This summer, I participated in several interesting conferences. This entry documents my slides and describes a few of my favorite talks from the summer. Here are links to my talks:

- Packings in real projective spaces, FoCM and SPIE
- Explicit restricted isometries, ILAS
- Probably certifiably correct k-means clustering, ILAS
- Equiangular tight frames from association schemes, SIAM AG17
- Open problems in finite frame theory, SIAM AG17

Now for my favorite talks from FoCM, ILAS, SIAM AG17 and SPIE:

**Ben Recht — Understanding deep learning requires rethinking generalization**

In machine learning, you hope to fit a model so as to be good at prediction. To do this, you fit to a training set and then evaluate with a test set. In general, if a simple model fits a large training set pretty well, you can expect the fit to generalize, meaning it will also fit the test set. By conventional wisdom, if the model happens to fit the training set exactly, then your model is probably not simple enough, meaning it will not fit the test set very well. According to Ben, this conventional wisdom is wrong. He demonstrates this by presenting some observations he made while training neural nets. In particular, he allowed the number of parameters to far exceed the size of the training set, and in doing so, he fit the training set exactly, and yet he still managed to fit the test set well. He suggested that generalization was successful here because stochastic gradient descent implicitly regularizes. For reference, in the linear case, stochastic gradient descent (aka the randomized Kaczmarz method) finds the solution of minimal 2-norm, and it converges faster when the optimal solution has smaller 2-norm. Along these lines, Ben has some work to demonstrate that even in the nonlinear case, fast convergence implies generalization.