No, NYT journalists do not know linear algebra. In fact, I think this is a microcosm of a complex but large media shift ahead. Let me explain. For decades, prior to modern social media, the people who wrote the mainstream media articles we read were professional journalists. They certainly often had an establishment bias and less diversity of viewpoints, which some decry now. But this also had a real advantage: it encouraged a culture of rigor factual review and a sense of professional responsibility, something that is fostered by the best news organizations. However, what was taken for granted was that journalists were invariably college graduates in humanities or social studies. People who fundamental loved writing and stories and language. People with some academic focus in liberal arts and not STEM. Since the rise of social media and podcasts, attention is driven by different people. Often with different backgrounds, and increasingly a subset are much more technical. The math nerds did well. This is a good thing, because increasingly, understanding the technologies that shape our economy requires analytical or technical skills. So we are now seeing how apparent it is we were missing basic technical literacy in journalism for a long time. At the same time, the shift from mainstream media means we are losing something. It is the depth of the professional writer or journalist. And most technology-savvy bloggers and podcasters are not strong here. This is a serious issue, because just as French literature doesn’t help you understand eigenvectors, knowing LLM training doesn’t help you understand history or politics or the nuanced responsibilities of being a public intellectual. My hope is that somehow we’ll see a rise of the polymath, rigorous, ethical, and analytical writer. Or the rise of smaller journalistic orgs that combine such skills in new ways. In these rapidly evolving times, we certainly need it.

Goodness, “Symmetry” in ML is much deeper and more beautiful than that. It lives in very matrices (tensors) through which we impose or discover structure in the data. CNNs take advantage of the knowledge that a cat is a cat whether it’s at the upper-right or lower-left of an image—translational invariance (equivariance for the fastidious). And generalization emerges when models discover symmetries in data, when their internal operations A commute with the transformations T that leave meaning unchanged, i.e. AT = TA