Abstract
Research on Explainable Artificial Intelligence has recently started exploring the idea of producing explanations that, rather than being expressed in terms of low-level features, are encoded in terms of interpretable concepts learned from data. How to reliably acquire such concepts is, however, still fundamentally unclear. An agreed-upon notion of concept interpretability is missing, with the result that concepts used by both post hoc explainers and concept-based neural networks are acquired through a variety of mutually incompatible strategies. Critically, most of these neglect the human side of the problem: a representation is understandable only insofar as it can be understood by the human at the receiving end. The key challenge in human-interpretable representation learning (hrl) is how to model and operationalize this human element. In this work, we propose a mathematical framework for acquiring interpretable representations suitable for both post hoc explainers and concept-based neural networks. Our formalization of hrl builds on recent advances in causal representation learning and explicitly models a human stakeholder as an external observer. This allows us derive a principled notion of alignment between the machine's representation and the vocabulary of concepts understood by the human. In doing so, we link alignment and interpretability through a simple and intuitive name transfer game, and clarify the relationship between alignment and a well-known property of representations, namely disentanglement. We also show that alignment is linked to the issue of undesirable correlations among concepts, also known as concept leakage, and to content-style separation, all through a general information-theoretic reformulation of these properties. Our conceptualization aims to bridge the gap between the human and algorithmic sides of interpretability and establish a stepping stone for new research on human-interpretable representations.