On Sun, Jul 9, 2023 at 10:20 AM John Rose <[email protected]> wrote:
> I do wonder though what criteria would be used to discern amongst various > computable models of AIXI assuming there is spectrum of them. I already have > a model for that but I wonder what the specialists in the field say... Good predictors (including AIXI, other AI, and lossless compression) are necessarily complex. The simple proof: Suppose you have a simple program that can learn to predict any computable sequence of bits. Then I have a simple program that generates a stream you can't predict. My program runs a copy of your program and outputs the opposite bit. Two examples: 1. SINDy, mentioned earlier, predicts a time series of real numbers by testing against a library of different functions and choosing the simplest combination. The bigger the library, the better it works. 2. The top compressors on most benchmarks have a lot of code because they look for all the special cases and different file formats to pick from. For example, PAQ searches for JPEG images embedded in other files and applies a special model to compress them. PreComp searches for deflate streams and unzips them so they can be recompressed with better algorithms. But these are common formats. The best compressors could look for hundreds or thousands of obscure formats and never get all of them. For example, how would you compress the bit sequence x[i] = x[i-24] XOR x[i-55]? It looks like a random bit sequence (until it repeats after 2^55 - 1 bits) unless you know to look for this particular pattern. How would you compress an RC4 generated stream if it appears random unless you know the key? AIXI^tl would eventually discover the key by brute force search, but not before the heat death of the universe. -- -- Matt Mahoney, [email protected] ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Taf667527679b18c3-M60401287acbf6e66404b0660 Delivery options: https://agi.topicbox.com/groups/agi/subscription
