Keenan Crane

keenancrane.bsky.social

10 October 2026 07:05

We often think of an "equilibrium" as something standing still, like a scale in perfect balance. But many equilibria are dynamic, like a flowing river which is never changing—yet never standing still. These dynamic equilibria are nicely described by so-called "detailed balance"

Keenan Crane

keenancrane.bsky.social

10 October 2026 07:02

My student Zoë Marschner has a nice paper that discusses the difference, why it matters, and what you can do about it (in the setting of neural SDFs): zoemarschner.com/research/csg...

Keenan Crane

keenancrane.bsky.social

10 October 2026 07:02

I don't know who needs to hear this but: "SDF" has, for some, become a catch-all term that actually means "a function that tells you if you're inside/outside a shape, and a number that roughly indicates how far." A true signed *distance* function really gives you *distance.*

Keenan Crane

keenancrane.bsky.social

10 October 2026 07:01

Here's a nice "proof without words": The sum of the squares of several positive values can never be bigger than the square of their sum. This picture helps make sense of how ℓ₁ and ℓ₂ norms regularize and sparsify solutions (resp.). [1/n]

Keenan Crane

keenancrane.bsky.social

10 October 2026 07:00

I'll let you in on one of my deep diagramming secrets: When I see a “square”, I replace it with a square. When I see a “cube”, I replace it with a cube. It's easy to forget where these words come from. The only mistake we made as a species is not calling numbers “segments.”