Yuksekgonul 2026 learning discover test time

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M. Yuksekgonul, D. Koceja, X. Li, F. Bianchi, J. McCaleb, X. Wang, J. Kautz, Y. Choi, J. Zou, C. Guestrin and Y. Sun, Learning to Discover at Test Time, arXiv:2601.16175v1 [cs.LG], 22 January 2026, 72 pp. The problem page cites the copy at https://test-time-training.github.io/discover.pdf, which is not held and was not compared.

The retained folder-name PDF is arXiv version 1 (arXiv-generated PDF with a text layer; 72 pages, physical page equal to the preprint's printed page). Provenance: the folder's arXiv sidecar records these bytes as fetched from https://arxiv.org/pdf/2601.16175v1 on 2026-09-23; 1,282,384 bytes. Read status: claims checked for the minimum-overlap statements of Section 4.1.1, which were read clause by clause from the text layer; the rest of the paper describes a machine-learning method and its other applications and was not read beyond the abstract and the section headings. The arXiv record (https://arxiv.org/abs/2601.16175, read 2026-10-02) names the Creative Commons Attribution 4.0 license.

Contents

Only the material on the minimum overlap problem is recorded.

• Section 4.1.1 (p. 7) states the problem: partition $\{1,\dots,2n\}$ into $A$ and $B$ of size $n$, let $M_k$ be the number of solutions of $a_i-b_j=k$ with $a_i\in A$, $b_j\in B$, let $M(n)=\min_{A,B}\max_kM_k$, and bound $c=\lim_{n\to\infty}M(n)/n$. It records the bounds before AlphaEvolve as $0.379005<c<0.380927$, the upper bound due to Haugland (the paper's [20], arXiv:1609.08000) and the lower bound to White (the paper's [76], Acta Arith. 208 (2023), 235--255), and AlphaEvolve's improvement of the upper bound to $0.380924$ (the paper's [49] and [14]).
• Method (p. 8): following AlphaEvolve, the search optimizes step functions $f$ describing the limiting density of $A$ on $[1,2n]$; by a result of Swinnerton-Dyer as reported by Haugland [20], such density functions give valid upper bounds on $\lim M(n)/n$ without explicit partitions, subject to $f(x)\in[0,1]$ and $\int f=1$.
• Result (p. 8; Table 2 and Figure 2): a 600-piece asymmetric step function with $c\le0.380876$, against AlphaEvolve's symmetric 95-piece function ($0.380924$) and Haugland's 51-piece one ($0.380927$). Table 2 also lists $0.380906$ for a best-of-25600 sampling baseline with the same model and $0.380932$ for a smaller model. The construction is said to be released with the authors' code; the PDF does not print the step function, and no certificate is held here.
• Section 4.1.4 (pp. 10--11), "Expert Review": an invited reviewer's paragraph says that verifying such a bound is straightforward, by evaluating the functional at the finitely many points determined by the step function's breakpoints and checking the norm constraints. This is a statement in the paper, not a check made by this repository.

Compiled scope

Only Section 4.1.1, the corresponding rows of Table 2, Figure 2 and the paragraph of Section 4.1.4 on the minimum overlap problem were read. The bound $0.380876$ is recorded as the authors' claim: the certificate is not in the PDF and was not recomputed here. The paper contains no proof about the problem beyond this numerical construction; the lower bound $0.379005$ and the reduction to step functions are quoted from other sources. Nothing has been independently reviewed.

Bears on. #36: reports a claimed upper bound $0.380876$ (January 2026) on the problem's constant $c$, by a 600-piece step function found by test-time reinforcement learning; the certificate is external to the PDF and was not checked here.