

... (read more)

[-]aysja21d132

I guess I'm not sure what you mean by "most scientific progress," and I'm missing some of the history here, but my sense is that importance-weighted science happens proportionally more outside of academia. E.g., Einstein did his miracle year outside of academia (and later stated that he wouldn't have been able to do it, had he succeeded at getting an academic position), Darwin figured out natural selection, and Carnot figured out the Carnot cycle, all mostly on their own, outside of academia. Those are three major scientists who arguably started entire fields (quantum mechanics, biology, and thermodynamics). I would anti-predict that future scientific progress, of the field-founding sort, comes primarily from people at prestigious universities, since they, imo, typically have some of the most intense gatekeeping dynamics which make it harder to have original thoughts.

8Alexander Gietelink Oldenziel20d

Good point. I do wonder to what degree that may be biased by the fact that there were vastly less academic positions before WWI/WWII. In the time of Darwin and Carnot these positions virtually didn't exist. In the time of Einstein they did exist but they were quite rare still. How many examples do you know of this happening past WWII? Shannon was at Bell Labs iirc As counterexample of field-founding happening in academia: Godel, Church, Turing were all in academia.

6Thomas Kwa23d

Oh, I actually 70% agree with this. I think there's an important distinction between legibility to laypeople vs legibility to other domain experts. Let me lay out my beliefs: * In the modern history of fields you mentioned, more than 70% of discoveries are made by people trying to discover the thing, rather than serendipitously. * Other experts in the field, if truth-seeking, are able to understand the theory of change behind the research direction without investing huge amounts of time. * In most fields, experts and superforecasters informed by expert commentary will have fairly strong beliefs about which approaches to a problem will succeed. The person working on something will usually have less than 1 bit advantage about whether their framework will be successful than the experts, unless they have private information (e.g. already did the crucial experiment). This is the weakest belief and I could probably be convinced otherwise just by anecdotes. * The successful researchers might be confident they will succeed, but unsuccessful ones could be almost as confident on average. So it's not that the research is illegible, it's just genuinely hard to predict who will succeed. * People often work on different approaches to the problem even if they can predict which ones will work. This could be due to irrationality, other incentives, diminishing returns to each approach, comparative advantage, etc. If research were illegible to other domain experts, I think you would not really get Kuhnian paradigms, which I am pretty confident exist. Paradigm shifts mostly come from the track record of an approach, so maybe this doesn't count as researchers having an inside view of others' work though.

[-]Alexander Gietelink Oldenziel23d119

Thank you, Thomas. I believe we find ourselves in broad agreement. The distinction you make between lay-legibility and expert-legibility is especially well-drawn.

One point: the confidence of researchers in their own approach may not be the right thing to look at. Perhaps a better measure is seeing who can predict not only their own approach will succed but explain in detail why other approaches won't work. Anecdotally, very succesful researchers have a keen sense of what will work out and what won't - in private conversation many are willing to share detailed models why other approaches will not work or are not as promising. I'd have to think about this more carefully but anecdotally the most succesful researchers have many bits of information over their competitors not just one or two. (Note that one bit of information means that their entire advantage could be wiped out by answering a single Y/N question. Not impossible, but not typical for most cases)

5Seth Herd24d

What areas of science are you thinking of? I think the discussion varies dramatically. I think allowing less legibility would help make science less plodding, and allow it to move in larger steps. But there's also a question of what direction it's plodding. The problem I saw with psych and neurosci was that it tended to plod in nearly random, not very useful directions. And what definition of "smart"? I'm afraid that by a common definition, smart people tend to do dumb research, in that they'll do galaxy brained projects that are interesting but unlikely to pay off. This is how you get new science, but not useful science. In cognitive psychology and neuroscience, I want to see money given to people who are both creative and practical. They will do new science that is also useful. In psychology and neuroscience, scientists pick the grantees, and they tend to give money to those whose research they understand. This produces an effect where research keeps following one direction that became popular long ago. I think a different method of granting would work better, but the particular method matters a lot. Thinking about it a little more, having a mix of personality types involved would probably be useful. I always appreciated the contributions of the rare philospher who actually learned enough to join a discussion about psych or neurosci research. I think the most important application of meta science theory is alignment research.

3ChristianKl22d

It might also be that a legible path would be low status to pursue in the existing scientific communities and thus nobody pursues it. If you look at a low-hanging fruit that was unpicked for a long time, airborne transmission of many viruses like the common cold, is a good example. There's nothing illegible about it.

2Alexander Gietelink Oldenziel20d

mmm Good point. Do you have more examples?

2ChristianKl19d

The core reason for holding the belief is because the world does not look to me like there's little low hanging fruit in a variety of domains of knowledge I have thought about over the years. Of course it's generally not that easy to argue for the value of ideas that the mainstream does not care about publically. Wei Dei recently wrote: If you look at the broader field of rationality, the work of Judea Pearl and that of Tetlock both could have been done twenty years earlier. Conceptually, I think you can argue that their work was some of the most important work that was done in the last decades. Judea Pearl writes about how allergic people were against the idea of factoring in counterfactuals and causality.

2Garrett Baker24d

I don’t think the application to EA itself would be uncontroversial.

[-]Alexander Gietelink Oldenziel9d270

Encrypted Batteries

(I thank Dmitry Vaintrob for the idea of encrypted batteries. Thanks to Adam Scholl for the alignment angle. Thanks to the Computational Mechanics at the receent compMech conference. )

There are no Atoms in the Void just Bits in the Description. Given the right string a Maxwell Demon transducer can extract energy from a heatbath.

Imagine a pseudorandom heatbath + nano-Demon. It looks like a heatbath from the outside but secretly there is a private key string that when fed to the nano-Demon allows it to extra lots of energy from the heatbath.

P.S. Beyond the current ken of humanity lies a generalized concept of free energy that describes the generic potential ability or power of an agent to achieve goals. Money, the golden calf of Baal is one of its many avatars. Could there be ways to encrypt generalized free energy batteries to constraint the user to only see this power for good? It would be like money that could be only spent on good things.

[-]gwern9d133

Imagine a pseudorandom heatbath + nano-Demon. It looks like a heatbath from the outside but secretly there is a private key string that when fed to the nano-Demon allows it to extra lots of energy from the heatbath.

What would a 'pseudorandom heatbath' look like? I would expect most objects to quickly depart from any sort of private key or PRNG. Would this be something like... a reversible computer which shuffles around a large number of blank bits in a complicated pseudo-random order every timestep*, exposing a fraction of them to external access? so a daemon with the key/PRNG seed can write to the blank bits with approaching 100% efficiency (rendering it useful for another reversible computer doing some actual work) but anyone else can't do better than 50-50 (without breaking the PRNG/crypto) and that preserves the blank bit count and is no gain?

* As I understand reversible computing, you can have a reversible computer which does that for free: if this is something like a very large period loop blindly shuffling its bits, it need erase/write no bits (because it's just looping through the same states forever, akin to a time crystal), and so can be computed indefinitely at arbitrarily low energy cost. So any external computer which syncs up to it can also sync at zero cost, and just treat the exposed unused bits as if they were its own, thereby saving power.

2Alexander Gietelink Oldenziel8d

That is my understanding, yes.

2mako yass8d

Yeah I'm pretty sure you would need to violate heisenberg uncertainty in order to make this and then you'd have to keep it in a 0 kelvin cleanroom forever. A practical locked battery with tamperproofing would mostly just look like a battery.

[-]Alexander Gietelink Oldenziel7mo164

Corrupting influences

The EA AI safety strategy has had a large focus on placing EA-aligned people in A(G)I labs. The thinking was that having enough aligned insiders would make a difference on crucial deployment decisions & longer-term alignment strategy. We could say that the strategy is an attempt to corrupt the goal of pure capability advance & making money towards the goal of alignment. This fits into a larger theme that EA needs to get close to power to have real influence.

[See also the large donations EA has made to OpenAI & Anthropic. ]

Whether this strategy paid off... too early to tell.

What has become apparent is that the large AI labs & being close to power have had a strong corrupting influence on EA epistemics and culture.

Many people in EA now think nothing of being paid Bay Area programmer salaries for research or nonprofit jobs.
There has been a huge influx of MBA blabber being thrown around. Bizarrely EA funds are often giving huge grants to for profit organizations for which it is very unclear whether they're really EA-aligned in the long-term or just paying lip service. Highly questionable that EA should be trying to do venture

... (read more)

7Daniel Murfet5mo

As a supervisor of numerous MSc and PhD students in mathematics, when someone finishes a math degree and considers a job, the tradeoffs are usually between meaning, income, freedom, evil, etc., with some of the obvious choices being high/low along (relatively?) obvious axes. It's extremely striking to see young talented people with math or physics (or CS) backgrounds going into technical AI alignment roles in big labs, apparently maximising along many (or all) of these axes! Especially in light of recent events I suspect that this phenomenon, which appears too good to be true, actually is.

5RHollerith7mo

Yes!

6Thomas Kwa7mo

I'm not too concerned about this. ML skills are not sufficient to do good alignment work, but they seem to be very important for like 80% of alignment work and make a big difference in the impact of research (although I'd guess still smaller than whether the application to alignment is good) * Primary criticisms of Redwood involve their lack of experience in ML * The explosion of research in the last ~year is partially due to an increase in the number of people in the community who work with ML. Maybe you would argue that lots of current research is useless, but it seems a lot better than only having MIRI around * The field of machine learning at large is in many cases solving easier versions of problems we have in alignment, and therefore it makes a ton of sense to have ML research experience in those areas. E.g. safe RL is how to get safe policies when you can optimize over policies and know which states/actions are safe; alignment can be stated as a harder version of this where we also need to deal with value specification, self-modification, instrumental convergence etc.

5Alexander Gietelink Oldenziel7mo

I mostly agree with this. I should have said 'prestige within capabilities research' rather than ML skills which seems straightforwardly useful. The former is seems highly corruptive.

0Noosphere897mo

I'd arguably say this is good, primarily because I think EA was already in danger of it's AI safety wing becoming unmoored from reality by ignoring key constraints, similar to how early Lesswrong before the deep learning era around 2012-2018 turned out to be mostly useless due to how much everything was stated in a mathematical way, and not realizing how many constraints and conjectured constraints applied to stuff like formal provability, for example..

[-]Alexander Gietelink Oldenziel5mo134

Pockets of Deep Expertise

Why am I so bullish on academic outreach? Why do I keep hammering on 'getting the adults in the room'?

It's not that I think academics are all Super Smart.

I think rationalists/alignment people correctly ascertain that most professors don't have much useful to say about alignment & deep learning and often say silly things. They correctly see that much of AI congress is fueled by labs and scale not ML academia. I am bullish on non-ML academia, especially mathematics, physics and to a lesser extent theoretical CS, neuroscience, some parts of ML/ AI academia. This is because while I think 95 % of academia is bad and/or useless there are Pockets of Deep Expertise. Most questions in alignment are close to existing work in academia in some sense - but we have to make the connection!

A good example is 'sparse coding' and 'compressed sensing'. Lots of mech.interp has been rediscovering some of the basic ideas of sparse coding. But there is vast expertise in academia about these topics. We should leverage these!

Other examples are singular learning theory, computational mechanics, etc

[-]Alexander Gietelink Oldenziel7mo131

Fractal Fuzz: making up for size

GPT-3 recognizes 50k possible tokens. For a 1000 token context window that means there are $(5 \cdot 10^{5})^{10^{3}} \approx 10^{5000}$ possible prompts. Astronomically large. If we assume the output of a single run of gpt is 200 tokens then for each possible prompt there are $\approx 10^{2500}$ possible continuations.

GPT-3 is probabilistic, defining for each possible prompt $x$ ( $\approx 10^{5000}$ ) a distribution $q (x)$ on a set of size $10^{2500}$ , in other words a $10^{2500} - 1$ dimensional space. ^[1]

Mind-boggingly large. Compared to these numbers the amount of data (40 trillion tokens??) and the size of the model (175 billion parameters) seems absolutely puny in comparison.

I won't be talking about the data, or 'overparameterizations' in this short, that is well-explained by Singular Learning Theory. Instead, I will be talking about nonrealizability.

Nonrealizability & the structure of natural data

Recall the setup of (parametric) Bayesian learning: there is a sample space $Ω$ , a true distribution $q (x)$ on $Ω$ and a parameterized family of probability distributions $p (x | w), w \in W \subset R^{d}$ .

It is often assumed that the true distrib... (read more)

1Zach Furman7mo

Very interesting, glad to see this written up! Not sure I totally agree that it's necessary for W to be a fractal? But I do think you're onto something. In particular you say that "there are points y in the larger dimensional space that are very (even arbitrarily) far from W," but in the case of GPT-4 the input space is discrete, and even in the case of e.g. vision models the input space is compact. So the distance must be bounded. Plus if you e.g. sample a random image, you'll find there's usually a finite distance you need to travel in the input space (in L1, L2, etc) until you get something that's human interpretable (i.e. lies on the data manifold). So that would point against the data manifold being dense in the input space. But there is something here, I think. The distance usually isn't that large until you reach a human interpretable image, and it's quite easy to perturb images slightly to have completely different interpretations (both to humans and ML systems). A fairly smooth data manifold wouldn't do this. So my guess is that the data "manifold" is in fact not a manifold globally, but instead has many self-intersections and is singular. That would let it be close to large portions of input space without being literally dense in it. This also makes sense from an SLT perspective. And IIRC there's some empirical evidence that the dimension of the data "manifold" is not globally constant.

2Alexander Gietelink Oldenziel7mo

The input and output spaces etc Ω are all discrete but the spaces of distributions Δ(Ω) on those spaces are infinite (but still finite-dimensional). It depends on what kind of metric one uses, compactness assumptions etc whether or not you can be arbitrarily far. I am being rather vague here. For instance, if you use the KL-divergence, then K(q|puniform) is always bounded - indeed it equals the entropy of the true distribution H(q)! I don't really know what ML people mean by the data manifold so won't say more about that. I am talking about the space W of parameter values of a conditional probability distribution p(x|w). I think that W having nonconstant local dimension doesn't seem that relevant since the largest dimensional subspace would dominate? Self-intersections and singularities could certainly occur here. (i) singularities in the SLT sense have to do with singularities in the level sets of the KL-divergence (or loss function) - don't see immediately how these are related to the singularities that you are talking about here (ii) it wouldn't increase the dimensionality (rather the opposite). The fractal dimension is important basically because of space-filling curves : a space that has a low-dimensional parameterization can nevertheless have a very large effective dimensions when embedded fractally into a larger-dimensional space. These embeddings can make a low-dimensional parameterization effectively have higher dimension.

1Zach Furman7mo

Sorry, I realized that you're mostly talking about the space of true distributions and I was mainly talking about the "data manifold" (related to the structure of the map x↦p(x∣w∗) for fixed w∗). You can disregard most of that. Though, even in the case where we're talking about the space of true distributions, I'm still not convinced that the image of W under p(x∣w) needs to be fractal. Like, a space-filling assumption sounds to me like basically a universal approximation argument - you're assuming that the image of W densely (or almost densely) fills the space of all probability distributions of a given dimension. But of course we know that universal approximation is problematic and can't explain what neural nets are actually doing for realistic data.

3Alexander Gietelink Oldenziel7mo

Obviously this is all speculation but maybe I'm saying that the universal approximation theorem implies that neural architectures are fractal in space of all distributtions (or some restricted subset thereof)? Curious what's your beef with universal approximation? Stone-weierstrass isn't quantitative - is that the reason? If true it suggest the fractal dimension (probably related to the information dimension I linked to above) may be important.

1Zach Furman7mo

Oh I actually don't think this is speculation, if (big if) you satisfy the conditions for universal approximation then this is just true (specifically that the image of W is dense in function space). Like, for example, you can state Stone-Weierstrass as: for a Hausdorff space X, and the continuous functions under the sup norm C(X,R), the Banach subalgebra of polynomials is dense in C(X,R). In practice you'd only have a finite-dimensional subset of the polynomials, so this obviously can't hold exactly, but as you increase the size of the polynomials, they'll be more space-filling and the error bound will decrease. The problem is that the dimension of W required to achieve a given ϵ error bound grows exponentially with the dimension d of your underlying space X. For instance, if you assume that weights depend continuously on the target function, ϵ-approximating all Cn functions on [0,1]d with Sobolev norm ≤1 provably takes at least O(ϵ−d/n) parameters (DeVore et al.). This is a lower bound. So for any realistic d universal approximation is basically useless - the number of parameters required is enormous. Which makes sense because approximation by basis functions is basically the continuous version of a lookup table. Because neural networks actually work in practice, without requiring exponentially many parameters, this also tells you that the space of realistic target functions can't just be some generic function space (even with smoothness conditions), it has to have some non-generic properties to escape the lower bound.

2Alexander Gietelink Oldenziel7mo

Ooooo okay so this seems like it's directly pointing to the fractal story! Exciting!

2Alexander Gietelink Oldenziel7mo

Obviously this is all speculation but maybe I'm saying that the universal approximation theorem implies that neural architectures are fractal in space of all distributtions (or some restricted subset thereof)? Stone-weierstrass isn't quantitative. If true it suggest the fractal dimension (probably related to the information dimension I linked to above) may be important.

[-]Alexander Gietelink Oldenziel1y132

The Vibes of Mathematics:

Q: What is it like to understand advanced mathematics? Does it feel analogous to having mastery of another language like in programming or linguistics?

A: It's like being stranded on a tropical island where all your needs are met, the weather is always perfect, and life is wonderful.

Except nobody wants to hear about it at parties.

Vibes of Maths: Convergence and Divergence

level 0: A state of ignorance. you live in a pre-formal mindset. You don't know how to formalize things. You don't even know what it would even mean 'to prove something mathematically'. This is perhaps the longest. It is the default state of a human. Most anti-theory sentiment comes from this state. Since you've neve

You can't productively read Math books. You often decry that these mathematicians make books way too hard to read. If they only would take the time to explain things simply you would understand.

level 1 : all math is amorphous blob

You know the basic of writing an epsilon-delta proof. Although you don't know why the rules of maths are this or that way you can at least follow the recipes. You can follow simple short proofs, albeit slowly.

You know there are differen... (read more)

7PhilGoetz1y

I say that knowing particular kinds of math, the kind that let you model the world more-precisely, and that give you a theory of error, isn't like knowing another language. It's like knowing language at all. Learning these types of math gives you as much of an effective intelligence boost over people who don't, as learning a spoken language gives you above people who don't know any language (e.g., many deaf-mutes in earlier times). The kinds of math I mean include: * how to count things in an unbiased manner; the methodology of polls and other data-gathering * how to actually make a claim, as opposed to what most people do, which is to make a claim that's useless because it lacks quantification or quantifiers * A good example of this is the claims in the IPCC 2015 report that I wrote some comments on recently. Most of them say things like, "Global warming will make X worse", where you already know that OF COURSE global warming will make X worse, but you only care how much worse. * More generally, any claim of the type "All X are Y" or "No X are Y", e.g., "Capitalists exploit the working class", shouldn't be considered claims at all, and can accomplish nothing except foment arguments. * the use of probabilities and error measures * probability distributions: flat, normal, binomial, poisson, and power-law * entropy measures and other information theory * predictive error-minimization models like regression * statistical tests and how to interpret them These things are what I call the correct Platonic forms. The Platonic forms were meant to be perfect models for things found on earth. These kinds of math actually are. The concept of "perfect" actually makes sense for them, as opposed to for Earthly categories like "human", "justice", etc., for which believing that the concept of "perfect" is coherent demonstrably drives people insane and causes them to come up with things like Christianity. They are, however, like Aristotle's Forms, in that the u

3Daniel Murfet5mo

You seem to do OK... This is an interesting one. I field this comment quite often from undergraduates, and it's hard to carve out enough quiet space in a conversation to explain what they're doing wrong. In a way the proliferation of math on YouTube might be exacerbating this hard step from tourist to troubadour.

[-]Alexander Gietelink Oldenziel1mo110

Feature request: author-driven collaborative editing [CITATION needed] for the Good and Glorious Epistemic Commons.

Often I find myself writing claims which would ideally have citations but I don't know an exact reference, don't remember where I read it, or am simply too lazy to do the literature search.

This is bad for scholarship is a rationalist virtue. Proper citation is key to preserving and growing the epistemic commons.

It would be awesome if my lazyness were rewarded by giving me the option to add a [CITATION needed] that others could then suggest (push) a citation, link or short remark which the author (me) could then accept. The contribution of the citator is acknowledged of course. [even better would be if there was some central database that would track citations & links like with crosslinking etc like wikipedia]

a sort hybrid vigor of Community Notes and Wikipedia if you will. but It's collaborative, not adversarial*

author: blablablabla

sky is blue [citation Needed]

blabblabla

intrepid bibliographer: (push) [1] "I went outside and the sky was blue", Letters to the Empirical Review

*community notes on twitter has been a universally lauded concept when it first launched. We are already seeing it being abused unfortunately, often used for unreplyable cheap dunks. I still think it's a good addition to twitter but it does show how difficult it is to create shared agreed-upon epistemics in an adverserial setting.

[-]Alexander Gietelink Oldenziel4mo80

[see also Hanson on rot, generalizations of the second law to nonequilibrium systems (Baez-Pollard, Crutchfield et al.) ]

Imperfect Persistence of Metabolically Active Engines

All things rot. Indidivual organisms, societies-at-large, businesses, churches, empires and maritime republics, man-made artifacts of glass and steel, creatures of flesh and blood.

Conjecture #1 There is a lower bound on the amount of dissipation / rot that any metabolically-active engine creates.

Conjecture #2 Metabolic Rot of an engine is proportional to (1) size and complexity o... (read more)

[-]Alexander Gietelink Oldenziel9d60

Clem's Synthetic- Physicalist Hypothesis

The mathematico-physicalist hypothesis states that our physical universe is actually a piece of math. It was famously popularized by Max Tegmark.

It's one of those big-brain ideas that sound profound when you first hear about it, then you think about it some more and you realize it's vacuous.

Recently, in a conversation with Clem von Stengel they suggested a version of the mathematico-physicalist hypothesis that I find provoking.

Synthetic mathematics

'Synthetic' mathematics is a bit of weird name... (read more)

[-]Alexander Gietelink Oldenziel24d62

Know your scientific competitors.

In trading, entering a market dominated by insiders without proper research is a sure-fire way to lose a lot of money and time. Fintech companies go to great lengths to uncover their competitors' strategies while safeguarding their own.

A friend who worked in trading told me that traders would share subtly incorrect advice on trading Discords to mislead competitors and protect their strategies.

Surprisingly, in many scientific disciplines researchers are often curiously incurious about their peers' work.

The long f... (read more)

2Viliam24d

Makes sense, but wouldn't this also result in even fewer replications (as a side effect of doing less superfluous work)?

[-]Alexander Gietelink Oldenziel2mo50

Idle thoughts about UDASSA I: the Simulation hypothesis

I was talking to my neighbor about UDASSA the other day. He mentioned a book I keep getting recommended but never read where characters get simulated and then the simulating machine is progressively slowed down.

One would expect one wouldn't be able to notice from inside the simulation that the simulating machine is being slowed down.

This presents a conundrum for simulation style hypotheses: if the simulation can be slowed down 100x without the insiders noticing, why not 1000x or 10^100x or ... (read more)

2Dagon2mo

In most conceptions of simulation, there is no meaning to "slowed down", from the perspective of the simulated universe. Time is a local phenomenon in this view - it's just a compression mechanism so the simulators don't have to store ALL the states of the simulation, just the current state and the rules to progress it. Note that this COULD be said of a non-simulated universe as well - past and future states are determined but not accessible, and the universe is self-discovering them by operating on the current state via physics rules. So there's still no inside-observable difference between simulated and non-simulated universes. UDASSA seems like anthropic reasoning to include Boltzmann Brain like conceptions of experience. I don't put a lot of weight on it, because all anthropic reasoning requires an outside-view of possible observations to be meaningful. And of course, none of this relates to upload, where a given sequence of experiences can span levels of simulation. There may or may not be a way to do it, but it'd be a copy, not a continuation.

2Alexander Gietelink Oldenziel2mo

The point you make in the your first paragraph is contained in the original shortform post. The point of the post is exactly that an UDASSA-style argument can nevertheless recover something like a 'distribution of likely slowdown factors'. This seems quite curious. I suggest reading Falkovich's post on UDASSA to get a sense whats so intriguing abouy the UDASSA franework.

[-]Alexander Gietelink Oldenziel5d40

Why (talk-)Therapy

Therapy is a curious practice. Therapy sounds like a scam, quackery, pseudo-science but it seems RCT consistently show therapy has benefits above and beyond medication & placebo.

Therapy has a long history. The Dodo verdict states that it doesn't matter which form of therapy you do - they all work equally well. It follows that priests and shamans served the functions of a therapist. In the past, one would confessed ones sins to a priest, or spoken with the local shaman.

There is also the thing that therapy ... (read more)

1lukehmiles5d

I suspect that past therapists existed in your community and knew what you're actually like so were better able to give you actual true information instead of having to digest only your bullshit and search for truth nuggets in it. Furthermore, I suspect they didn't lose their bread when they solve your problem! We have a major incentive issue in the current arrangement!

2M. Y. Zuo5d

There's a market for lemons problem, similar to the used car market, where neither the therapist nor customer can detect all hidden problems, pitfalls, etc., ahead of time. And once you do spend enough time to actually form a reasonable estimate there's no takebacks possible. So all the actually quality therapists will have no availability and all the lower quality therapists will almost by definition be associated with those with availability. Edit: Game Theory suggests that you should never engage in therapy or at least never with someone with available time, at least until someone invents the certified pre-owned market.

2ChristianKl3d

That would be prediction-based medicine. It works in theory, it's just that someone would need to put it into practice.

2Garrett Baker5d

This style of argument proves too much. Why not see this dynamic with all jobs and products ever?

5lukehmiles5d

Have you ever tried hiring someone or getting a job? Mostly lemons all around (apologies for the offense, jobseekers, i'm sure you're not the lemon)

2localdeity5d

Yup. Many programmer applicants famously couldn't solve FizzBuzz. Which is probably because:

2Garrett Baker5d

But such people are very obvious. You just give them a FizzBuzz test! This is why we have interviews, and work-trials.

2Alexander Gietelink Oldenziel5d

If therapist quality would actually matter why don't we see this reflected in RCTs?

2ChristianKl3d

We see it reflected in RCTs. One aspect of therapist quality is for example therapist empathy and empathy is a predictor for treatment outcomes. The style of therapy does not seem to be important according to RCTs but that doesn't mean that therapist skill is irrelevant.

4Alexander Gietelink Oldenziel3d

Thank you practicing the rationalist virtue of scholarship Christian. I was not aware of this paper. You will have to excuse me for practicing rationalist vice and not believing nor investigating further this paper. I have been so traumatized by the repeated failures of non-hard science, I reject most social science papers as causally confounded p-hacked noise unless it already confirms my priors or is branded correct by somebody I trust.

2ChristianKl3d

As far as this particular paper goes I just searched for one on the point in Google Scholar. I'm not sure what you believe about Spencer Greenberg but he has two interviews with people who believe that therapist skills (where empathy is one of the academic findings) matter: https://podcast.clearerthinking.org/episode/070/scott-miller-why-does-psychotherapy-work-when-it-works-at-all/ https://podcast.clearerthinking.org/episode/192/david-burns-cognitive-behavioral-therapy-and-beyond/

2Alexander Gietelink Oldenziel5d

I internalized the Dodo verdict and concluded that the specific therapist or therapist style didn't matter anyway. A therapist is just a human mirror. The answer was inside of you all along Miles

[-]Alexander Gietelink Oldenziel2mo40

[This is joint thinking with Sam Eisenstat. Also thanks to Caspar Oesterheld for his thoughtful comments. Thanks to Steve Byrnes for pushing me to write this out.]

The Hyena problem in long-term planning

Logical induction is a nice framework to think about bounded reasoning. Very soon after the discovery of logical induction people tried to make logical inductor decision makers work. This is difficult to make work: one of two obstacles is

Obstacle 1: Untaken Actions are not Observable

Caspar Oesterheld brilliantly solved this problem by using auction ma... (read more)

[-]Alexander Gietelink Oldenziel10mo40

Latent abstractions Bootlegged.

Let $X_{1}, . . ., X_{n}$ be random variables distributed according to a probability distribution $p$ on a sample space $Ω$ .

Defn. A (weak) natural latent of $X_{1}, . . ., X_{n}$ is a random variable $Λ$ such that

(i) $X_{i}$ are independent conditional on $Λ$

(ii) [reconstructability] $p (Λ = λ | X_{1}, . . .,_{i}, . . ., X_{n}) = p (Λ = λ | X_{1}, . . ., X_{n})$ for all $i = 1$

[This is not really reconstructability, more like a stability property. The information is contained in many parts of the system... I might al... (read more)

[-]Alexander Gietelink Oldenziel9mo140

Inspired by this Shalizi paper defining local causal states. The idea is so simple and elegant I'm surprised I had never seen it before.

Basically, starting with a a factored probability distribution $X_{t} = (X_{1} (t), . . ., X_{k_{t}} (t))$ over a dynamical DAG $D_{t}$ we can use Crutchfield causal state construction locally to construct a derived causal model factored over the dynamical DAG as $X_{t}^{'}$ where $X_{t}^{'}$ is defined by considering the past and forward lightcone of $X_{t}$ defined as $L^{-} (X_{t}), L^{+} (X_{t})$ all those points/ variables $Y_{t_{2}}$ which influence $X_{t}$ respectively are influenced by $X_{t}$ (in a causal interventional sense) . Now take define the equivalence relatio on realization $a_{t} \sim b_{t}$ of $L^{-} (X_{t})$ (which includes $X_{t}$ by definition)^[1] whenever the conditional probability distribution $p (L^{+} (X_{t}) | a_{t}) = p (L^{+} (X_{t}) | b_{t})$ on the future light cones are equal.

These factored probability distributions over dynamical DAGs are called 'fields' by physicists. Given any field $F (x, t)$ we define a derived local causal state field $ϵ (F (x, t))$ in the above way. Woah!

... (read more)

8johnswentworth10mo

That condition doesn't work, but here's a few alternatives which do (you can pick any one of them): * Λ=(x↦P[X=x|Λ]) - most conceptually confusing at first, but most powerful/useful once you're used to it; it's using the trick from Minimal Map. * Require that Λ be a deterministic function of X, not just any latent variable. * H(Λ)=I(X,Λ) (The latter two are always equivalent for any two variables X,Λ and are somewhat stronger than we need here, but they're both equivalent to the first once we've already asserted the other natural latent conditions.)

[-]Alexander Gietelink Oldenziel11mo40

Reasons to think Lobian Cooperation is important

Usually the modal Lobian cooperation is dismissed as not relevant for real situations but it is plausible that Lobian cooperation extends far more broadly than what is proved currently.

It is plausible that much of cooperation we see in the real world is actually approximate Lobian cooperation rather than purely given by traditional game-theoretic incentives.
Lobian cooperation is far stronger in cases where the players resemble each other and/or have access to one another's blueprint. This is ... (read more)

5Noosphere8911mo

I definitely agree that cooperation can definitely be way better in the future, and Lobian cooperation, especially with Payor's Lemma, might well be enough to get coordination across entire solar system. That stated, it's much more tricky to expand this strategy to galactic scales, assuming our physical models aren't wrong, because light speed starts to become a very taut constraint under a galaxy wide brain, and acausal strategies will require a lot of compute to simulate entire civilizations. Even worse, they depend on some common structure of values, and I suspect it's impossible to do in the fully general case.

[-]Alexander Gietelink Oldenziel1y40

"I dreamed I was a butterfly, flitting around in the sky; then I awoke. Now I wonder: Am I a man who dreamt of being a butterfly, or am I a butterfly dreaming that I am a man?"- Zhuangzi

Questions I have that you might have too:

why are we here?
why do we live in such an extraordinary time?
Is the simulation hypothesis true? If so, is there a base reality?
Why do we know we're not a Boltzmann brain?
Is existence observer-dependent?
Is there a purpose to existence, a Grand Design?
What will be computed in the Far Future?

In this shortform I will try and... (read more)

2Richard_Kennaway1y

In this comment I will try and write the most boring possible reply to these questions. 😊 These are pretty much my real replies. "Ours not to reason why, ours but to do or do not, there is no try." Someone must. We happen to be among them. A few lottery tickets do win, owned by ordinary people who are perfectly capable of correctly believing that they have won. Everyone should be smart enough to collect on a winning ticket, and to grapple with living in interesting (i.e. low-probability) times. Just update already. It is false. This is base reality. But I can still appreciate Eliezer's fiction on the subject. The absurdity heuristic. I don't take BBs seriously. Even in classical physics there is no observation without interaction. Beyond that, no, however many quantum physicists interpret their findings to the public with those words, or even to each other. Not that I know of. (This is not the same as a flat "no", but for most purposes rounds off to that.) Either nothing in the case of x-risk, nothing of interest in the case of a final singleton, or wonders far beyond our contemplation, which may not even involve anything we would recognise as "computing". By definition, I can't say what that would be like, beyond guessing that at some point in the future it would stand in a similar relation to the present that our present does to prehistoric times. Look around you. Is this utopia? Then that future won't be either. But like the present, it will be worth having got to. Consider a suitable version of The Agnostic Prayer inserted here against the possibility that there are Powers Outside the Matrix who may chance to see this. Hey there! I wouldn't say no to having all the aches and pains of this body fixed, for starters. Radical uplift, we'd have to talk about first.

[-]Alexander Gietelink Oldenziel5d30

Does internal bargaining and geometric rationality explain ADHD & OCD?

Self- Rituals as Schelling loci for Self-control and OCD

Why do people engage in non-social Rituals 'self-rituals'? These are very common and can even become pathological (OCD).

High-self control people seem to more often have OCD-like symptoms.

One way to think about self-control is as a form of internal bargaining between internal subagents. From this perspective, Self-control, time-discounting can be seen as a resource. In the absence of self-control the superagent
D... (read more)

[-]quetzal_rainbow5d125

I feel like the whole "subagent" framework suffers from homunculus problem: we fail to explain behavior using the abstraction of coherent agent, so we move to the abstraction of multiple coherent agents, and while it can be useful, I don't think it displays actual mechanistic truth about minds.

When I plan something and then fail to execute plan it's mostly not like "failure to bargain". It's just when I plan something I usually have good consequences of plan in my imagination and this consequences make me excited and then I start plan execution and get hit by multiple unpleasant details of reality. Coherent structure emerges from multiple not-really-agentic pieces.

2Alexander Gietelink Oldenziel5d

You are taking subagents too literally here. If you prefer take another word like shard, fragment, component, context-dependent action impulse generator etc

2quetzal_rainbow5d

When I read word "bargaining" I assume that we are talking about entities that have preferences, action set, have beliefs about relations between actions and preferences and exchange information (modulo acausal interaction) with other entities of the same composition. Like, Kelly betting is good because it equals to Nash bargaining between versions of yourself from inside different outcomes and this is good because we assume that you in different outcomes are, actually, agent with all arrtibutes of agentic system. Saying "systems consist of parts, this parts interact and sometimes result is a horrific incoherent mess" is true, but doesn't convey much of useful information.

[-]Alexander Gietelink Oldenziel4mo31

(conversation with Scott Garrabrant)

Destructive Criticism

Sometimes you can say something isn't quite right but you can't provide an alternative.

rejecting the null hypothesis
give a (partial) countermodel that shows that certain proof methods can't prove $A$ without proving $\neg A$.
Looking at Scott Garrabrant's game of life board - it's not white noise but I can't say why

Difference between 'generation of ideas' and 'filtration of ideas' - i.e. babble and prune.

ScottG: Bayesian learning assumes we are in a babble-rich environment and only does pr... (read more)

[-]Alexander Gietelink Oldenziel6mo3-3

Reasonable interpretations of Recursive Self Improvement are either trivial, tautological or false?

(Trivial) AIs will do RSI by using more hardware - trivial form of RSI
(Tautological) Humans engage in a form of (R)SI when they engage in meta-cognition. i.e. therapy is plausibly a form of metacognition. Meta-cognition is plausible one of the remaining hallmarks of true general intelligence. See Vanessa Kosoy's "Meta-Cognitive Agents".
In this view, AGIs will naturally engage in meta-cognition because they're generally intelligent. The

... (read more)

3Vladimir_Nesov6mo

SGD finds algorithms. Before the DL revolution, science studied such algorithms. Now, the algorithms become inference without as much as a second glance. With sufficient abundance of general intelligence brought about by AGI, interpretability might get a lot out of studying the circuits SGD discovers. Once understood, the algorithms could be put to more efficient use, instead of remaining implicit in neural nets and used for thinking together with all the noise that remains from the search.

2Michaël Trazzi6mo

I think most interpretations of RSI aren't useful. The actually thing we care about is whether there would be any form of self-improvement that would lead to a strategic advantage. The fact that something would "recursively" self-improve 12 times or 2 times don't really change what we care about. With respect to your 3 points. 1) could happen by using more hardware, but better optimization of current hardware / better architecture is the actually scary part (which could lead to the discovery of "new physics" that could enable an escape even if the sandbox was good enough for the model before a few iterations of the RSI). 2) I don't think what you're talking about in terms of meta-cognition is relevant to the main problem. Being able to look at your own hardware or source code is though. 3) Cf. what I said at the beginning. The actual "limit" is I believe much higher than the strategic advantage threshold.

2niplav6mo

:insightful reaction: I give this view ~20%: There's so much more info in some datapoints (curvature, third derivative of the function, momentum, see also Empirical Bayes-like SGD, the entire past trajectory through the space) that seems so available and exploitable!

2acertain6mo

What about specialized algorithms for problems (e.g. planning algorithms)?

2Alexander Gietelink Oldenziel6mo

What do you mean exactly? There are definitely domains in which humans have not yet come close to optimal algorithms.

2Thomas Kwa6mo

What about automated architecture search?

2Alexander Gietelink Oldenziel6mo

Architectures mostly don't seem to matter, see 3. When they do (like in Vanessa's meta-MDPs) I think it's plausible automated architecture search is a simply an instantiation of the algorithm for general intelligence (see 2.)

1lukehmiles6mo

I think the AI will improve (itself) via better hardware and algorithms, and it will be a slog. The AI will frequently need to do narrow tasks where the general algorithm is very inefficient.

2Alexander Gietelink Oldenziel6mo

As I state in the OP I don't feel these examples are nontrivial examples of RSI.

[-]Alexander Gietelink Oldenziel7mo30

Trivial but important

Aumann agreement can fail for purely epistemic reasons because real-world minds do not do Bayesian updating. Bayesian updating is intractable so realistic minds sample from the prior. This is how e.g. gradient descent works and also how human minds work.

In this situation a two minds can end in two different basins with similar loss on the data. Because of computational limitations. These minds can have genuinely different expectation for generalization.

(Of course this does not contradict the statement of the theorem which is correct.)

[-]Alexander Gietelink Oldenziel8mo30

Imprecise Information theory

Would like a notion of entropy for credal sets. Diffractor suggests the following:

let $C \subset C r e d a l (Ω)$ be a credal set.

Then the entropy of $C$ is defined as

$HDiffractor(C)=suppH(p)$

where $H (p)$ denotes the usual Shannon entropy.

I don't like this since it doesn't satisfy the natural desiderata below.

Instead, I suggest the following. Let $m e_{C} \in C$ denote the (absolute) maximum entropy distribution, i.e. $H (m e_{C}) = m a x_{p \in C} H (p)$ and let $H (C) = H_{n e w} (C) = H (m e_{c})$ .

Desideratum 1: $H ({p}$ ... (read more)

[-]Alexander Gietelink Oldenziel1y33

Roko's basilisk is a thought experiment which states that an otherwise benevolent artificial superintelligence (AI) in the future would be incentivized to create a virtual reality simulation to torture anyone who knew of its potential existence but did not directly contribute to its advancement or development.

Why Roko's basilisk probably doesn't work for simulation fidelity reasons:

Roko's basilisk threatens to simulate and torture you in the future if you don't comply. Simulation cycles cost resources. Instead of following through on torturing our wo... (read more)

2Vladimir_Nesov1y

If the agents follow simple principles, it's simple to simulate those principles with high fidelity, without simulating each other in all detail. The obvious guide to the principles that enable acausal coordination is common knowledge of each other, which could be turned into a shared agent that adjudicates a bargain on their behalf.

1Richard_Kennaway1y

I have always taken Roko's Basilisk to be the threat that the future intelligence will torture you, not a simulation, for not having devoted yourself to creating it.

1TAG1y

How do you know you are not in a low fidelity simulation right now? What could you compare it against?

[-]Alexander Gietelink Oldenziel5d20

Four levels of information theory

There are four levels of information theory.

Level 1: Number Entropy

Information is measured by Shannon entropy

$H (X) = \sum_{i} p (X = x_{i}) log p (X = x_{i})$

Level 2: Random variable

look at the underlying random variable ('surprisal') $log p (X = x_{i})$ of which entropy is the expectation.

Level 3: Coding functions

Shannon's source coding theorem says entropy of a source $X$ is the expected number of bits for an optimal encoding of samples of $X$ .

Related quantity like mutual information, relative entropy, cross e... (read more)

[-]Alexander Gietelink Oldenziel4mo21

All concepts can be learnt. All things worth knowing may be grasped. Eventually.

All can be understood - given enough time and effort.

For Turing-complete organism, there is no qualitive gap between knowledge and ignorance.

No qualitive gap but one. The true qualitative difference: quantity.

Often we simply miss a piece of data. The gap is too large - we jump and never reach the other side. A friendly hominid who has trodden the path before can share their journey. Once we know the road, there is no mystery. Only effort and time. Some hominids choose not to share their journey. We keep a special name for these singular hominids: genius.

4Viliam4mo

Well, that's exactly the problem.

[-]Alexander Gietelink Oldenziel5mo20

Abnormalised sampling?
Probability theory talks about sampling for probability distributions, i.e. normalized measures. However, non-normalized measures abound: weighted automata, infra-stuff, uniform priors on noncompact spaces, wealth in logical-inductor esque math, quantum stuff?? etc.

Most of probability theory constructions go through just for arbitrary measures, doesn't need the normalization assumption. Except, crucially, sampling.

What does it even mean to sample from a non-normalized measure? What is ~~unnormalized~~ abnormal sampling?

I don't know.... (read more)

[-]Alexander Gietelink Oldenziel7mo20

SLT and phase transitions

The morphogenetic SLT story says that during training the Bayesian posterior concentrates around a series of subspaces $W_{0} (1) ⇝ . . . ⇝ W_{0} (n)$ with rlcts $λ_{1} < . . . < λ_{n}$ and losses $L_{1} = L (w_{1}), . . ., L_{n} = L (w_{n}), w_{i} \in W_{0} (i)$ . As the size of the data sample $N$ is scaled the Bayesian posterior makes transitions $W_{0} (i) ⇝ W_{0} (i + 1)$ trading off higher complexity (higher $λ_{i + 1} > λ_{i}$ ) for better accuracy (lower loss $L_{i + 1} < L_{i}$ ).

This is the radical new framework of SLT: phase transitions happen i... (read more)

[-]Alexander Gietelink Oldenziel7mo24

Alignment by Simulation?

I've heard this alignment plan that is a variation of 'simulate top alignment researchers' with an LLM. Usually the poor alignment researcher in question is Paul.

This strikes me as deeply unserious and I am confused why it is having so much traction.

That AI-assisted alignment is coming (indeed, is already here!) is undeniable. But even somewhat accurately simulating a human from textdata is a crazy sci-fi ability, probably not even physically possible. It seems to ascribe nearly magical abilities to LLMs.

Predicting... (read more)

[-]Alexander Gietelink Oldenziel7mo20

Optimal Forward-chaining versus backward-chaining.

In general, this is going to depend on the domain. In environments for which we have many expert samples and there are many existing techniques backward-chaining is key. (i.e. deploying resources & applying best practices in business & industrial contexts)

In open-ended environments such as those arising Science, especially pre-paradigmatic fields backward-chaining and explicit plans breakdown quickly.

Incremental vs Cumulative

Incremental: 90% forward chaining 10% backward chaining f... (read more)

[-]Alexander Gietelink Oldenziel8mo20

Thin versus Thick Thinking

Thick: aggregate many noisy sources to make a sequential series of actions in mildly related environments, model-free RL

carnal sins: failure of prioritization / not throwing away enough information , nerdsnipes, insufficient aggegration, trusting too much in any particular model, indecisiveness, overfitting on noise, ignoring consensus of experts/ social reality

default of the ancestral environment

CEOs, general, doctors, economist, police detective in the real world, trader

Thin: precise, systematic analysis, preferably ... (read more)

[-]Alexander Gietelink Oldenziel8mo20

[Thanks to Vlad Firoiu for helping me]

An Attempted Derivation of the Lindy Effect
Wikipedia:

The Lindy effect (also known as Lindy's Law^[1]) is a theorized phenomenon by which the future life expectancy of some non-perishable things, like a technology or an idea, is proportional to their current age.

Laplace Rule of Succesion

What is the probability that the Sun will rise tomorrow, given that is has risen every day for 5000 years?

Let $p$ denote the probability that the Sun will rise tomorrow. A priori we have no information on the value of&... (read more)

2JBlack8mo

I haven't checked the derivation in detail, but the final result is correct. If you have a random family of geometric distributions, and the density around zero of the decay rates doesn't go to zero, then the expected lifetime is infinite. All of the quantiles (e.g. median or 99%-ile) are still finite though, and do depend upon n in a reasonable way.

[-]Alexander Gietelink Oldenziel9mo20

Generalized Jeffrey Prior for singular models?

For singular models the Jeffrey Prior is not well-behaved for the simple fact that it will be zero at minima of the loss function.
Does this mean the Jeffrey prior is only of interest in regular models? I beg to differ.

Usually the Jeffrey prior is derived as parameterization invariant prior. There is another way of thinking about the Jeffrey prior as arising from an 'indistinguishability prior'.

The argument is delightfully simple: given two weights $w_{1}, w_{2} \in W$ if they encode the same distributi... (read more)

1Daniel Murfet5mo

You might reconstruct your sacred Jeffries prior with a more refined notion of model identity, which incorporates derivatives (jets on the geometric/statistical side and more of the algorithm behind the model on the logical side).

2Alexander Gietelink Oldenziel4mo

Is this the jet prior I've been hearing about? I argued above that given two weights w1,w2 such that they have (approximately) the same conditional distribution p(x|y,w1)∼=p(x|y,w2) the 'natural' or 'canonical' prior should assign them equal prior weights ϕ(w1)=ϕ(w2). A more sophisticated version of this idea is used to argue for the Jeffrey prior as a canonical prior. Some further thoughts: * imposing this uniformity condition would actually contradict some version of Occam's razor. Indeed, w1 could be algorithmically much more complex (i.e. have much higher description length) than w2 but they still might have similar or the same predictions. * The difference between same-on-the-nose versus similar might be very material. Two conditional probability distributions might be quite similar [a related issue here is that the KL-divergence is assymetric so similarity is a somewhat ill-defined concept], yet one intrinsically requires far more computational resources. * A very simple example is the uniform distribution puniform(x)=1N and another distribution p′(x) that is a small perturbation of the uniform distribution but whose exact probabilities p′(x) have decimal expansions that have very large description length (this can be produced by adding long random strings to the binary expansion). * [caution: CompMech propaganda incoming] More realistic examples do occur i.e. in finding optimal predictors of dynamical systems at the edge of chaos. See the section on 'intrinsic computation of the period-doubling cascade', p.27-28 of calculi of emergence for a classical example. * Asking for the prior ϕ to restrict to be uniform for weights wi that have equal/similar conditional distributions p(x|y,wi) seems very natural but it doesn't specify how the prior should relate weights with different conditional distributions. Let's say we have two weights w1, w2 with very different conditional probability distributions. Let Wi={w∈W|p(x|y,w)∼=p(x|y,wi)}. How sh

1Daniel Murfet4mo

I think there's no such thing as parameters, just processes that produce better and better approximations to parameters, and the only "real" measures of complexity have to do with the invariants that determine the costs of those processes, which in statistical learning theory are primarily geometric (somewhat tautologically, since the process of approximation is essentially a process of probing the geometry of the governing potential near the parameter). From that point of view trying to conflate parameters w1,w2 such that p(x|w1)≈p(x|w2) is naive, because w1,w2 aren't real, only processes that produce better approximations to them are real, and so the ∂∂w derivatives of p(x|w1),p(x|w2) which control such processes are deeply important, and those could be quite different despite p(x|w1)≈p(x|w2) being quite similar. So I view "local geometry matters" and "the real thing are processes approximating parameters, not parameters" as basically synonymous.

[-]Alexander Gietelink Oldenziel1y20

"The links between logic and games go back a long way. If one thinks of a debate as a kind of game, then Aristotle already made the connection; his writings about syllogism are closely intertwined with his study of the aims and rules of debating. Aristotle’s viewpoint survived into the common medieval name for logic: dialectics. In the mid twentieth century Charles Hamblin revived the link between dialogue and the rules of sound reasoning, soon after Paul Lorenzen had connected dialogue to constructive foundations of logic." from the Stanford Encyclopedia ... (read more)

[-]Alexander Gietelink Oldenziel1y20

Ambiguous Counterfactuals

[Thanks to Matthias Georg Mayer for pointing me towards ambiguous counterfactuals]

Salary is a function of eXperience and Education

$S = a E + b X$

We have a candidate $C$ with given salary, experience $(X = 5)$ and education $(E = 5)$ .

Their current salary is given by

$S = a \cdot 5 + b \cdot 5$

We 'd like to consider the counterfactual where they didn't have the education $(E = 0)$ . How do we evaluate their salary in this counterfactual?

This is slightly ambiguous - there are two counterfactuals:

$E = 0, X = 5$ or $E = 0, X = 10$

In the second c... (read more)

[-]Alexander Gietelink Oldenziel1y20

Insights as Islands of Abductive Percolation?

I've been fascinated by this beautiful paper by Viteri & DeDeo.

What is a mathematical insight? We feel intuitively that proving a difficult theorem requires discovering one or more key insights. Before we get into what the Dedeo-Viteri paper has to say about (mathematical) insights let me recall some basic observations on the nature of insights:

(see also my previous shortform)

There might be a unique decomposition, akin to prime factorization. Alternatively, there might many roads to Rome: some theorems

... (read more)

Evidence Manipulation and Legal Admissible Evidence

[This was inspired by Kokotaljo's shortform on comparing strong with weak evidence]

In the real world the weight of many pieces of weak evidence is not always comparable to a single piece of strong evidence. The important variable here is not strong versus weak per se but the source of the evidence. Some sources of evidence are easier to manipulate in various ways. Evidence manipulation, either consciously or emergently, is common and a large obstactle to truth-finding.

Consider aggregating many ... (read more)

2ChristianKl1y

In other cases like medicine, many people argue that direct observation should be ignored ;)

Imagine a data stream

$. . . X_{- 3}, X_{- 2}, X_{- 1}, X_{0}, X_{1}, X_{2}, X_{3} . . .$

assumed infinite in both directions for simplicity. Here $X_{0}$ represents the current state ( the "present") and while $. . . X_{- 3}, X_{- 2}, X_{- 1}$ and $X_{1}, X_{2}, X_{3}, . . .$ represents the future

Predictible Information versus Predictive Information

Predictible information is the maximal information (in bits) that you can derive about the future given the access to the past. Predictive information is the amount of bits that you need from the past to make that optimal prediction.

Suppose you are... (read more)

Agent Foundations Reading List [Living Document]
This is a stub for a living document on a reading list for Agent Foundations.

Causality

Book of Why, Causality - Pearl

Probability theory
Logic of Science - Jaynes