We study the feasibility of identifying epistemic uncertainty (reflecting a lack of knowledge), as opposed to aleatoric uncertainty (reflecting entropy in the underlying distribution), in the outputs of large language models (LLMs) over free-form text. In the absence of ground-truth probabilities, we explore a setting where, in order to (approximately) disentangle a given LLM's uncertainty, a significantly larger model stands in as a proxy for the ground truth. We show that small linear probes trained on the embeddings of frozen, pretrained models accurately predict when larger models will be more confident at the token level and that probes trained on one text domain generalize to others. Going further, we propose a fully unsupervised method that achieves non-trivial accuracy on the same task. Taken together, we interpret these results as evidence that LLMs naturally contain internal representations of different types of uncertainty that could potentially be leveraged to devise more informative indicators of model confidence in diverse practical settings.

One good way to frame the question of the limits of Deep Learning is in the context of the Principle of Computational Equivalence by Stephen Wolfram. Wolfram showed that simple cellular automation are able to exhibit complex behaviour that cannot be predicted from initial conditions or the simple rules that specify its incremental behaviour. Certain kinds of cellular automata can exhibit complex behaviour that cannot be reduced to a mathematical model that capture its behaviour in closed form. Wolfram examples of an'irreducible' system that exhibits this complex behaviour are the brain and weather systems. Wolfram classifies these kinds of systems as exhibiting "Universality".