The 1W-MINDS Seminar was founded in the early days of the COVID-19 pandemic to mitigate the impossibility of travel. We have chosen to continue the seminar since to help form the basis of an inclusive community interested in mathematical data science, computational harmonic analysis, and related applications by providing free access to high quality talks without the need to travel. In the spirit of environmental and social sustainability, we welcome you to participate in both the seminar, and our slack channel community! Zoom talks are held on Thursdays at 2:30 pm New York time. To find and join the 1W-MINDS slack channel, please click here.
Current Organizers (September 2026 - May 2027): March Boedihardjo (Michigan State University), Hung-Hsu Chou (University of Pittsburgh), Longxiu Huang (Michigan State University), Mark Iwen (Principal Organizer, Michigan State University), and Kunlun Qi (Michigan State University).
Most previous talks are on the seminar YouTube channel. You can catch up there, or even subscribe if you like.
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To join MINDS slack channel, click here.
Passcode: the smallest prime > 100
The Johnson--Lindenstrauss lemma asserts that every set of $n$ points in $d$-dimensional Euclidean space embeds into $O(\varepsilon^{-2}\log n)$-dimensional Euclidean space with distortion at most $1+\varepsilon$. Larsen and Nelson conjectured that the optimal target dimension throughout the full range of the parameters $n,d, \varepsilon$ is
\[
\Theta\left(\min\left\{d,n-1,\frac{\log(2+\varepsilon^2n)}{\varepsilon^2}\right\}\right).
\]
In this talk, we will discuss a proof of this conjecture.
Given a feedforward ReLU neural network with a finite sample, prior works by Freeman, Bruna, Nguyen, Hein and many others have established results on the connectivity of sublevel sets of the loss function on different settings. With Eli Grigsby and Kathryn Lindsey, we proved that if all hidden layers have width at least the same as the number of samples, the zero loss set is path connected. We also show that this width bound is optimal: for shallow networks where the hidden layer has one fewer neuron than the sample, one can choose the sample points so that this set is no longer connected. I will also discuss further examples we found for the mechanism for disconnectedness and possible implications these may have on the training dynamics.