Classical learning theory makes a clear prediction. A model with far more parameters than training examples should memorise the data and fail on anything new, and the bounds that formalise this intuition are elegant and were considered settled. Modern deep networks have orders of magnitude more parameters than data points, can fit pure random labels when asked, and nonetheless generalise well on real tasks. That is not a minor discrepancy at the edge of a theory, it is the central prediction failing in the most visible possible way, and a remarkable amount of teaching in this field simply declines to mention it.
This course is where the discrepancy gets confronted. The first section builds the classical apparatus properly, uniform convergence, Rademacher complexity, covering numbers, margin theory, the generalisation bounds that follow. You need this even though it does not explain deep learning, partly because it is genuinely correct within its assumptions and partly because you cannot appreciate why the deep learning case is strange until you understand what the theory predicts. Tengyu Ma teaches it cleanly and does not pad it.
The second section is the interesting one. The course moves into non-convex optimisation, why gradient descent finds good solutions in a landscape with no convexity guarantees, the neural tangent kernel and the infinite-width limit that makes some analysis tractable, and implicit regularisation, the idea that the optimiser itself has preferences beyond the loss function it is minimising and that those preferences are doing work we did not ask for and do not fully understand. What I appreciated most is the candour. Ma is explicit about which results are satisfying, which are partial, and which rely on assumptions that do not hold for any network anyone actually trains.
The infinite-width results are a good example, mathematically real and importantly not a description of the finite networks in production, and the course says so rather than letting the student assume the question is closed. That honesty is rarer than it should be in theory teaching, where there is a temptation to present a tidy narrative and let the gaps go unmentioned. The lecture notes deserve separate praise and are, for many people, the better artefact. They are carefully written, maintained on GitHub, and complete enough to work through independently.
Video availability varies by offering and the recording quality is inconsistent, so my practical recommendation is to treat the notes as primary and use whichever lecture videos you can find as support when a derivation resists you. That is the opposite of my usual advice and it is right in this case. The prerequisites are serious and understating them would do nobody a favour. You need real analysis, probability at the level where concentration inequalities are tools rather than obstacles, and enough mathematical maturity that a proof several steps long does not lose you.
This is not a course you can follow passively while doing something else. If you have not proved things recently, expect to be slow at first, and expect that to be normal rather than a signal to stop. The honest caveat about usefulness is that there is very little here that will change your practice. Understanding Rademacher complexity will not improve your validation accuracy.
The value is different in kind, it is about no longer accepting that things work for reasons nobody can articulate, and about being able to evaluate a claim in a paper rather than taking it on trust. That matters enormously for some people and not at all for others, and I would rather say so than pretend theory pays immediate practical dividends. Four point two. Excellent within its scope, with the rating reflecting the narrow audience and the uneven video situation rather than any weakness in the teaching.