CAS II: Symmetric Partitions as Kolmogorov Models
Quick summary
arXiv:2609.40290v1 Announce Type: cross Abstract: In algorithmic statistics a string x is explained by a finite set containing it, and Kolmogorov's structure function records the smallest such model at each level of complexity. Vereshchagin's strong models, those computable from the data by a total algorithm, are essentially the cells of simple partitions. We read a partition of binary strings as a hypothesis, with the cell containing x as its model, and develop algorithmic statistics over symmetric partitions: the orbit partitions of groups acting on strings. The Galois connection between sub
Key takeaways
- arXiv:2609.40290v1 Announce Type: cross Abstract: In algorithmic statistics a string x is explained by a finite set containing it, and Kolmogorov's structure function records the smallest such model at each level of complexity.
- Vereshchagin's strong models, those computable from the data by a total algorithm, are essentially the cells of simple partitions.
- We read a partition of binary strings as a hypothesis, with the cell containing x as its model, and develop algorithmic statistics over symmetric partitions: the orbit partitions of groups acting on strings.
Why it matters
This model development creates a new option for users and a new testing obligation for developers. A fixed evaluation set comparing quality, cost and failure behavior is more useful than launch claims.
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