About

In technical terms, a Circuit-Wasserstein ball is an uncertainty set defined by the Circuit-Wasserstein distance—a Wasserstein-type metric between probabilistic circuits that restricts couplings to coupling circuits, remains a metric on compatible circuits, and upper-bounds the classical Wasserstein distance while staying tractable for structured-decomposable PCs:

In community terms, it is the neighborhood we are willing to defend in public.

Our reading list begins withOptimal Transport for Probabilistic Circuits, which introduces the Circuit-Wasserstein distance and its transport plans, and continues withPeTeR, which uses ε-Circuit-Wasserstein balls for data-free post-training robustification. Everything else on this site is commentary, minutes, and the occasional clarification.

What we are not

We are not a fan club for Big Wasserstein. Big Wasserstein is expensive, often intractable, and has a habit of arriving late to meetings with a linear program the size of a continent. We treat it as a theoretical antagonist: useful to name, unwise to worship, and never to be confused with the circuit distances ($\mathsf{CW}$) we can actually compute.

We are also not OpenCW. OpenCW is a well-funded parody of openness that appears to conduct Circuit-Wasserstein research behind closed doors. If their blog posts sound familiar, that is coincidental. If their internal memos sound familiar, that is concerning.

What we publish

• Dispatches on $\mathsf{CW}$ distances, coupling circuits, and ε-ball etiquette
• Notes on PeTeR-style robustification without retraining from scratch
• Public minutes, corrections, and gently hostile asides about closed research

“If the coupling is not a circuit, we do not call it Circuit-Wasserstein. If the ball is not public, we do not call it ours.”

Membership is informal. If you can say “compatible structured-decomposable PC” without flinching, you are already close enough.