Distributions Part II: What can we do with distributions?
As promised in part I, we can do a lot of the same things with Schwartz distributions as with classical functions. To see how, we’ll cover derivatives, convolutions, and Fourier transforms of distributions.
Mar 6, 2022
7 min read
Visualizing random vs grid search
Random search usually works better than grid search for hyperparameter optimization. This brief post suggests a way to visualize the reason for this geometrically.
Dec 22, 2021
2 min read
Extensions of Karger's algorithm
If you prefer videos, check out our ICCV presentation, which covers similar content as this blog post. For more details, see our paper. Karger’s contraction algorithm is a fast and very famous method for finding global minimum graph cuts.
Sep 10, 2021
8 min read
Distributions Part I: the Delta distribution
Did you always want to know kind of object this weird Dirac delta “function” actually is? Well, it’s a Schwartz distribution. If that doesn’t help much, then keep reading.
Jul 6, 2021
9 min read
Scripting for personal productivity
If you can program, you can use that to support your habits and automate some routines. This post gives a few examples.
Apr 14, 2021
5 min read
Troubles with the Bias-Variance tradeoff
The bias-variance tradeoff is a key idea in machine learning. But I’ll argue that we know surprisingly little about it: when does it hold? How does it relate to the Double Descent phenomenon? And what do we even formally mean when we talk about it?
Apr 7, 2021
13 min read
Collection of quick computer tips
Many of us spend a lot of time working with our computer, so it’s worth spending some time to make that experience as pleasent and productive as possible. This is a collection of tips that are relatively quick to implement and still very valuable in the long run in my opinion. Mainly geared towards developers and others who work with the shell a lot.
Mar 31, 2021
7 min read
State formally, reason informally
There’s a style of teaching mathematics that I really like: stating definitions and theorems as formally as in any textbook, but focusing on informal arguments for why they should be true.
Mar 24, 2021
4 min read
Emacs as an amazing LaTeX editor
Emacs has some really amazing features for writing LaTeX; this post gives an overview of some of them, either to convince you to give Emacs a try, or to make you aware that these features exist if you’re already using Emacs but didn’t know about them.
Mar 17, 2021
6 min read
Perspectives on spherical harmonics
Spherical harmonics are ubiquitous in math and physics, in part because they naturally appear as solutions to several problems; in particular they are the eigenfunctions of the spherical Laplacian and the irreducible representations of SO(3). But why should the solutions to these problems be the same? And why are they called spherical harmonics?
Mar 10, 2021
5 min read