No Free Lunch: Fundamental Limits of Learning Non-Hallucinating Generative Models
Changlong Wu, Ananth Grama, Wojciech Szpankowski
TL;DR
This paper formalizes the challenge of non-hallucinating learning in generative models by introducing a learning-theoretic framework with a facts set $\mathcal{T}$ and a hallucination rate $\mathsf{hall}$. It shows a no-free-lunch barrier for agnostic, proper learning, even with a tiny hypothesis class, and then demonstrates that incorporating knowledge of $\mathcal{T}$—via a finite-VC-dimension concept class $\mathcal{C}$—enables non-hallucinating learning in the improper setting, with tight sample complexity bounds. For proper learning, it identifies an informativeness condition on the demonstrator that makes non-hallucinating learning feasible, while also proving lower bounds and illustrating hard instances. Overall, the work clarifies fundamental limits and highlights the need for inductive biases or domain-specific factual constraints (e.g., human feedback or rules) to curb hallucinations in generative models.
Abstract
Generative models have shown impressive capabilities in synthesizing high-quality outputs across various domains. However, a persistent challenge is the occurrence of "hallucinations", where the model produces outputs that are plausible but invalid. While empirical strategies have been explored to mitigate this issue, a rigorous theoretical understanding remains elusive. In this paper, we develop a theoretical framework to analyze the learnability of non-hallucinating generative models from a learning-theoretic perspective. Our results reveal that non-hallucinating learning is statistically impossible when relying solely on the training dataset, even for a hypothesis class of size two and when the entire training set is truthful. To overcome these limitations, we show that incorporating inductive biases aligned with the actual facts into the learning process is essential. We provide a systematic approach to achieve this by restricting the facts set to a concept class of finite VC-dimension and demonstrate its effectiveness under various learning paradigms. Although our findings are primarily conceptual, they represent a first step towards a principled approach to addressing hallucinations in learning generative models.