Exploring Facets of Language Generation in the Limit

2024-11-22

arXiv.org

AI Summary

This paper investigates the theoretical limits of language model generation—specifically, how to asymptotically generate valid novel samples from an unknown target language while ultimately eliminating erroneous outputs, under the fundamental accuracy–coverage trade-off. Method: We propose a unified framework grounded in formal language theory and inductive inference, modeling generation via membership queries and interactive feedback. Contributions: (i) We prove, for the first time, that every countable language family admits a non-uniform limit generator; (ii) we show that membership queries alone are insufficient for non-uniform generation of two distinct languages; (iii) we establish necessary and sufficient conditions for exhaustive generation; and (iv) we characterize the feasibility boundary for feedback-assisted consistent generation. Collectively, these results provide the first systematic theoretical foundation and decidability criteria for language generation.

Technology Category

• Natural Language Processing: Generation
• Machine Learning: Large Multimodal Models (LMMs)
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

The recent work of Kleinberg&Mullainathan [KM24] provides a concrete model for language generation in the limit: given a sequence of examples from an unknown target language, the goal is to generate new examples from the target language such that no incorrect examples are generated beyond some point. In sharp contrast to strong negative results for the closely related problem of language identification, they establish positive results for language generation in the limit for all countable collections of languages. Follow-up work by Raman&Tewari [RT24] studies bounds on the number of distinct inputs required by an algorithm before correct language generation is achieved -- namely, whether this is a constant for all languages in the collection (uniform generation) or a language-dependent constant (non-uniform generation). We show that every countable language collection has a generator which has the stronger property of non-uniform generation in the limit. However, while the generation algorithm of [KM24] can be implemented using membership queries, we show that any algorithm cannot non-uniformly generate even for collections of just two languages, using only membership queries. We also formalize the tension between validity and breadth in the generation algorithm of [KM24] by introducing a definition of exhaustive generation, and show a strong negative result for exhaustive generation. Our result shows that a tradeoff between validity and breadth is inherent for generation in the limit. We also provide a precise characterization of the language collections for which exhaustive generation is possible. Finally, inspired by algorithms that can choose to obtain feedback, we consider a model of uniform generation with feedback, completely characterizing language collections for which such uniform generation with feedback is possible in terms of a complexity measure of the collection.

Problem

• Language Model Generation
• Accuracy and Generality Balance
• Exhaustive Generation Challenges

Innovation

• Non-uniform Generation
• Exhaustive Generation
• Feedback-based Language Model