Rough is easy to find and not worth much.
Diamonds are much harder to find and worth a lot more.
I once read a post by someone who was unimpressed with the paper that introduced Generative Adversarial Networks (GANs). They pointed out some sloppy math and other such problems and were confused why such a paper had garnered so much praise.
Someone replied that, in her decades of reading research papers, she learned that finding flaws is easy and uninteresting. The real trick is being able to find the rare glint of insight that a paper brings to the table. Understanding how even a subtle idea can move a whole field forward. I kinda sympathize as a software developer.
I remember when I first tried to slog through Marcus Hutter’s book on AIXI, I found the idea absurd. I have no formal background in mathematics, so I chalked some of that up to me not fully understanding what I was reading. I kept coming back to the question (among many others): “If AIXI is incomputable, how can Hutter supposedly prove that it performs ‘optimally’? What does ‘optimal’ even mean? Surely it should include the computational complexity of the agent itself!”
I tried to modify AIXI to include some notion of computational resource utilization until I realized that any attempt to do so would be arbitrary. Some problems are much more sensitive to computational resource utilization than others. If I’m designing a computer chip, I can afford to have the algorithm run an extra month if it means my chip will be 10% faster. The algorithm that produces a sub-optimal solution in milliseconds using less than 20 MB of RAM doesn’t help me. At the same time, if a saber-toothed tiger jumps out of a bush next to me. I don’t have months to figure out a 10% faster route to get away.
I believe there are problems with AIXI, but lots of digital ink has been spilled on that subject. I plan on contributing a little to that in the near future, but I also wanted to point out that, it’s easy to look at an idea like AIXI from the wrong perspective and miss a lot of what it truly has to say.
I disagree. This is like saying, “we don’t need fluid dynamics, we just need airplanes!”. General mathematical formalizations like AIXI are just as important as special theories that apply more directly to real-world problems, like embedded agents. Without a grounded formal theory, we’re stumbling in the dark. You simply need to understand it for what it is: a generalized theory, then most of the apparent paradoxes evaporate.
Kolmogorov complexity tells us there is no such thing as a universal lossless compression algorithm, yet people happily “zip” data every day. That doesn’t mean Kolmogorov wasted his time coming up with his general ideas about complexity. Real world data tends to have a lot of structure because we live in a low-entropy universe. When you take a photo or record audio, it doesn’t look or sound like white noise because there’s structure in the universe. In math-land, the vast majority of bit-strings would look and sound like incompressible white noise.
The same holds true for AIXI. The vast majority of problems drawn from problem space would essentially be, “map this string of random bits to some other string of random bits” in which case, the best you can hope for is a brute-force tree-search of all the possibilities weighted by Occam’s razor (i.e. Solomonoff inductive inference).
I can’t speak to the motivations or processes of others, but these sound like assumptions without much basis. The reason I tend to define intelligence outside of the environment is because it generalizes much better. There are many problems where the system providing the solution can be decoupled both in time and space from the agent acting upon said solution. Agents solving problems in real-time are a special case, not a general case. The general case is: an intelligent system produces a solution/policy to a problem and an agent in an environment acts upon that solution/policy. An intelligent system might spend all night planning how to most efficiently route mail trucks the next morning, the drivers then follow those routes. A real-time model in which the driver has to plan her routs while driving is a special case. You can think of it as the drivers brain coming up with the solution/policy and the driver acting on it in situ.
You could make the case that the driver has to do on-line/real-time problem solving to navigate the roads and avoid collisions, etc. in which case the full solution would be a hybrid of real-time and off-line formulation (which is probably representative of most situations). Either way, constraining your definition of intelligence to only in-situ problem solving excludes many valid examples of intelligence.
Also, it doesn’t seem like you understand what Solomonoff inductive inference is. The weighted average is used because there will typically be multiple world models that explain your experiences at any given point in time and Occam’s razor says to favor shorter explanations that give the same result, so you weight the predictions of each model by the inverse of the length of the model (in bits, usually).
I think you’re confusing behavior with implementation. When people talk about neural nets being “universal function approximators” they’re talking about the input-output behavior, not the implementation. Obviously the implementation of an XOR gate is different than a neural net that approximates an XOR gate.