On the Power of Interactive Proofs for Learning
Bibliographic record
Abstract
We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. We construct an interactive protocol for learning the t largest Fourier characters of a given function f ∶ {0,1}n → {0,1} up to an arbitrarily small error, wherein the verifier uses poly(t) random examples. This improves upon the Interactive Goldreich-Levin protocol of Goldwasser, Rothblum, Shafer, and Yehudayoff (ITCS 2021) whose sample complexity is poly(t,n). For agnostically learning the class AC0[2] under the uniform distribution, we build on the work of Carmosino, Impagliazzo, Kabanets, and Kolokolova (APPROX/RANDOM 2017) and design an interactive protocol, where given a function f ∶ {0,1}n → {0,1}, the verifier learns the closest hypothesis up to polylog(n) multiplicative factor, using quasi-polynomially many random examples. In contrast, this class has been notoriously resistant even for constructing realisable learners (without a prover) using random examples. For agnostically learning k-juntas under the uniform distribution, we obtain an interactive protocol, where the verifier uses O(2k) random examples to a given function f ∶ {0,1}n → {0,1}. Crucially, the sample complexity of the verifier is independent of n. We also show that if we do not insist on doubly-efficient proof systems, then the model becomes trivial. Specifically, we show a protocol for an arbitrary class C of Boolean functions in the distribution-free setting, where the verifier uses O(1) labeled examples to learn f.
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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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; both teacher heads agree on what is shown here.
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".