No Free Lunch: Fundamental Limits of Learning Non-Hallucinating Generative Models

TL;DR

This paper provides a theoretical analysis of the fundamental limits in learning non-hallucinating generative models, showing that relying solely on data is insufficient and that inductive biases are necessary for factual accuracy.

Contribution

It introduces a formal framework for understanding the learnability of non-hallucinating models and demonstrates the necessity of inductive biases with finite VC-dimension to overcome inherent limitations.

Findings

Learning non-hallucinating models from data alone is statistically impossible.

Incorporating inductive biases aligned with facts is essential for factual correctness.

The approach is effective across various learning paradigms.

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.