Assumed background: Kolmogorov complexity and Solomonoff induction.

Suppose I have some data , and I go looking for the models (i.e. programs) which best compress that data. I find two different programs, and , which both reproduce the data using approximately the same number of bits, and that seems to be roughly the best compression possible. On examination, I find that the two models do totally different things internally.

It would be really nice if I could provably construct a third program, , which in some sense "combines the internal structure" of the two programs and , while still achieving approximately the same compression. This would be a result in the general cluster of natural abstraction and interoperable semantics. Very roughly speaking, it would say that if a human and an alien both have approximately-best-compressing models in some domain, but their models have totally alien internal structure, then we can construct a new model which finds both of the original models intelligible, while still achieving basically-optimal compression.

I don't have a perfect theorem like that with all the kinks worked out. But I can give some math which seems like it would allow a result along those lines, with [...]

---

Outline:

(01:16) Some K-Complexity Math

(03:29) Summary

---

First published:
May 20th, 2026

Source:
https://www.lesswrong.com/posts/Fxv3qvjk65Pehpbea/toward-interoperability-of-minimal-programs

---

Narrated by TYPE III AUDIO.