arXiv:2507.08017v1 Announce Type: cross Abstract: Recent findings in mechanistic interpretability (MI), the field probing the inner workings of Large Language Models (LLMs), challenge the view that these models rely solely on superficial statistics. Here, we offer an accessible synthesis of these findings that doubles as an introduction to MI, all while integrating these findings within a novel theoretical framework for thinking about machine understanding. We argue that LLMs develop internal structures that are functionally analogous to the kind of understanding that consists in seeing connections. To sharpen this idea, we propose a three-tiered conception of machine understanding. First, conceptual understanding emerges when a model forms "features" as directions in latent space, thereby learning the connections between diverse manifestations of something. Second, state-of-the-world understanding emerges when a model learns contingent factual connections between features and dynamically tracks changes in the world. Third, principled understanding emerges when a model ceases to rely on a collection of memorized facts and discovers a "circuit" that connects these facts. However, we conclude by exploring the "parallel mechanisms" phenomenon, arguing that while LLMs exhibit forms of understanding, their cognitive architecture remains different from ours, and the debate should shift from whether LLMs understand to how their strange minds work.