
What learning algorithms can predict that our physics theories might not - ad510
http://firstestprinciple.com/2016/07/10/learning.html
======
Strilanc
I wasn't expecting this article to be about Sleeping Beauty problems and
Solomonoff induction. There are people trying to apply real machine learning
algorithms to real physics problems (e.g. [1][2]). This article is not about
that.

It should go without saying that Solomonoff induction is totally useless for
practical applications, if interesting theoretically. Brute forcing the space
of all programs is ridiculously mindbogglingly universe-crushingly expensive.
(Actually, even if the process was magically tractable, there would still be
limitations and dangers [3].)

1:
[http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108...](http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.058301)

2; [http://arxiv.org/abs/1404.1333](http://arxiv.org/abs/1404.1333)

3:
[http://lesswrong.com/lw/jg1/solomonoff_cartesianism/](http://lesswrong.com/lw/jg1/solomonoff_cartesianism/)

~~~
cel1ne
Could Solomonoff induction guess sequences of prime-numbers?

~~~
cousin_it
You can think of Solomonoff induction as a weighted set of experts. At each
step, each expert makes a prediction, and the overall prediction is the one
that gets the highest total weight. Then the true data comes in, and the
weight of each expert is increased or decreased based on whether that expert
was right or wrong. And here's the kicker, the experts are all possible
prediction programs, initially weighted by 2^-(program length). So yeah, in
the long run Solomonoff induction will be at least as good as you at
predicting any particular sequence, including prime numbers etc., because your
own prediction algorithm is somewhere in the Solomonoff mixture. That also
explains why approximating Solomonoff induction takes a huge amount of
computation time. It's mostly a theoretical idea.

~~~
eutectic
More specifically, every incorrect expert is removed at each step, and the
remaining experts have their probabilities uniformly rescaled to sum to 1.

~~~
hacker42
That relies on noiseless, unbiased data, right? What if an expert gets ruled
out by accident?

~~~
eutectic
Being able to average over every possible computer program is so powerful that
it doesn't really matter.

------
Xcelerate
This is a very interesting article. Scott Aaronson touches on some of these
ideas related to quantum cloning and the concept of "you" in his blog posts.

I've always thought this kind of concept might define the limits of standard
science, as currently practiced. Science requires reproducibility. But by
whom? Well, other scientists of course. If every scientist tries your
experiment and gets the same result, then you have a validated scientific
theory.

But suppose that you manage to set up an experiment where the perception of
which measurement resulted depends upon who is perceiving the result (I can
think of a few ways that this scenario might arise if we could ever figure out
a way to generate macroscopic, human-scale, superpositions [which is unlikely,
I'll add]). That would really throw a wrench in things. In that case, you
would have to have each scientist convincingly prove to each other scientist
that they all see something different, in which case perhaps the result could
still be universally accepted. But there may be a limit on how much consensus
we can ultimately get.

~~~
marcosdumay
Hum... That looks odd because it is. Things do not work this way.

Actually, the reproducibility applies to the hypothesis (conclusion), not to
the experiment. It's only that, since the observer is irrelevant, people
simplify and call it "reproducing the experiment".

If your experiment depends on the observer, and you get to know that, that
dependence will go on the conclusion, and the people reproducing your
experiment will expect to see the result your hypothesis say they would, not
the same one you got. If you have a correct predicting model, everybody will
conclude it's correct.

------
djokkataja
> What if instead of connecting just 2 people’s brains together, we connected
> everyone’s brains like that to the internet? Would that mean that every
> human being on Earth would feel like they are just one small body part of a
> single, greater being?

I don't think that joining everyone's brains together would make everyone feel
like a small body part of a single, greater being, because our brain
architecture _really_ wouldn't support that. You might be able to handle some
shared "input" with another person or a small group of people (like these
conjoined twins who share a thalamus[0]), but you're going to run into
bandwidth issues pretty quickly given that there are only ~1-2 million nerves
in each optic nerve[1]--if you're trying to split that 7 billion ways, you're
going to have a difficult time getting coherent information through, let alone
processing it.

The second major limitation to joining brains together is the speed of light--
once we're able to open up communication between brains to allow
"communicating via thoughts", we'll be communicating at the speed of our
thoughts, which is much faster than physical speech. Connecting your brain
with the brain of someone on the other side of the world might be a pretty
disappointing experience because they wouldn't be nearly as responsive as
someone physically nearby. Uploading brains and running them at higher "clock
speeds" than biological hardware permits would make this limitation more
significant, because you might subjectively experience a communication time
lag that would feel like hours, days, or longer when connected to someone far
away. In other words, there would be a limiting radius in physical reality for
effective brain-connecting communication that varied depending on the speed of
your subjective experience.

Those limitations aside, sign me up! Brain-AI merging and brain-brain
communication are going to be the bees knees.

[0]:
[https://en.wikipedia.org/wiki/Krista_and_Tatiana_Hogan#Progr...](https://en.wikipedia.org/wiki/Krista_and_Tatiana_Hogan#Progression_to_childhood)

[1]:
[https://en.wikipedia.org/wiki/Optic_nerve#Structure](https://en.wikipedia.org/wiki/Optic_nerve#Structure)

------
millstone
Question about this paragraph:

> Is it possible to define a process that Solomonoff induction cannot predict?
> The short answer is yes, but the kinds of computers needed to simulate these
> processes don’t exist in the real world, and it’s unlikely that we’ll ever
> be able to build them.

Doesn't "pick a truly random number" qualify? And we can build those today.

~~~
ad510
When I wrote "predict" there, I was referring to whether the predicted
probabilities approach the true underlying probabilities, and Solomonoff
induction can "predict" a true random number generator in that sense because
its predicted probabilities will approach those of the random number
generator. [1] However, if you tried to use it to predict a halting oracle,
the halting oracle would be deterministic but Solomonoff induction would never
be able to predict it with complete confidence, and this is what I was
referring to in that paragraph.

But you're right that random numbers are inherently unpredictable; maybe I
should add another footnote explaining what I meant there. (Edit: I added a
clarification to the paragraph you quoted.)

[1] [http://twistedoakstudios.com/blog/Post5623_solomonoffs-
mad-s...](http://twistedoakstudios.com/blog/Post5623_solomonoffs-mad-
scientist) in the "Thinking with Programs: Random Data" section

~~~
goldenkey
One of the principles of turing machines is that they are deterministic. In
that vain, there exists no programmable RNG except for pseudo random ones. One
has to ask oneself if piping a transform of the digits of a transcendental
real number is a violation to this rule -- thus what is random really? Is
random the lack of ability to find a correlation or program to reproduce it --
or is it something more like Komogrolov complexity? These are tough and
inscrutable questions. Shannon, Turing, Curry, Church, Post, and others
explored them deeply. Information theory gets extremely existential and
esoteric. Is randomness a monad of our universe? Or is physicals and natural
chaos just extremely leathery when it comes to extracting the generating
program? Our lives depend on it. But either way, we'll carry on. Nature you
goddamn enigma.

------
EGreg
Did someone have to be on drugs to write this?

------
ad510
Well, I must say that I'm pleasantly surprised with the comments so far. I was
actually expecting that this would be quickly shot down as either unoriginal
or fundamentally flawed. But instead it seems no one has caught on to what
this post is actually claiming, so I suppose I should now be very blunt about
it.

At the beginning of the blog post, it claims that it explains 2 things:

1\. where _exactly_ might you be able to use learning algorithms where you
can't just use existing physics theories instead 2\. a hands on guide to
applying learning algorithms in these situations

This is physicist code for "this blog post claims that it solves a major
unsolved problem in physics." Let me explain.

Currently, we have the standard model and general relativity, which have been
experimentally verified to extreme precision but are fundamentally
incompatible with each other. So people have proposed theories of everything
such as string theory, loop quantum gravity, and information/digital physics
(which I'm obviously a fan of) to resolve these incompatibilities.

One of the biggest problems in fundamental physics right now is that the
standard model and general relativity have been verified to such precision
that it's hard to think of a practical experiment to show how they are wrong.
The conventional wisdom is that this is only possible if we do things like
measure the Planck scale or what happens inside a black hole, which are
completely impractical on human timescales.

What this post proposes is that you actually don't need to measure the Planck
scale or what happens in a black hole in order to test the proposed theories
of everything, and instead you can do it with a sufficiently powerful computer
simulation and a sufficiently good brain-computer interface. If our technology
keeps improving exponentially, this may be possible in the next several
decades.

So yeah, I made a bit of a white lie when I framed this post as a summary of
recent research in information physics. I can back up almost everything in the
post with the sources I linked to, but the part about the 0 or 1 experiment
and predicting its outcome using Solomonoff induction is actually original
research on my part, and I suspect it would actually be a very big deal if
this works the way I think it does.

So here are the possible outcomes for this blog post:

1\. The problem in physics I just described is actually already solved. 2\.
The blog post is fundamentally flawed, and/or it actually doesn't solve the
problem that I'm claiming it solves. 3\. The blog post actually does solve a
major unsolved problem in physics, and this is a huge deal.

This is why I am so surprised at the comments I'm getting so far, since this
proposal for experimentally testing theories of everything seems to be passing
the internet commenter test. So if no one on HN finds anything seriously wrong
with the blog post, can we get people like Scott Aaronson, John Baez, Juergen
Schmidhuber, Stephen Hawking, or people of that caliber to look at it so we
can get a more definitive answer to whether this actually solves an unsolved
problem in physics?

Also, kudos to Xcelerate's comment, which is the closest to the point I was
trying to get at with the blog post.

~~~
jerf
It is not clear to me that you realize that Solomonoff induction is a
mathematical argument, not a practical algorithm. To run it at the level of
generality necessary to discover the laws of physics is computationally
infeasible. In fact, it's one of those cases where calling it "computationally
infeasible" is an inadvertent understatement of the problem, because English
doesn't have gradations for this level of difficulty. Merely a "singularity"
doesn't help this problem; you need more computation than our physics appears
to allow.

~~~
ad510
Yes, I know that Solomonoff induction is completely impractical for real life
machine learning. My point was that if you can survive in the simulation to
the point where you see either the 0 or the 1, we don't have any way even in
theory (let alone in practice) to guess the probabilities of seeing a 0 or 1,
unless you use some sort of learning algorithm. You can use any learning
algorithm for this; it doesn't have to be Solomonoff induction.

~~~
jerf
But your argument seems to fundamentally rest on Solomonoff induction. Put any
_real_ algorithm in there, and now you need to ensure that 1. the biases of
the algorithm encompass a hypothesis that matches the data and 2. the
algorithm will be able to arrive at that hypothesis given a real data stream,
and, ideally, a real amount of computation. Both of these are hard questions,
in the strongest sense of the term.

And once you open that door, well, all you've really done is restate the fact
that learning how the universe works seems to be really difficult.

~~~
ad510
OK, I see what you're saying now. In that case, can you think of a better way
of predicting whether you see a 0 or 1 in that situation?

~~~
jerf
If I had an answer to that question, I probably wouldn't be putting it on HN.
:) I'd be firing it at the market and making boodles of moolah.

