## Posts

Is there software for goal factoring? 2020-02-18T19:55:37.764Z · score: 4 (1 votes)
Hard Problems in Cryptocurrency: Five Years Later - Buterin 2019-11-24T09:38:20.045Z · score: 19 (6 votes)
crabman's Shortform 2019-09-14T12:30:37.482Z · score: 3 (1 votes)
Reneging prosocially by Duncan Sabien 2019-06-18T18:52:46.501Z · score: 59 (16 votes)
How to determine if my sympathetic or my parasympathetic nervous system is currently dominant? 2019-05-31T20:40:30.664Z · score: 20 (8 votes)
AI Safety Prerequisites Course: Revamp and New Lessons 2019-02-03T21:04:16.213Z · score: 33 (11 votes)
Fundamentals of Formalisation Level 7: Equivalence Relations and Orderings 2018-08-10T15:12:46.683Z · score: 9 (3 votes)
Fundamentals of Formalisation Level 6: Turing Machines and the Halting Problem 2018-07-23T09:46:42.076Z · score: 11 (4 votes)
Fundamentals of Formalisation Level 5: Formal Proof 2018-07-09T20:55:04.617Z · score: 15 (3 votes)
Fundamentals of Formalisation Level 4: Formal Semantics Basics 2018-06-16T19:09:16.042Z · score: 15 (3 votes)
Fundamentals of Formalisation Level 3: Set Theoretic Relations and Enumerability 2018-06-09T19:57:20.878Z · score: 20 (5 votes)
Idea: OpenAI Gym environments where the AI is a part of the environment 2018-04-12T22:28:20.758Z · score: 10 (3 votes)

Comment by crabman on crabman's Shortform · 2020-02-26T17:37:44.648Z · score: 1 (1 votes) · LW · GW

A new piece of math notation I've invented which I plan to use whenever I am writing proofs for myself (rather than for other people).

Sometimes when writing a proof, for some long property P(x) I want to write:

It follows from foo, that there exists x such that P(x). Let x be such that P(x). Then ...

I don't like that I need to write P(x) twice here. And the whole construction is too long for my liking, especially when the reason foo why such x exists is obvious. And if I omit the first sentence It follows from foo, that there exists x such that P(x). and just write

Let x be such that P(x). Then ...

then it's not clear what I mean. It could be that I want to show that such x exists and that from its existence some statement of interest follows. Or it could be that I want to prove some statement of form

For each x such that P(x), it holds that Q(x).

Or it could even be that I want to show that something follows from existence of such x, but I am not asserting that such x exists.

The new notation I came up with is to write L∃t in cases when I want to assert that such x exists and to bound the variable x in the same place. An example (an excerpt, not a complete proof):

• Suppose is a countably infinite set, suppose is a set of subsets of , suppose .
• L∃t be a bijection from onto .
• L∃t such that , if is in , otherwise .
• By recursion theorem, L∃t be such that , .
• L∃t .
• ...
Comment by crabman on Rationalist prepper thread · 2020-01-29T15:39:21.247Z · score: 2 (2 votes) · LW · GW

That's why I multiplied it by 10.

Comment by crabman on Rationalist prepper thread · 2020-01-28T22:23:30.826Z · score: 12 (6 votes) · LW · GW

I've done a very rough fermi estimate (I even pull some numbers out of my ass), according to which I don't need to worry. The probability of me dying due to ncov 2019 is

• Here is my expected number of infected people, which I got by looking at median according to metaculus, which is 311k, and multiplying it by 10 (a number I pulled out of my ass), since I think the probability density function of the probability distribution of the number of infections is mostly convex. is Earth population.
• is the probability of a random person dying if given that they were infected - I got this number by seeing on EA forum a comment that said 3% of identified ncov 2019 cases die, and that probably many infected people haven't been identified but most deaths have, so I decreased it to 1% (another number out of my ass).
• - I multiply the probability by 4 for myself since I live in a dense city, and my girlfriend works in a large office with a lot of people. (another number out of my ass)
• - since mostly old people die, with another number pulling I decrease my probability of dying by 5.
• - my immune system seems weaker than average, since I often get common cold.

In total I get approximately 6 micromort, which is really low - on average I probably get about 25 micromort per day according to wikipedia.

Comment by crabman on How to Throw Away Information in Causal DAGs · 2020-01-08T11:03:49.611Z · score: 4 (3 votes) · LW · GW

Instead of saying " contains all information in relevant to ", it would be better to say that, contains all information in that is relevant to if you don't condition on anything. Because it may be the case that if you condition on some additional random variable , no longer contains all relevant information.

Example:

Let be i.i.d. binary uniform random variables, i.e. each of the variables takes the value 0 with probability 0.5 and the value 1 with probability 0.5. Let be a random variable. Let be another random variable, where is the xor operation. Let be the function .

Then contains all information in that is relevant to . But if we know the value of , then no longer contains all information in that is relevant to .

Comment by crabman on ozziegooen's Shortform · 2019-12-23T10:30:47.864Z · score: 5 (4 votes) · LW · GW

It's definitely the first. The second is bizarre. The third can be steelmanned as "Given my evidence, an ideal thinker would estimate the probability to be 20%, and we all here have approximately the same evidence, so we all should have 20% probabilities", which is almost the same as the first.

Comment by crabman on Understanding Machine Learning (I) · 2019-12-23T10:22:47.045Z · score: 4 (3 votes) · LW · GW

Two nitpicks:

like if you want it to recognize spam emails, but you only show it aspects of the emails such that there is at best a statistically weak correlation between them and whether the email is spam or not-spam

Here "statistically weak correlation" should be "not a lot of mutual information", since correlation is only about linear dependence between random variables.

i.d.d.

Should be i.i.d.

Comment by crabman on [Personal Experiment] One Year without Junk Media · 2019-12-15T16:36:06.094Z · score: 1 (1 votes) · LW · GW

Comment by crabman on crabman's Shortform · 2019-11-20T17:36:43.972Z · score: 6 (3 votes) · LW · GW

In my understanding, here are the main features of deep convolutional neural networks (DCNN) that make them work really well. (Disclaimer: I am not a specialist in CNNs, I have done one masters level deep learning course, and I have worked on accelerating DCNNs for 3 months.) For each feature, I give my probability, that having this feature is an important component of DCNN success, compared to having this feature to the extent that an average non-DCNN machine learning model has it (e.g. DCNN has weight sharing, an average model doesn't have weight sharing).

1. DCNNs heavily use transformations, which are the same for each window of the input - 95%
2. For any set of pixels of the input, large distances between pixels in the set make the DCNN model interactions between these pixels less accurately - 90% (perhaps usage of dilution in some DCNNs is a counterargument to this)
3. Large depth (together with the use of activation functions) lets us model complicated features, interactions, logic - 82%
4. Having a lot of parameters lets us model complicated features, interactions, logic - 60%
5. Given 3 and 4, SGD-like optimization works unexpectedly fast for some reason - 40%
6. Given 3 and 4, SGD-like optimization with early stopping doesn't overfit too much for some reason - 87% (I am not sure if S in SGD is important, and how important is early stopping)
7. Given 3 and 4, ReLu-like activation function works really well (compared to, for example, sigmoid).
8. Modern deep neural network libraries are easy to use compared to the baseline of not having specific well-developed libraries - 60%
9. Deep neural networks work really fast, when using modern deep neural network libraries and modern hardware - 33%
10. DCNNs find such features in photos, which are invisible to the human eye and to most ML algorithms - 20%
11. Dropout helps reducing overfitting a lot - 25%
12. Batch normalization improve quality of the model a lot for some reason - 15%
13. Batch normalization makes the optimization much faster - 32%
14. Skip connections (or residual connections, I am not sure if there's a difference) help a lot - 20%

Let me make it more clear how I was assigning the probabilities and why I created this list. I am trying to come up with a tensor network based machine learning model, which would have the main advantages of DCNNs, but which would not, itself, be a deep relu neural network. So I decided to make this list to see which important components my model has.

Comment by crabman on cousin_it's Shortform · 2019-10-27T12:26:26.044Z · score: 1 (1 votes) · LW · GW

Would it be correct to say that (2) and (3) can be replaced with just "apply any linear operator"?

Also, what advantages does working with amplitudes have compared to working with probabilities? Why don't we just use probability theory?

Comment by crabman on Raemon's Scratchpad · 2019-10-21T11:51:12.249Z · score: 1 (1 votes) · LW · GW

Talk to your roommates and make an agreement, that each of you, in round robin order, orders apartment cleaning service, with period equal to X weeks. This will alleviate part of the problem.

Comment by crabman on What's going on with "provability"? · 2019-10-13T15:39:51.573Z · score: 3 (2 votes) · LW · GW

So it is perfectly okay to have a statement that is obviously true, but still cannot be proved using some set of axioms and rules.

The underlying reason is that if you imagine a Platonic realm where all abstractions allegedly exist, the problem is that there are actually multiple abstractions ["models"] compatible with ZF, but different from each other in many important ways.

So, when you say Godel's sentence is obviously true, in which "abstraction" is it true?

Comment by crabman on What funding sources exist for technical AI safety research? · 2019-10-01T16:43:46.069Z · score: 1 (1 votes) · LW · GW

Are you interested in AI safety jobs, i.e. to be hired by a company and work in their office?

Comment by crabman on The first step of rationality · 2019-09-30T21:45:31.005Z · score: 2 (2 votes) · LW · GW

The article's title is misleading. He didn't harass or rape anyone. He had sex with prostitutes and hid that from his wife.

Comment by crabman on The Zettelkasten Method · 2019-09-30T10:24:30.417Z · score: 3 (2 votes) · LW · GW

When you go outside, how do you choose decks to take with you?

Small cards seem awful for writing sequences of transformations of large equations - do you sometimes do things like that and if yes then do you do that outside of Zettelkasten?

When developing an idea I use paper as an expansion of my working memory, so it becomes full of things which become useless right after I finish. Do you throw away such "working memory dumps" and only save actually useful pieces of knowledge?

Comment by crabman on Idols of the Mind Pt. 1 (Novum Organum Book 1: 38–52) · 2019-09-28T10:15:48.874Z · score: 1 (1 votes) · LW · GW

This mischief insinuates itself more subtly into philosophy and the sciences: there, when a proposition has found favour it colours other propositions and brings them into line with itself, even when they ·in their undisguised form· are sounder and better than it is.

A kinda example of this: the idea of minimum description length and solomonoff induction colours Occam's razor. But I wouldn't say that Occam's razor in its original form is better.

Comment by crabman on crabman's Shortform · 2019-09-26T18:29:26.959Z · score: 10 (4 votes) · LW · GW

In my MSc courses the lecturer gives proofs of important theorems, while unimportant problems are given as homework. This is bad for me, because it makes me focus on actually figuring out not too important stuff. I think it works like this because the course instructors want to • make the student do at least something and • check whether the student has learned the course material.

Ideally I would like to study using interactive textbooks where everything is a problem to solve on my own. Such a textbook wouldn't show an important theorem's proof right away. Instead it would show me the theorem's statement and ask me to prove it. There should be hints available and, obviously, I should be able to see the author's proof when I want to see it.

Also, for textbooks about Turing machines, recursive functions, and stuff like that: having an interpreter of Turing machines would be very nice. (googling Turing machine interpreter and using whatever you find is a bad idea, because they all have different flavors)

Comment by crabman on NaiveTortoise's Short Form Feed · 2019-09-23T20:57:39.312Z · score: 1 (1 votes) · LW · GW

Unfortunately I don't know any quantum stuff. I learned them for machine learning purposes.

A monograph by Cichocki et al. (part 1, part 2) is an overview of how tensor decompositions, tensor formats, and tensor networks can be used in machine learning and signal processing. I think it lacks some applications, including acceleration and compression of neural networks by compression of weights of layers using tensor decompositions (this also sometimes improves accuracy, probably by reducing overfit).

Tensor decompositions and Applications by Kolda, Bader 2009 - this is an overview of tensor decompositions. It doesn't have many machine learning applications. Also it doesn't talk of tensor networks, only about some simplest tensor decompositions and specific tensor formats which are the most popular types of tensor networks. This paper was the first thing I read about all the tensor stuff, and it's one of the easier things to read. I recommend you read it first and then look at the topics that seem interesting to you in Cichocki et al.

Tensor spaces and numerical tensor calculus - Hackbusch 2012 - this textbook covers mathematics of tensor formats and tensor decompositions for hilbert and banach spaces. No applications, a lot of math, functions analysis is kinda a prerequisite. Very dense and difficult to read textbook. Also doesn't talk of tensor networks, only about specific tensor formats.

Handwaving and interpretive dance - This is simple, it's about tensor networks, not other tensor stuff. It's for physicists but chapter 1 and maybe other chapters can be read without physics background.

Regarding the TensorNetwork library. I've skim-read it. I haven't tried using it. I think it's in early alpha or something. How usable it is for me depends on how well it can interact with pytorch and how easy it is to do autodifferentiation w.r.t. core tensors and use the tensor network in a pytorch model. Intuitively the API seemed nice. I think their idea is to that you take a tensor, make it into a matrix, do truncated svd, now you have 2 matrices, turn them back to tensors. Now you do the same for them. This way you can perform some but not all popular tensor decomposition algorithms.

P.S. Fel free to message me if you have questions about tensor decomposition/network/formats stuff

Comment by crabman on NaiveTortoise's Short Form Feed · 2019-09-23T18:08:23.164Z · score: 1 (1 votes) · LW · GW

I've been studying tensor decompositions and approximate tensor formats for half a year. Since I've learned about tensor networks, I've noticed that I can draw them to figure out how to code some linear operations on tensors.

Once I used this to figure out how to implement backward method of some simple neural network layer (not something novel, it was for the sake of learning how deep learning frameworks work). Another time I needed to figure out how to implement forward method for a Conv2d layer with weights tensor in CP format. After drawing its output as a tensor network diagram, it was clear that I could just do a sequence of 3 Conv2d layers: pointwise, depthwise, pointwise.

I am not saying that you should learn tensor networks, it's probably a lot of buck for not too large bang unless you want to work with tensor decompositions and formats.

Comment by crabman on The Inadequacy of Current Science (Novum Organum Book 1: 1-37) · 2019-09-23T18:01:43.202Z · score: 4 (3 votes) · LW · GW

Bacon seems to dislike "logic" and "dialectics". Why? Isn't logic the best thing ever? And what did 17th century european intellectuals mean by these words? After 10 minutes of googling I still don't understand that.

The preface says

[Bacon’s dialectica, sometimes translated as ‘logic’, refers more narrowly to the formalized and rule-governed use of logic, especially in debates.]

but this post also says

[[Reminder that ‘dialectics’ is Bacon’s term for logic.]]

dialectic is a form of reasoning based upon dialogue of arguments and counter-arguments, advocating propositions (theses) and counter-propositions (antitheses). The outcome of such a dialectic might be the refutation of a relevant proposition, or of a synthesis, or a combination of the opposing assertions, or a qualitative improvement of the dialogue.

So, (epistemic status: this is my best guess, probably at least a part of it is wrong) I imagine 17th century european intellectuals were fond of using sentential logic and maybe quantified logic when arguing with each other, and maybe they liked the notion of counterarguments and they liked thinking of propositions as proved or disproved (or not enough info for either), but didn't understand different degrees of certainty. And perhaps Bacon disliked this rigidity.

Comment by crabman on Novum Organum: Preface · 2019-09-21T14:00:03.737Z · score: 5 (3 votes) · LW · GW

retain ·the evidence of· the senses subject to certain constraints

If you are led •by the evidence of your senses

What does Francis mean by "the evidence of senses" here?

The passage that says it's madness to do intellectual work without tools, I am not sure if I understand what those tools are. I guess they are something like principles of empiricism and rationality. If Francis looked at the state of science in different time points between the time he wrote the book and now, would he say that scientists mostly used the tools? Because it seems science is in an ok shape now.

I think the book's title "The new organon" is bailey, and the passage about not wanting rivalry with ancient philosophers is motte.

Comment by crabman on crabman's Shortform · 2019-09-15T19:25:15.701Z · score: 1 (1 votes) · LW · GW

Many biohacking guides suggest using melatonin. Does liquid melatonin spoil under high temperature if put in tea (95 degree Celcius)?

More general question: how do I even find answers to questions like this one?

Comment by crabman on crabman's Shortform · 2019-09-14T12:30:37.731Z · score: 15 (4 votes) · LW · GW

A competition on solving math problems via AI is coming. https://imo-grand-challenge.github.io/

• The problems are from the International math olympiad (IMO)
• They want to formalize all the problems in Lean (theorem prover) language. They haven't figured out how to do that, e.g. how to formalize problems of form "determine the set of objects satisfying the given property", as can be seen in https://github.com/IMO-grand-challenge/formal-encoding/blob/master/design/determine.lean
• A contestant must submit a computer program that will take a problem's description as input and output a solution and its proof in Lean.

I would guess that this is partly a way to promote Lean. I think it would be interesting to pose questions about this on metaculus.

Comment by crabman on Free-to-Play Games: Three Key Trade-Offs · 2019-09-10T18:25:40.272Z · score: 3 (3 votes) · LW · GW

Where does Eternal, a game you seem to like, lie in the space of these tradeoffs?

Comment by crabman on Buck's Shortform · 2019-08-18T10:17:57.936Z · score: 11 (5 votes) · LW · GW

How do you spend time with the tutor? Whenever I tried studying with a tutor, it didn't seem more efficient than studying using a textbook. Also when I study on my own, I interleave reading new materials and doing the exercises, but with a tutor it would be wasteful to do exercises during the tutoring time.

Comment by crabman on Rethinking Batch Normalization · 2019-08-07T14:08:08.256Z · score: 1 (1 votes) · LW · GW

I want to clarify in what domain this theory of batch normalization holds.

The evidence we have is mostly about batch normalization in those types of feedforward neural networks that are often used in 2019, right? So, residual CNNs, VGG-like CNNs, other CNNs, transformers. Maybe other types of feedforward neural networks. But not RNNs.

Has anyone explored the applicability of batch normalization or similar techniques to non neural network functions which we optimize by gradient descent like algorithms? Perhaps to tensor networks?

Comment by crabman on AALWA: Ask any LessWronger anything · 2019-08-03T11:58:14.723Z · score: 1 (1 votes) · LW · GW

Hi. At http://www.weidai.com/everything.html you say:

Why do we believe that both the past and the future are not completely random, but the future is more random than the past?

I don't understand what you mean saying that the future is more random than the past. Care to explain?

Comment by crabman on Understanding Batch Normalization · 2019-08-01T22:27:53.242Z · score: 2 (2 votes) · LW · GW

How do we check empirically or otherwise whether this explanation of what batch normalization does is correct?

I am imagining this internal covariate shift thing like this: the neural network together with its loss is a function which takes parameters θ as input and outputs a real number. Large internal covariate shift means that if we choose ε>0, perform some SGD steps, get some θ, and look at the function's graph in ε-area of θ, it doesn't really look like a plane, it's more curvy like. And small internal covariate shift means that the function's graph is more like a plane. Hence gradient descent works better. Is this intuition correct?

Why does the internal covariate shift become less, even though we have μ and β terms?

About the example, it seems to me that the main problem here is that if a gradient descent step changes the sign of an even number of weights, then it might be that the step didn't really achieve anything. Can we fix it somehow? What if we make an optimizer that allows only 1 weight to change sign at each iteration? For actual neural networks allow only weights from one layer to change sign at any given step. Which layer to choose? The one where there are most components want to change sign. (I am not sure what to do about the fact that we use activation functions and biases)

Does batch normalization really cause the distribution of activations of a neuron be more like a Gaussian? Is that like an empirical observation of what happens when a neural network with batch normalization is optimized by an SGD-like optimizer?

P.S. I like the fact that you are posting about deep learning on LessWrong. Maybe there are many rationalists who practice machine learning but they are not sure if there are other people like that on LessWrong, so they don't post about it here?

Comment by crabman on Insights from Linear Algebra Done Right · 2019-07-14T19:22:49.628Z · score: 3 (2 votes) · LW · GW

Ok. It's just that when I learned that, we didn't even talk about dual spaces in linear algebraic sense, we worked just fine in .

Comment by crabman on Insights from Linear Algebra Done Right · 2019-07-14T18:59:19.663Z · score: 1 (1 votes) · LW · GW

Do you mean solving convex optimization problems by solving their dual problems instead?

Comment by crabman on Insights from Linear Algebra Done Right · 2019-07-14T18:42:50.106Z · score: 8 (3 votes) · LW · GW

I wonder, what do you think about the chapter about dual spaces, dual maps, annihilator, etc.? To me it seemed not too connected with everything else, and that's bad. If I remember correctly, the author uses duality just to prove a few results and then throws duality away and never uses it again. Also in real life (numerical linear algebra, machine learning, and stuff) I am not aware of any use for those concepts.

So for “general” operators, this is always true, but there do exist specific operators for which it isn’t.

I believe when mathematicians say that in general P(x) holds, they mean that for any x in the domain of interest P(x) holds. Perhaps you want to you typical instead of general here. E.g. there is a notion called typical tensor rank of tensors of given shape, which means a tensor rank which occurs with non-zero probability when a random tensor of given shape is sampled.

Comment by crabman on Everybody Knows · 2019-07-08T13:11:11.641Z · score: -5 (5 votes) · LW · GW

including 20% who think the Sun revolves around the Earth

The sun does revolve around the Earth. The sun revolving around the earth is equivalent to the Earth revolving around the sun.

Comment by crabman on What would be the signs of AI manhattan projects starting? Should a website be made watching for these signs? · 2019-07-06T13:05:48.605Z · score: 2 (2 votes) · LW · GW

Why the government? Perhaps a government?

Comment by crabman on Reneging prosocially by Duncan Sabien · 2019-06-19T04:17:01.397Z · score: -3 (3 votes) · LW · GW

If I loan you an item ostensibly for a month, and regret it, I will do significantly less damage asking you to return it in a week than asking you to return it immediately.

So, a good samaritan Alice gave her friend John an item for some time, then she realized she wants to use the item herself. It's already the case that only John is getting something out of this agreement, so why should Alice take on additional costs of waiting another week?

Edit: unless John actually gave Alice money for borrowing her item. IMO people should pay each other money for various acts that provide value much more often than the do.

Comment by crabman on And My Axiom! Insights from 'Computability and Logic' · 2019-05-10T17:29:22.982Z · score: 3 (2 votes) · LW · GW

It seems "Computability and Logic" doesn't include Kleene's recursion theorem and Rice's theorem. What sources would you recommend for learning those theorems, their proofs, and their corollaries? Also, which chapters of "Computability and Logic" are required to understand them?

Comment by crabman on AI Safety Prerequisites Course: Revamp and New Lessons · 2019-03-16T16:04:12.213Z · score: 1 (1 votes) · LW · GW

Comment by crabman on Embedded World-Models · 2019-03-16T00:52:02.095Z · score: 3 (2 votes) · LW · GW

I think this article is too vague, because for almost almost claims in it I am not sure if I understand the author correctly. Below I am posting my notes. If you want to help me and others clarify understanding of this article, consider answering questions in bold, or, if you see a mistake in my notes, correcting it. Also I hope my notes help the author as a piece of feedback. I've only finished 2/3 of the article so far, but posting notes because I might become less interested in this later.

Also it's unfortunate that unlike in https://intelligence.org/2018/11/02/embedded-models/ version of this article we don't have hyperlinks to explanations of various concepts here. Perhaps you could add them under the corresponding images? Or have images themselves be hyperlinks or reference links (like in academic articles) to the bottom of the document where all relevant links would be stored grouped by image number.

The post says an embedded agent can't hold an exact model of the environment in its head, can't think through the consequences of every potential course of action, can't hold in its head every possible way the environment could be. I think this may not be necessarily true and I am not sure what assumptions the author used here.

It seems the whole article assumes countable probability spaces (even before the AIXI part). I wonder why and I wonder how realizability is defined for uncountable probability space.

--

Regarding relative bounded loss and what this bound is for, my best guess is as follows. Here I use non-conditional probability notation instead of . Let be the elementary event that is actually true. Let "expert" be a (not necessarily elementary) event, such that . Then loss of the expert is . Loss of the prior is . For their difference it holds that .

Initially, is your initial trust in expert h, and in each case where it is even a little bit more correct than you, you increase your trust accordingly; the way you do this ensures you assign an expert probability 1 and hence copy it precisely before you lose more than compared to it.

Remember, . It follows that probability of h increases given evidence e if and only if , i.e. h "is even a little bit more correct than you". But I don't understand the bit about copying the expert h precisely before losing more than . If the expert is an event, how can you "copy" it?

Combining this with the previous idea about viewing Bayesian learning as a way of allocating “trust” to “experts” which meets a bounded loss condition, we can see the Solomonoff prior as a kind of ideal machine learning algorithm which can learn to act like any algorithm you might come up with, no matter how clever.

It is assuming all possible algorithms are computable, not that the world is.

I don't understand this. Our probability space is the cartesian product of the set of all possible UTM programs and the set of all possible UTM working tape initial configurations. Or, equivalently, the set of outputs of UTM under these conditions. Hence our whole hypothesis space only includes computable worlds. What does "can learn to act like any algorithm" mean here? "It's getting bounded loss on its predictive accuracy as compared with any computable predictor." Huh? Does predictor here mean expert h? If yes, what does it mean that h is computable and why? All in all, is the author claiming it's impossible to have a better computable predictor than AIXI with Solomonoff prior, even if it has non-computable worlds in the probability space?

probabilities may not be calibrated identification of causal structure may not work

What do these mean? I only know informally what calibration means related to forecasting.

So, does AIXI perform well without a realizability assumption?

How is AIXI even defined without realizability, i.e. when the actual world isn't in the probability space, or it has zero prior probability?

This is fine if the world “holds still” for us; but because the map is in the world, it may implement some function.

Is this about the world changing because of the agent just thinking? Or something else?

It should be noted, though, that there are additional barriers to getting this property in a game-theoretic setting; so in their common usage cases, "grain of truth" is technically demanding while "realizability" is a technical convenience.

...

In game theory, on the other hand, the assumption itself may be inconsistent. This is because games commonly yield paradoxes of self-reference.

From the former paragraph I don't understand anything except that (the author claims) game theory has more problems with grain of truth / realizability, than AIXI. After the latter paragraph, my best guess is: for any game, if there is no pure strategy equilibrium in it, then we say it has no grain of truth, because for every possible outcome rational agents wouldn't choose it.

If we put weight in both places until a proof rules one out, the beliefs just oscillate forever rather than doing anything useful.

Weights represent possible worlds, therefore they are on the scales right from the beginning (the prior), we never put new weights on the scales. My probably incorrect guess of what the author is saying is some agent which acts like AIXI but instead of updating on pieces of evidence as soon as he receives it, he stockpiles it, and at some points he (boundedly) searches for proofs that these pieces of evidence are in favor of some hypothesis and performs update only when he finds them. But still, why oscillation?

Any computable beliefs about logic must have left out something, since the tree will grow larger than any container.

I interpret it as there are infinitely many theorems, hence an agent with finite amount of space or finite amount of computation steps can't process all of them.

Another consequence of the fact that the world is bigger than you is that you need to be able to use high-level world models: models which involve things like tables and chairs.

This is related to the classical symbol grounding problem; but since we want a formal analysis which increases our trust in some system, the kind of model which interests us is somewhat different. This also relates to transparency and informed oversight: world-models should be made out of understandable parts.

No idea what the second quoted paragraph means.

All in all, I doubt that high level world models are necessary. And it's very not clear what is meant by "high level" or "things" here. Perhaps embedded agents can (boundedly) reason about the world in other ways, e.g. by modeling only part of the world.

https://intelligence.org/files/OntologicalCrises.pdf explains the ontological crisis idea better. Suppose our AIXI-like agent thinks the world is an elementary outcome of some parameterized probability distribution with the parameter θ. θ is either 1 or 2. We call the set of elementary outcomes with θ=1 the first ontology (e.g. possible worlds running on classical mechanics), and the set of elementary outcomes with θ=2 the second ontology (e.g. possible worlds running on superstrings theory). The programmer has only programmed the agent's utility functiom for θ=1 part, i.e. a u function from ontology 1 to real numbers. The agent keeps count of which value of θ is more probable and chooses actions by considering only current ontology. If at some point he decides that the second ontology is more useful, he switches to it. The agent should extrapolate the utility function to θ=2 part. How can he do it?

Comment by crabman on AI Safety Prerequisites Course: Revamp and New Lessons · 2019-02-06T11:13:45.569Z · score: 3 (2 votes) · LW · GW

maybe recent machine learning topics are a point of comparative advantage

Do you mean recent ML topics related to AI safety, or just recent ML topics?

RAISE is already working on the former, it's another course which we internally call "main track". Right now it has the following umbrella topics: Inverse Reinforcement Learning; Iterated Distillation and Amplification; Corrigibility. See https://www.aisafety.info/online-course

Comment by crabman on The 3 Books Technique for Learning a New Skilll · 2019-01-29T14:08:45.406Z · score: 1 (1 votes) · LW · GW

Is the point of your comment that you think people very rarely read (completely or almost completely) 3 books in one field?

(if yes, then I agree)

Comment by crabman on What are good ML/AI related prediction / calibration questions for 2019? · 2019-01-04T21:47:52.011Z · score: 1 (1 votes) · LW · GW

I find your predictions 1 through 3 not clearly defined.

Does OpenAI bot need to defeat a pro team in unconstrained dota 2 at least once during 2019? Or does it need to win at least one and more than 50% games against pro teams in 2019?

Suppose tesla releases a video footage or a report of their car reaching from one coast to the other, but it had some minor or not so minor problems. How minor should they be to count? Are humans allowed to help it recharge or anything like that?

How do you define "skilled" in SC II?

Comment by crabman on Good Samaritans in experiments · 2018-12-08T02:26:11.176Z · score: 1 (1 votes) · LW · GW

How did you conclude that people who prepared GS are actually more likely to help than other people? Just from eyeballing 10/19 and 6/21 I can't conclude that this is enough evidence, only that this is suggestive.

Comment by crabman on Current AI Safety Roles for Software Engineers · 2018-12-07T02:12:18.268Z · score: 4 (3 votes) · LW · GW

Could you please elaborate what kind of culture fit MIRI require?

Comment by crabman on The First Rung: Insights from 'Linear Algebra Done Right' · 2018-11-27T22:16:04.008Z · score: 1 (1 votes) · LW · GW

What is the point of spending a section on dual maps, I wonder? Is the sole purpose to show that row rank equals column rank, I wonder? If so, then a lot of my time spent on exercises on dual maps might be wasted.

Comment by crabman on Embedded Agents · 2018-11-01T00:16:09.791Z · score: 4 (3 votes) · LW · GW

Is this the first post in the sequence? It's not clear.

Comment by crabman on Things I Learned From Working With A Marketing Advisor · 2018-10-10T14:01:03.759Z · score: 4 (3 votes) · LW · GW

You say

Epistemic Status: Opinions stated without justification

but from the text it seems you believe that acting according to the described opinions is useful and that many of them are true. I don't like this, I think you should clarify epistemic status.

Comment by crabman on [Math] Towards Proof Writing as a Skill In Itself · 2018-06-19T08:38:45.491Z · score: 2 (1 votes) · LW · GW

Can you elaborate? What is a constructive proof? Why should on care?

Comment by crabman on Terrorism, Tylenol, and dangerous information · 2018-05-13T16:46:01.141Z · score: 3 (1 votes) · LW · GW

Extremely low amount of deaths is due to terrorist attacks (https://i.redd.it/5sq16d2moso01.gif, https://owenshen24.github.io/charting-death/), so this is not important, and people should care about such things less.

Comment by crabman on Looking for AI Safety Experts to Provide High Level Guidance for RAISE · 2018-05-06T10:36:49.824Z · score: 6 (2 votes) · LW · GW

What does this have in common with https://www.lesswrong.com/posts/kK67yXhmDYwXLqXoQ/fundamentals-of-formalisation-level-1-basic-logic ?

Comment by crabman on Mere Addition Paradox Resolved · 2018-04-28T21:25:49.957Z · score: 10 (3 votes) · LW · GW

Adding resources to this thought experiment is just adding noise. If something other than life quality values matters in this model, then the model is bad.

A>B is correct in average utilitarianism and incorrect in total utilitarianism. The way to resolve this is to send average utilitarianism into the trash can, because it fails in so many desidarata.

Comment by crabman on The First Rung: Insights from 'Linear Algebra Done Right' · 2018-04-23T13:49:42.592Z · score: 19 (5 votes) · LW · GW

How many hours did it take you to read the whole book and do all the exercises that you did? I am reading it too, so far I've spent somewhere between 12 and 22 hours and I'm at exercises 2.A. Also I recommend watching https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/playlists Linear Algebra Essence playlist to get (or remind yourself of) some geometric intuitions.

Comment by crabman on Idea: OpenAI Gym environments where the AI is a part of the environment · 2018-04-12T23:03:25.120Z · score: 2 (1 votes) · LW · GW

I haven't, thanks.

Btw was your goal to show me the link or to learn whether I have seen it before? If the former, then I don't need to respond. If the latter, then you want my response I guess.