Language Generation in the Limit (2404.06757v1)

Abstract: Although current LLMs are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new strings from the language that don't already appear in the training data. Here we ask what we can conclude about language generation using only this specification, without further assumptions. In particular, suppose that an adversary enumerates the strings of an unknown target language L that is known only to come from one of a possibly infinite list of candidates. A computational agent is trying to learn to generate from this language; we say that the agent generates from L in the limit if after some finite point in the enumeration of L, the agent is able to produce new elements that come exclusively from L and that have not yet been presented by the adversary. Our main result is that there is an agent that is able to generate in the limit for every countable list of candidate languages. This contrasts dramatically with negative results due to Gold and Angluin in a well-studied model of language learning where the goal is to identify an unknown language from samples; the difference between these results suggests that identifying a language is a fundamentally different problem than generating from it.

• The paper establishes that language generation is always feasible in adversarial settings, contrasting sharply with the impossibility of language identification.
• It introduces the concept of 'generation in the limit,' enabling an agent to produce previously unseen language elements from a finite sample sequence.
• The research extends to robust prompt-driven methods, offering fresh insights into the inherent capabilities of language models and their practical applications.

Language Generation under Adversarial Conditions

Introduction

The advent of LLMs has catalyzed a renewed interest in the theoretical underpinnings of language generation. A fundamental aspect of language generation involves producing unseen strings from a given language based on a finite sample. This task assumes an adversarial setting where an unknown target language is gradually revealed. Contrasting with the known challenge in language identification, this paper introduces a nuanced perspective that showcases the feasibility of language generation in an adversarial context.

Core Results

The principal finding of the research is that language generation, unlike language identification, is always feasible under the classical adversarial model. The paper establishes that there exists an agent capable of generating new elements from the target language after observing a finite sequence of samples, even when the language comes from a possibly infinite list of candidates. This result provides a striking contrast to the well-documented impossibility of language identification for even simple language families in a similar setting.

Methodological Insights

The methodology hinges on a nuanced understanding of the adversarial model, distinguishing between language identification and generation. The authors employ the notion of "generation in the limit," wherein an agent is tasked with producing strings from the unseen remainder of the language post a finite enumeration of samples. This approach sidesteps the impossibility results tied to language identification by focusing on continual generation from the evolving knowledge of the language.

Implications for LLMling

This research subtly underscores that the effectiveness of LLMs might not solely depend on their ability to capture distributional properties or empirical regularities in language. Instead, it points towards a more intrinsic capability tied to the essence of language generation, suggesting that the underlying challenge is more tractable than previously thought, even in the absence of probabilistic assumptions or regularities. This perspective potentially invites a reevaluation of current methodologies and assumptions in the field of generative language processing.

Extension to Prompted Generation

An intriguing extension of this work examines the role of prompts in the language generation process. By introducing the concept of "robust" prompts—those allowing for an arbitrary prolongation fitting within any candidate language—the paper extends its main results to scenarios more closely mirroring practical language generation tasks. Furthermore, when considering non-trivial prompts, where each prompt guarantees at least one valid continuation, the research delineates the conditions under which successful generation can be achieved, albeit with the aid of computationally more potent models capable of answering specific queries about the inclusion relation between languages and regular sets.

Conclusion

The insights presented in this paper not only challenge the prevailing narratives around the complexity of language generation in the face of adversarial constraints but also broaden the horizon for understanding the fundamental capabilities of LLMs. By distinguishing between the tasks of identification and generation, the research paves the way for developing a more nuanced theory of language learning and generation, potentially influencing future explorations in the generative capabilities of artificial intelligence.