Max Tegmark: Ai And Physics | Lex Fridman Podcast #155

Have you ever been amazed by the capabilities of artificial intelligence and neural networks? It's incredible how these machines can learn and optimize their performance to achieve remarkable feats. From dancing robots to defeating human opponents, neural networks have become a force to be reckoned with. But have you ever wondered how they actually work? It's a fascinating question, and one that has puzzled many of us.

You see, neural networks are designed to optimize their performance based on the input-output relationship. You simply provide the computer with some good definitions, and it continuously fine-tunes these parameters until it performs as best as possible. The result is something that you can observe, but understanding the inner workings of it is incredibly difficult. You could print out a table with millions of parameters, but that wouldn't give you much insight into how it actually works. Some people seem content with this level of understanding, but I disagree. It's like stopping halfway.

There's a notion that the unexplainable nature of neural networks is what gives them their power, a touch of mysticism if you will. But I believe that their true power lies in their differentiability. What do I mean by that? Well, the output only undergoes smooth changes when you tweak the parameters. And that's where all the powerful methods we have in science come into play. We can optimize and fine-tune, seeing if things get better or worse. This is the essence of machine learning – the machine itself can continuously optimize until it gets better.

Imagine if you wrote an algorithm in Python or any other programming language, and the parameters were just random changes to the letters in the code. That would be a complete failure. You change one thing, and instead of printing, it shows a syntax error. You have no idea if that's good or bad. The basic power of neural networks lies in the fact that you can tweak the parameters, and each setting becomes a program. You can optimize and refine, and every time you do, you see if it gets better or worse. That's the basic idea of machine learning.

Machine Learning and the Search for Equations

Let's dive a little deeper into the world of machine learning. One fascinating area is the search for equations. How do you automatically discover equations that describe a given set of data? This is a profound and challenging problem. If I were to ask you to prove a mathematical theorem, you could write down a series of logical steps, symbolically, and once you find it, it's straightforward to write a program to check if it's a valid proof. But why is proving so difficult? It's because there are just too many possible candidate proofs. Even if a proof is just 10,000 symbols long, and each symbol has just 10 choices, that's 10 to the power of 1,000 possible proofs – more than the number of atoms in the universe.

You might say, well, these problems are easy. You just write a program to generate all the strings and check if it's a valid proof, and if not, move on to the next one. But there are so many possibilities, and it's fundamentally a search problem. You're searching in this space of strings, trying to find one that has the properties of a proof. There's a whole field of machine learning called search, which teaches you how to search in a vast space and find that needle in the haystack. In some cases, if there's a clear metric, like not just right or wrong, but good or bad, you can find some clues to guide your search.

That's why we talk about how neural networks work, because they're well-suited for this kind of problem