Language models suffer from a curse of ambiguity

2026-08-15

AI Summary

This study addresses the learning difficulties arising from ambiguous discrete probability distributions in large language models by introducing the concept of the "Curse of Ambiguity." Through theoretical analysis and experiments on both synthetic and real-world datasets, we elucidate the fundamental mechanism whereby high-ambiguity distributions necessitate increased model capacity, embedding dimensions, and training steps while amplifying sampling noise. Our findings confirm the ubiquity of this phenomenon and explain its origins from architectural and learning dynamics perspectives. This work not only deepens the understanding of the statistical capabilities of large models but also provides a novel theoretical perspective and practical framework for evaluating the reliability of their output distributions.

Abstract

Large language models increasingly rely on sampling as a driver of their own improvement, making the fidelity of their learned distributions more critical than ever. Yet, not all distributions are equally easy to learn. In this work, we identify a curse of ambiguity: in large language models, and more broadly in all neural networks that produce discrete probability distributions, the more ambiguous a next-token distribution is, the harder it is to learn accurately. Through an extensive theoretical analysis, we trace this curse to architectural and learning roots. More ambiguous distributions require more capacity to be stored, larger embeddings to be represented, more steps to be fitted, and amplify token-sampling noise. We validate these findings on synthetic tasks with controlled ground truth and observe the same signatures in language models trained on real data. Our results provide a new perspective on the statistical capabilities of large language models and a practical framework for when to trust their output distribution.

Problem

• curse of ambiguity
• large language models
• discrete probability distributions
• next-token prediction
• distribution learning

Innovation

• Curse of Ambiguity
• Discrete Probability Distribution
• Learning Difficulty
• Token Sampling Noise
• Distribution Fidelity