Large language models are trained to predict the most likely next word based on their training data. But likely is not the same as true: rare events happen every day, and repeated lies remain false. Relying on likelihood alone can make models produce fluent but incorrect outputs, a problem known as hallucination.
The authors argue that truth should be judged by invariance, meaning a statement is true if it holds steady across many different situations or transformations of the environment. They draw on philosophy (Nozick's view that objective facts are what remain unchanged when perspective shifts) and on machine learning work about out-of-distribution generalization.
The main finding is that likelihood is neither necessary nor sufficient for truth, and invariance offers a better criterion. This matters because it points toward building AI systems that can distinguish what is merely probable from what is actually true, particularly when deployed in new, unfamiliar environments.