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This is: An Intuitive Explanation of Solomonoff Induction , published by Alex_Altair on the AI Alignment Forum.
This is the completed article that Luke wrote the first half of. My thanks go to the following for reading, editing, and commenting; Luke Muehlhauser, Louie Helm, Benjamin Noble, and Francelle Wax.
People disagree about things. Some say that television makes you dumber; other say it makes you smarter. Some scientists believe life must exist elsewhere in the universe; others believe it must not. Some say that complicated financial derivatives are essential to a modern competitive economy; others think a nation's economy will do better without them. It's hard to know what is true.
And it's hard to know how to figure out what is true. Some argue that you should assume the things you are most certain about and then deduce all other beliefs from your original beliefs. Others think you should accept at face value the most intuitive explanations of personal experience. Still others think you should generally agree with the scientific consensus until it is disproved.
Wouldn't it be nice if determining what is true was like baking a cake? What if there was a recipe for finding out what is true? All you'd have to do is follow the written directions exactly, and after the last instruction you'd inevitably find yourself with some sweet, tasty truth!
In this tutorial, we'll explain the closest thing we’ve found so far to a recipe for finding truth: Solomonoff induction.
There are some qualifications to make. To describe just one: roughly speaking, you don't have time to follow the recipe. To find the truth to even a simple question using this recipe would require you to follow one step after another until long after the heat death of the universe, and you can't do that.
But we can find shortcuts. Suppose you know that the exact recipe for baking a cake asks you to count out one molecule of H2O at a time until you have exactly 0.5 cups of water. If you did that, you might not finish the cake before the heat death of the universe. But you could approximate that part of the recipe by measuring out something very close to 0.5 cups of water, and you'd probably still end up with a pretty good cake.
Similarly, once we know the exact recipe for finding truth, we can try to approximate it in a way that allows us to finish all the steps sometime before the sun burns out.
This tutorial explains that best-we've-got-so-far recipe for finding truth, Solomonoff induction. Don’t worry, we won’t be using any equations, just qualitative descriptions.
Like Eliezer Yudkowsky's Intuitive Explanation of Bayes' Theorem and Luke Muehlhauser's Crash Course in the Neuroscience of Human Motivation, this tutorial is long. You may not have time to read it; that's fine. But if you do read it, we recommend that you read it in sections.
Contents:
Background
1. Algorithms — We’re looking for an algorithm to determine truth.
2. Induction — By “determine truth”, we mean induction.
3. Occam’s Razor — How we judge between many inductive hypotheses.
4. Probability — Probability is what we usually use in induction.
5. The Problem of Priors — Probabilities change with evidence, but where do they start?
The Solution
6. Binary Sequences — Everything can be encoded as binary.
7. All Algorithms — Hypotheses are algorithms. Turing machines describe these.
8. Solomonoff's Lightsaber — Putting it all together.
9. Formalized Science — From intuition to precision.
10. Approximations — Ongoing work towards practicality.
11. Unresolved Details — Problems, philosophical and mathematical.
Algorithms
At an early age you learned a set of precisely-defined steps — a 'recipe' or, more formally, an algorithm — that you could use to find the largest number in a list of numbers like this:
21, 18, 4, 19, 55, 12, 30
The algorithm you learn...
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