Kedar Karhadkar

Kedar Karhadkar

Math PhD student at UCLA

Blog posts

2025

Deep sets as universal approximators

3 minute read

Published:

Deep sets are a family of neural networks which parameterize functions on sets. The problem is as follows. Let $X$ be a compact Hausdorff space. We might be able to parameterize arbitrary continuous functions $X \to \mathbb{R}$ with universal approximators (e.g. MLPs). What if we instead need to parameterize functions $X^n \to \mathbb{R}$ which are permutation invariant? That is, we want functions $f$ such that

2024

Numerical submersions

1 minute read

Published:

Let $m \geq n$, and let $f: \mathbb{R}^m \to \mathbb{R}^n$ be a submersion. Then $f$ is not necessarily surjective. Consider, for example, $m = n = 1$, and $f(x) = \arctan(x)$. But this function fails to be surjective for a boring reason: it has a vanishing gradient as $x \to \infty$.