Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
On Union-Closedness of Language Generation
Authors: Steve Hanneke, Amin Karbasi, Anay Mehrotra, Grigoris Velegkas
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our first set of results resolve two open questions of [Li et al., 2025] by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is a non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single more powerful generator, prohibiting this notion of boosting. Our construction also addresses a third of [Li et al., 2025] s open questions on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li, Raman, and Tewari. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation. |
| Researcher Affiliation | Collaboration | Steve Hanneke Purdue University EMAIL Anay Mehrotra Yale University EMAIL Amin Karbasi Yale University EMAIL Grigoris Velegkas Google Research EMAIL |
| Pseudocode | No | No. The paper describes algorithmic approaches and theoretical constructions in natural language, for example under 'A Modified Diagonalization Argument' in Section 3.4 and 'Phase k (k >= 2)' in Appendix B.1, but it does not present them in structured pseudocode or an algorithm block format. |
| Open Source Code | No | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [NA] Justification: No data or code is used. |
| Open Datasets | No | No. The paper is theoretical and does not conduct experiments with datasets. The Neur IPS Paper Checklist states: 'Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [NA] Justification: No data or code is used.' |
| Dataset Splits | No | No. The paper does not conduct empirical experiments using datasets, therefore, no dataset splits are relevant or provided. The Neur IPS Paper Checklist states: 'Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)? Answer: [NA] Justification: No experiments are included.' |
| Hardware Specification | No | Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [NA] Justification: Justification: The paper does not include experiments. |
| Software Dependencies | No | No. The paper presents theoretical results and does not describe any experimental setup that would require specific software dependencies or their version numbers. The Neur IPS Paper Checklist states: 'Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [NA] Justification: The paper does not include experiments.' |
| Experiment Setup | No | Question: Does the paper contain SPECIFIC EXPERIMENTAL SETUP DETAILS (concrete hyperparameter values, training configurations, or system-level settings) in the main text? Answer: [NA] Justification: The paper does not include experiments. |