一维含噪函数全局最小值的一次定位：迭代神经最小化器、Set Transformer 与经典估计器的受控对比
One-Shot Localisation of the Global Minimum of a Noisy One-Dimensional Function: A Controlled Comparison of an Iterative Neural Minimizer, Set Transformers and Classical Estimators
AI 导读
一项被动全局优化研究用 20 个含噪样本、不再查询，估计一维函数全局最小值位置，并提出 Neural Function Minimizer（NFM）与同规模 Set Transformer 进行受控对比。
正文 · 原文
Abstract:We study passive global optimisation: from twenty noisy samples of an unknown one-dimensional function, with no further queries, estimate where its global minimum lies. We build a benchmark and a self-checking harness and use them for a controlled comparison. The Neural Function Minimizer (NFM), which we introduce, moves a position across the domain for fifteen steps and re-reads the samples from it at every step; a same-size Set Transformer answers in one pass. In a 2x2 design each has one output head or an added mixture head, with the same data and inputs and three seeds each. Within the training families the two are tied on location error, and the mixture loss lowers it by about 0.45 points of the domain in both. The NFM's answers have lower regret, by 2.90 and 3.12 points of the range with one and two heads (significant after correction, and again on a block of fresh cases), mainly because its right-basin answers lie closer to the floor; a Set Transformer looped to the NFM's computation does not reproduce this within the training families, though it has the lower error on unseen functions (exploratory). The NFM also differs from the Set Transformers in encoder, local read, activation, losses and training time. At near-tied minima the form of the answer decides: point answers hedge in about a quarter of exact ties, mixture modes almost never, mixture means in more than 80%. Gaussian-process estimators, with no training, have the lowest regret and are the most accurate on unseen functions. We will release the benchmark, the models and the harness.
| Comments: | 49 pages, 5 figures, 15 tables. Code, models and results will be released |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2604.03614 [cs.LG] |
| (or arXiv:2604.03614v5 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.03614 arXiv-issued DOI via DataCite |
Submission history
From: Qusay Muzaffar [view email]
[v1]
Sat, 4 Apr 2026 07:02:38 UTC (15 KB)
[v2]
Sat, 18 Jul 2026 14:19:09 UTC (39 KB)
[v3]
Tue, 6 Oct 2026 15:33:54 UTC (345 KB)
[v4]
Wed, 7 Oct 2026 07:08:45 UTC (345 KB)
[v5]
Tue, 27 Oct 2026 06:40:41 UTC (409 KB)
来源：arXiv cs.AI · arxiv.org