Recorded by Robert Miles: http://robertskmiles.com More information about the newsletter here: https://rohinshah.com/alignment-newsletter/ YouTube Channel: https://www.youtube.com/channel/UCfGGFXwKpr-TJ5HfxEFaFCg This newsletter is a combined summary + opinion for the Finite Factored Sets sequence by Scott Garrabrant. I (Rohin) have taken a lot more liberty than I usually do with the interpretation of the results; Scott may or may not agree with these interpretations.     Motivation     One view on the importance of deep learning is that it allows you to automatically learn the features that are relevant for some task of interest. Instead of having to handcraft features using domain knowledge, we simply point a neural net at an appropriate dataset, and it figures out the right features. Arguably this is the majority of what makes up intelligent cognition; in humans it seems very analogous to System 1, which we use for most decisions and actions. We are also able to infer causal relations between the resulting features. Unfortunately, existing models of causal inference don’t model these learned features -- they instead assume that the features are already given to you. Finite Factored Sets (FFS) provide a theory which can talk directly about different possible ways to featurize the space of outcomes, and still allows you to perform causal inference. This sequence develops this underlying theory, and demonstrates a few examples of using finite factored sets to perform causal inference given only observational data. Another application is to embedded agency (AN #31): we would like to think of “agency” as a way to featurize the world into an “agent” feature and an “environment” feature, that together interact to determine the world. In Cartesian Frames (AN #127), we worked with a function A × E → W, where pairs of (agent, environment) together determined the world. In the finite factored set regime, we’ll think of A and E as features, the space S = A × E as the set of possible feature vectors, and S → W as the mapping from feature vectors to actual world states.     What is a finite factored set?     Generalizing this idea to apply more broadly, we will assume that there is a set of possible worlds Ω, a set S of arbitrary elements (which we will eventually interpret as feature vectors), and a function f : S → Ω that maps feature vectors to world states. Our goal is to have some notion of “features” of elements of S. Normally, when working with sets, we identify a feature value with the set of elements that have that value. For example, we can identify “red” as the set of all red objects, and in some versions of mathematics, we define “2” to be the set of all sets that have exactly two elements. So, we define a feature to be a partition of S into subsets, where each subset corresponds to one of the possible feature values. We can also interpret a feature as a question about items in S, and the values as possible answers to that question; I’ll be using that terminology going forward. A finite factored set is then given by (S, B), where B is a set of factors (questions), such that if you choose a particular answer to every question, that uniquely determines an element in S (and vice versa). We’ll put aside the set of possible worlds Ω; for now we’re just going to focus on the theory of these (S, B) pairs. Let’s look at a contrived example. Consider S = {chai, caesar salad, lasagna, lava cake, sprite, strawberry sorbet}. Here are some possible questions for this S: - FoodType: Possible answers are Drink = {chai, sprite}, Dessert = {lava cake, strawberry sorbet}, Savory = {caesar salad, lasagna} - Temperature: Possible answers are Hot = {chai, lava cake, lasagna} and Cold = {sprite, strawberry sorbet, caesar salad}. - StartingLetter: Possible answers are “C” = {chai, caesar salad}, “L” = {lasagna, lava cake}, and “S” = {sprite, strawberry sorbet}. - NumberOfWords: Possible answers are “1” = {chai, lasagna, sprite} and “2” = {caesar sa