Improved Learning from Kolmogorov Complexity
Bibliographic record
Abstract
Carmosino, Impagliazzo, Kabanets, and Kolokolova (CCC, 2016) showed that the existence of natural properties in the sense of Razborov and Rudich (JCSS, 1997) implies PAC learning algorithms in the sense of Valiant (Comm. ACM, 1984), for boolean functions in P/poly, under the uniform distribution and with membership queries. It is still an open problem to get from natural properties learning algorithms that do not rely on membership queries but rather use randomly drawn labeled examples. Natural properties may be understood as an average-case version of MCSP, the problem of deciding the minimum size of a circuit computing a given truth-table. Problems related to MCSP include those concerning time-bounded Kolmogorov complexity. MKTP, for example, asks for the KT-complexity of a given string. KT-complexity is a relaxation of circuit size, as it does away with the requirement that a short description of a string be interpreted as a boolean circuit. In this work, under assumptions of MKTP and the related problem MK^tP being easy on average, we get learning algorithms for boolean functions in P/poly that - work over any distribution D samplable by a family of polynomial-size circuits (given explicitly in the case of MKTP), - only use randomly drawn labeled examples from D, and - are agnostic (do not require the target function to belong to the hypothesis class). Our results build upon the recent work of Hirahara and Nanashima (FOCS, 2021) who showed similar learning consequences but under a stronger assumption that NP is easy on average.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.052 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.013 |
| Open science | 0.004 | 0.007 |
| Research integrity | 0.002 | 0.008 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".