On the Limits of Language Generation: Trade-Offs Between Hallucination and Mode Collapse (2411.09642v2)

Abstract: Specifying all desirable properties of a LLM is challenging, but certain requirements seem essential. Given samples from an unknown language, the trained model should produce valid strings not seen in training and be expressive enough to capture the language's full richness. Otherwise, outputting invalid strings constitutes "hallucination," and failing to capture the full range leads to "mode collapse." We ask if a LLM can meet both requirements. We investigate this within a statistical language generation setting building on Gold and Angluin. Here, the model receives random samples from a distribution over an unknown language K, which belongs to a possibly infinite collection of languages. The goal is to generate unseen strings from K. We say the model generates from K with consistency and breadth if, as training size increases, its output converges to all unseen strings in K. Kleinberg and Mullainathan [KM24] asked if consistency and breadth in language generation are possible. We answer this negatively: for a large class of LLMs, including next-token prediction models, this is impossible for most collections of candidate languages. This contrasts with [KM24]'s result, showing consistent generation without breadth is possible for any countable collection of languages. Our finding highlights that generation with breadth fundamentally differs from generation without breadth. As a byproduct, we establish near-tight bounds on the number of samples needed for generation with or without breadth. Finally, our results offer hope: consistent generation with breadth is achievable for any countable collection of languages when negative examples (strings outside K) are available alongside positive ones. This suggests that post-training feedback, which encodes negative examples, can be crucial in reducing hallucinations while limiting mode collapse.

• The paper shows that next-token prediction models often cannot achieve both consistency and breadth simultaneously.
• It introduces a statistical framework and subset oracle constructs to analyze trade-offs and quantify learning rates in language generation.
• The study underscores the need for innovative training strategies to mitigate hallucinations while maintaining linguistic diversity.

Trade-Offs Between Hallucination and Mode Collapse in Language Generation Models

The challenge of balancing hallucination and mode collapse in language generation models is a critical issue for their efficacy and reliability. Hallucination occurs when a model generates plausible-sounding but incorrect outputs, while mode collapse leads to a lack of diversity in generated outputs. The key question tackled by the paper is whether it is feasible for a LLM to avoid both hallucination and mode collapse, and under what conditions this balance is possible.

Framework and Definitions

The authors investigate this problem within a statistical framework, focusing on generating unseen strings from a target language $K$. The model is provided with samples drawn from $K$, belonging to a possibly infinite collection of candidate languages. Language generation models are explored in terms of two critical properties: consistency, meaning the model does not hallucinate, and breadth, meaning the model captures diverse aspects of the target language without mode collapse.

Language collections are defined in a manner rooted in the tradition of Gold and Angluin's works on language identification. A model achieves consistency and breadth if its support converges to the set of all unseen strings in $K$ as the training set size grows. The authors examine the trade-offs between achieving consistency and breadth and provide insights into the conditions under which both properties can be satisfied or are mutually exclusive.

Main Contributions and Results

1. Impossibility of Consistency with Breadth: The paper establishes that for a broad class of LLMs, particularly those built on the next-token prediction paradigm, it is generally impossible to achieve both consistency and breadth. This contrastingly highlights the core distinction between generating with and without breadth.
2. Decidability and Rate of Generation: A major contribution is defining a class of generators for which the Membership Oracle Problem (MOP) is decidable. A key result is that certain iterative token-by-token generators, such as those used in contemporary LLMs, are shown to fit this category.
3. Statistical Learning Rates: The research also includes an in-depth analysis of the statistical learning rates achievable by LLMs. Exponential rates for consistent generation are shown to be possible for countable language collections, while achieving breadth imposes additional limitations equivalent to language identification.
4. Algorithmic Constructs: An approach leveraging subset oracles is proposed, providing a framework to identify languages without requiring tell-tale oracle access. This opens pathways for consistent generation under more complex settings, evidently useful for collections that satisfy Angluin's criteria.

Implications and Future Work

The implications of this research are significant for the future of LLM development. The findings underscore the inherent limitations of balancing hallucination avoidance with capturing linguistic diversity. This impacts practical applications such as AI-based text generation, where trustworthiness and versatility are often competing goals.

The negative results concerning consistency with breadth suggest that additional human feedback or supervised correction during model training could play a crucial role in mitigating hallucinations. This highlights the ongoing need for innovative training protocols, possibly involving negative examples, to enhance model reliability and expression capabilities.

Furthermore, the research opens several avenues for future development in AI. Expanding the family of languages for which consistency and breadth can simultaneously be achieved remains an open question. Investigating alternative generation methods that lie beyond the limitations imposed by current model architectures might yield substantial progress toward overcoming these trade-offs.

In conclusion, while achieving both consistency and breadth simultaneously in language generation models remains a tough challenge, this paper lays down a detailed theoretical foundation and points to directions where future innovations are needed to enhance model performance in these regards.