Theoretical Proof that Generated Text in the Corpus Leads to the Collapse of Auto-regressive Language Models

Auto-regressive language models (LMs) have been widely used to generate text on the World Wide Web. The generated text is often collected into the training corpus of the next generations of LMs. Previous work experimentally found that LMs collapse when trained on recursively generated text. This paper presents theoretical proof that once a corpus (such as the World Wide Web) begins to incorporate generated text, and the training text of each LM is sampled from this corpus, then no matter how small the amount of text generated by each LM that enters the corpus is, after a sufficient amount of time, LM collapse is bound to occur. Our proof is validated by a series of experiments showing that the collapsed LMs perform no better than an untrained LM with randomly initialized parameters. By proving the existence of LM collapse, we express our concerns about the current situation in which an increasing amount of generated text may be used in LM training. The source code is available in the online data warehouse:this https URL