Posts

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.

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?

Several new architectures for neural networks, such as Neural ODEs and deep equlibirum models can be understood as replacing classical layers that explicitly specify how to compute the output with implicit layers. These layers describe which conditions the output should specify but leave the actual computation up to some solver that can be chosen arbitrarily. This post contains a brief introduction to the main ideas behind implicit layers.

Reinforcement Learning consists of a few key building blocks that can be combined to create many of the well-known algorithms. Framing RL in terms of these building blocks can give a good overview and better understanding of these algorithms. This is the conclusion of a series with such an overview, covering model-based RL.

L1 regularization is famous for leading to sparse optima, in contrast to L2 regularization. There are several ways of understanding this but I’ll argue that it’s really all about one fact: the L1 norm has a singularity at the origin, while the L2 norm does not. And this is not just true for L1 and L2 regularization: singularities are always necessary to get sparse weights.

There is a “complexity barrier”: a number such that we can’t prove the Kolmogorov complexity of any specific string to be larger than that. The proof of this astonishing fact is closely related to some famous paradoxa and we’ll use this connection to get a better intuition for why the complexity barrier exists.

Reinforcement Learning consists of a few key building blocks that can be combined to create many of the well-known algorithms. Framing RL in terms of these building blocks can give a good overview and better understanding of these algorithms. This is part 2 of a series with such an overview, covering some policy optimization methods.

Proving things for object that have a lot of structure can be harder than for object with less structure, simply because the tree of possible proofs is much wider. This is probably why trying to prove a more general case is sometimes a helpful strategy.

In both classical mechanics and QM, there are transformations between position-based and momentum-based representations that preserve the dynamical laws. So from a mathematical perspective, position and momentum seem to play equivalent roles in physics. But they don’t play equivalent roles in our cognition, which is part of the physical universe – seemingly a paradox.

Reinforcement Learning consists of a few key building blocks that can be combined to create many of the well-known algorithms. Framing RL in terms of these building blocks can give a good overview and better understanding of these algorithms. This is part 1 of a series with such an overview, covering value-based methods (mainly in a tabular setting).