Variational Solomonoff Induction

February 18, 2021

$$ \newcommand{\mb}{\mathbb} \newcommand{\mc}{\mathcal} \newcommand{\E}{\mb{E}} \newcommand{\B}{\mb{B}} \newcommand{\R}{\mb{R}} \newcommand{\kl}[2]{D_{KL}\left(#1\ \| \ #2\right)} \newcommand{\argmin}[1]{\underset{#1}{\mathrm{argmin}}\ } \newcommand{\argmax}[1]{\underset{#1}{\mathrm{argmax}}\ } \newcommand{\abs}[1]{\left\lvert#1\right\rvert} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\ve}{\varepsilon} \newcommand{\t}{\theta} \newcommand{\T}{\Theta} \newcommand{\o}{\omega} \newcommand{\O}{\Omega} \newcommand{\sm}{\mathrm{softmax}} $$ The free energy principle is a variational Bayesian method for approximating posteriors. Can free energy minimization combined with program synthesis methods from machine learning tractably approximate Solomonoff induction (i.e. universal inference)? In these notes, I explore what the combination of these ideas looks like. Machine learning I want to make an important clarification about “Bayesian machine learning”.…

Active inference tutorial (actions)

February 7, 2021

$$ \newcommand{\mb}{\mathbb} \newcommand{\mc}{\mathcal} \newcommand{\E}{\mb{E}} \newcommand{\B}{\mb{B}} \newcommand{\kl}[2]{D_{KL}\left(#1\ \| \ #2\right)} \newcommand{\argmin}[1]{\underset{#1}{\mathrm{argmin}}\ } \newcommand{\argmax}[1]{\underset{#1}{\mathrm{argmax}}\ } \newcommand{\abs}[1]{\left\lvert#1\right\rvert} \newcommand{\atup}[1]{\left\langle#1\right\rangle} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\t}{\theta} \newcommand{\T}{\Theta} \newcommand{\p}{\phi} \newcommand{\r}{\rho} $$ Previous attempts: In Free Energy Principle 1st Pass, I used a tutorial to try to understand the free energy formalism. I figured out the “timeless” and actionless case, but I became confused when actions and time were added. In Free energy principle and Solomonoff induction, I tried to translate between the formalism presented in https://danijar.…

Free Energy Principle 1st Pass

February 7, 2021

$$ \newcommand{\mb}{\mathbb} \newcommand{\mc}{\mathcal} \newcommand{\E}{\mb{E}} \newcommand{\B}{\mb{B}} \newcommand{\kl}[2]{D_{KL}\left(#1\ \| \ #2\right)} \newcommand{\argmin}[1]{\underset{#1}{\mathrm{argmin}}\ } \newcommand{\abs}[1]{\left\lvert#1\right\rvert} \newcommand{\atup}[1]{\left\langle#1\right\rangle} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\t}{\theta} \newcommand{\T}{\Theta} \newcommand{\p}{\phi} $$ Related notes: The free-energy principle a unified brain theory Active inference tutorial (actions) Hackmd version of this note: https://hackmd.io/@z5RLVXyrTg-JLCnL9c_xOQ/r1KSFUjkO My current understanding Note on probability notation These are my informal notes. Probability notation can be cumbersome and overly verbose. As is customary in machine learning and many of the sciences, I’m not going to bother using probability notation correctly.…

How this blog works

February 6, 2021

This blog is a window into my second brain. That is where I store all of my personal notes, ranging from journal entries to productive materials like study notes and math problems. I can mark any of these items for publication on my blog, and I have a script take care of the rest. Second brain I use the Obsidian editor to organize my second brain. It looks like this:…

Blogging experiment

February 1, 2021

What is this blog? It’s a collection of notes pulled directly from my digital journal. My digital journal is a bunch of markdown files that I edit in obsidian. You could call it my “second brain”. I write everything here. It’s a journal in the traditional sense, in that I write about what’s going on in my life and what’s on my mind in order to collect my thoughts. I also write down logical stuff like TODO-lists, lists of links I want to keep, things I might want to look into.…