Check with definition 2.4. In the technical sense used in the document, a predictor is not defined as being something that outputs the sequence—it is defined as something that eventually learns how to predict the sequence—making at most a finite number of errors.
Strings with high Kolmogorov complexity being “predicted” by trivial algorithms is quite compatible with this notion of “prediction”.
Here’s an example from the paper that helps illustrate the difference: if the sequence is a gigabyte of random data repeated forever, it can be predicted with finitely many errors by the simple program “memorize the first gigabyte of data and then repeat it forever”, though the sequence itself has high K-complexity.
It looks like you just dislike the definitions in the paper and want to replace them with your own. I’m not sure there’s any point in arguing about that.
This is from your link.
But if it can be predicted by a trivial algorithm, it has LOW Kolmogorov complexity.
Check with definition 2.4. In the technical sense used in the document, a predictor is not defined as being something that outputs the sequence—it is defined as something that eventually learns how to predict the sequence—making at most a finite number of errors.
Strings with high Kolmogorov complexity being “predicted” by trivial algorithms is quite compatible with this notion of “prediction”.
So, above the last wrongly predicted output, the whole sequence is as complex as the (improved) predictor?
Here’s an example from the paper that helps illustrate the difference: if the sequence is a gigabyte of random data repeated forever, it can be predicted with finitely many errors by the simple program “memorize the first gigabyte of data and then repeat it forever”, though the sequence itself has high K-complexity.
No it has not. The algorithm for copying the first GB forever is small and the Kolmogorov’s complexity is just over 1GB.
For the entire sequence.
Yes, but the predictor’s complexity is much lower than 1GB.
The paper also gives an example of a single predictor that can learn to predict any eventually periodic sequence, no matter how long the period.
Predictor should remember what happened. It has learned. Now it’s 1 GB heavy.
It looks like you just dislike the definitions in the paper and want to replace them with your own. I’m not sure there’s any point in arguing about that.
I only stick with the Kolmogorov’s definition.