Language Generation in the Limit: Noise, Loss, and Feedback

• URL: http://arxiv.org/abs/2507.15319v1
• Date: Mon, 21 Jul 2025 07:18:04 GMT
• Title: Language Generation in the Limit: Noise, Loss, and Feedback
• Authors: Yannan Bai, Debmalya Panigrahi, Ian Zhang,
• Abstract summary: We show that a finite union of uniformly generatable collections is generatable in the limit, and asked if the same is true for non-uniform generation.<n>We show the equivalence of these models for uniform and non-uniform generation, and provide a characterization of non-uniform noisy generation.
• Score: 10.280148603465697
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Kleinberg and Mullainathan (2024) recently proposed a formal framework called language generation in the limit and showed that given a sequence of example strings from an unknown target language drawn from any countable collection, an algorithm can correctly generate unseen strings from the target language within finite time. This notion was further refined by Li, Raman, and Tewari (2024), who defined stricter categories of non-uniform and uniform generation. They showed that a finite union of uniformly generatable collections is generatable in the limit, and asked if the same is true for non-uniform generation. We begin by resolving the question in the negative: we give a uniformly generatable collection and a non-uniformly generatable collection whose union is not generatable in the limit. We then use facets of this construction to further our understanding of several variants of language generation. The first two, generation with noise and without samples, were introduced by Raman and Raman (2025) and Li, Raman, and Tewari (2024) respectively. We show the equivalence of these models for uniform and non-uniform generation, and provide a characterization of non-uniform noisy generation. The former paper asked if there is any separation between noisy and non-noisy generation in the limit -- we show that such a separation exists even with a single noisy string. Finally, we study the framework of generation with feedback, introduced by Charikar and Pabbaraju (2025), where the algorithm is strengthened by allowing it to ask membership queries. We show finite queries add no power, but infinite queries yield a strictly more powerful model. In summary, the results in this paper resolve the union-closedness of language generation in the limit, and leverage those techniques (and others) to give precise characterizations for natural variants that incorporate noise, loss, and feedback.

Related papers

• On Union-Closedness of Language Generation [48.36356615217017]
  We investigate language generation in the limit - a model by Kleinberg and Mullainathan and extended by Li, Raman, and Tewari.<n>Our results resolve two open questions of Li et al. by proving finite unions of generatable or non-uniformly generatable classes need not be generatable.<n>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.
  arXiv  Detail & Related papers  (2025-06-23T13:42:25Z)
• Representative Language Generation [4.601683217376771]
  "representative generation" is extended to address diversity and bias concerns in generative models.<n>We demonstrate feasibility for countably infinite hypothesis classes and collections of groups under certain conditions.<n>Our findings provide a rigorous foundation for developing more diverse and representative generative models.
  arXiv  Detail & Related papers  (2025-05-27T23:02:54Z)
• On Characterizations for Language Generation: Interplay of Hallucinations, Breadth, and Stability [16.30681257128492]
  [KM24] is an algorithm for generating from any countable language collection in the limit.<n>Recent work introduces different notions of breadth and explores when generation with breadth is possible.<n>Our results show that generation with many existing notions of breadth becomes equally hard, when stability is required.
  arXiv  Detail & Related papers  (2024-12-24T16:24:43Z)
• Exploring Facets of Language Generation in the Limit [10.18252143035175]
  We show that every countable language collection has a generator which has the stronger property of non-uniform generation in the limit.<n>We formalize the tension between validity and breadth in the generation algorithm of [KM24] by introducing a definition of exhaustive generation.<n>We also provide a precise characterization of the language collections for which exhaustive generation is possible.
  arXiv  Detail & Related papers  (2024-11-22T22:13:40Z)
• On the Limits of Language Generation: Trade-Offs Between Hallucination and Mode Collapse [16.30681257128492]
  Given samples from an unknown language, a language model should produce valid strings not seen in training.<n>Otherwise, outputting invalid strings constitutes "hallucination," and failing to capture the full range leads to "mode collapse"<n>We investigate this within a statistical language generation setting building on Gold and Angluin.
  arXiv  Detail & Related papers  (2024-11-14T18:06:55Z)
• Unlocking Anticipatory Text Generation: A Constrained Approach for Large Language Models Decoding [75.06872859716049]
  Large Language Models (LLMs) have demonstrated a powerful ability for text generation. undesired behaviors such as toxicity or hallucinations can manifest. We propose formalizing text generation as a future-constrained generation problem.
  arXiv  Detail & Related papers  (2023-12-11T06:35:33Z)
• The Stable Entropy Hypothesis and Entropy-Aware Decoding: An Analysis and Algorithm for Robust Natural Language Generation [59.7381286976957]
  We show that human-like'' generations usually lie in a narrow and nearly flat entropy band. We propose an entropy-aware decoding algorithm that respects these entropy bounds.
  arXiv  Detail & Related papers  (2023-02-14T02:02:33Z)
• Generating Sequences by Learning to Self-Correct [64.0249217590888]
  Self-Correction decouples an imperfect base generator from a separate corrector that learns to iteratively correct imperfect generations. We show that Self-Correction improves upon the base generator in three diverse generation tasks.
  arXiv  Detail & Related papers  (2022-10-31T18:09:51Z)
• Locally Typical Sampling [84.62530743899025]
  We show that today's probabilistic language generators fall short when it comes to producing coherent and fluent text.<n>We propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models.
  arXiv  Detail & Related papers  (2022-02-01T18:58:45Z)
• Conditional Hybrid GAN for Sequence Generation [56.67961004064029]
  We propose a novel conditional hybrid GAN (C-Hybrid-GAN) to solve this issue. We exploit the Gumbel-Softmax technique to approximate the distribution of discrete-valued sequences. We demonstrate that the proposed C-Hybrid-GAN outperforms the existing methods in context-conditioned discrete-valued sequence generation.
  arXiv  Detail & Related papers  (2020-09-18T03:52:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.