aixi

lecture10.md

@@ -7,6 +7,7 @@ Lecture 10: Artificial General Intelligence
 ???
 
 https://futureoflife.org/wp-content/uploads/2017/01/Jurgen-Schmidhuber.pdf?x56934
+http://machineintelligence.org/universal-ai.pdf
 
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@@ -61,6 +62,8 @@ https://futureoflife.org/wp-content/uploads/2017/01/Jurgen-Schmidhuber.pdf?x5693
 
 .center.width-40[![](figures/lec10/go.png)]
 
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
 ---
 
 class: smaller
@@ -71,6 +74,8 @@ class: smaller
 
 .center[Can we run AlphaGo on a robot for the Amazon Picking Challenge?]
 
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
 ---
 
 class: smaller
@@ -88,6 +93,8 @@ class: smaller
 - *Clear and fast evaluation*: not good
 - *Huge dataset available*: **challenge**
 
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
 ---
 
 # Artificial general intelligence
@@ -99,7 +106,7 @@ class: smaller
     - *plan*;
     - *learn*;
     - *communicate* in natural language;
-    - integrate all these skills towards *common goals*. 
+    - integrate all these skills towards *common goals*.
 
 ---
 
@@ -129,12 +136,14 @@ What happens when our computers get smarter than we are? Nick Bostrom
 Several working **hypothesis**:
 - *Supervised learning*: "It works, just scale up!"
 - *Unsupervised learning*: "It will work, if we only scale up!"
-- *AIXI*: "Guys, I can write down optimal AI."
+- *AIXI*: "Guys, I can write down an equation for optimal AI."
 - *Brain simulation*: "This will work one day, right?"
 - *Artificial life*: "Let just do what Nature did."
 
 Or maybe something else?
 
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
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 class: middle, center
@@ -143,6 +152,69 @@ class: middle, center
 
 ---
 
+# Start with an equation
+
+$$\Upsilon(\pi) := \sum\_{\mu \in E} 2^{-K(\mu)} V^{\pi}\_\mu$$
+
+- $\Upsilon(\pi)$ *formally* defines the **universal intelligence** of an agent $\pi$.
+- $\mu$ is the environment of the agent and $E$ is the set of all computable reward bounded environments.
+- $V^{\pi}\_\mu = \mathbb{E}\[ \sum\_{i=1}^\infty R\_i \]$ is the expected sum of future rewards when the agent $\pi$ interacts with environment $\mu$.
+- $K(.)$ is the Kolmogorov complexity, such that $2^{-K(\mu)}$ weights the agent's performance in each environment, inversely proportional to its complexity.
+    - Intuitively, $K(\mu)$ measures the complexity of the shortest Universal Turing Machine program that describes the environment $\mu$.
+
+---
+
+# AIXI
+
+$$\bar{\Upsilon} = \max\_\pi \Upsilon(\pi) = \Upsilon(\pi^{AIXI})$$
+
+- $\pi^{AIXI}$ is a **perfect** theoretical agent.
+- It always picks the action which has the greatest expected reward.
+- For every environment $\mu \in E$, the agent must:
+    - Take into account how likely it is that it is facing $\mu$ given the interaction history so far, and the prior probability of $\mu$.
+    - Consider all possible future interactions that might occur.
+    - Evaluate how likely they are.
+    - Then select the action that maximizes the expected future reward.
+
+---
+
+# System identification
+
+- Which Turing machine is the agent in? If it knew, it could plan perfectly.
+- Let's use the *Bayes rule* to update the agent beliefs given its experience so far.
+
+.center.width-100[![](figures/lec10/tm.png)]
+
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
+---
+
+# Optimal action
+
+.center.width-100[![](figures/lec10/optimal-action.png)]
+
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
+???
+
+The equation embodies in one line the major ideas of Bayes, Ockham, Epicurus,
+Turing, von Neumann, Bellman, Kolmogorov, and Solomonoff. The AIXI agent is
+rigorously shown by [Hut05] to be optimal in many different senses of the word.
+
+---
+
+# Intractability
+
+.center.width-100[![](figures/lec10/aixi-action.png)]
+
+.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)]
+
+---
+
+# Monte Carlo approximation
+
+.center.width-100[![](figures/lec10/mc-aixi.png)]
+
 ---
 
 
@@ -152,6 +224,36 @@ class: middle, center
 
 ---
 
+# Whole brain emulation
+
+.center.width-50[![](figures/lec10/brain.jpg)]
+
+- A hypothesis for AGI is **whole brain simulation**.
+    - A low-level brain model is built by scanning and mapping a biological brain in detail and copying its state into a computer system.
+    - The simulation is *so faithful* that it will behave in essentially the same way as the original.
+- Ongoing initiatives: BRAIN, Blue Brain Project, Human Brain Project, NeuraLink, etc.
+
+---
+
+# Obstacles
+
+- How to *measure* a complete brain state?
+- At what level of abstraction?
+- How to model the dynamics?
+- How do you simulate the environment to feed into senses?
+- Various **ethical dilemmas**.
+
+---
+
+# Mind upload
+
+- **Hypothetically**, whole brain emulation would enable *mind upload*.
+    - The mental state of a particular brain substrate could be scanned and copied into a computer.
+    - The computer could then run a simulation of the brain's information processing, such that it responds in the same way as the original brain.
+- That is, simulation would be indistinguishable from reality.
+
+.center.width-70[![](figures/lec10/simulation.png)]
+
 ---
 
 class: middle, center