layout: post | title: “New preprint on relative causal knowledge.” | date: 2025-03-13 9:07:00 +0100 | categories: preprints

Fresh off the press 📢 The Relativity of Causal Knowledge

Abstract: Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

THANK YOU to Claudio Battiloro for working side by side with me on this exciting project and making this article possible. Big thanks also to Hans Riess and Fabio Massimo Zennaro for their valuable feedback on an earlier version of the paper.

Below is why you should check out our paper.

If you’re into causality, we introduce the notion of perspective into Structural Causal Models (SCMs), making them subjective. But don’t worry, we’re not abandoning Pearl’s framework, we’re building on it. In fact, we define a new category of SCMs that retains the expressivity, while allowing for relative causal knowledge. Plus, causal abstraction plays a key role, highlighting its importance from a fresh angle. These are all relatively unexplored areas, so there’s a lot of work to be done!

If you are into mathematics, we introduce new category-theoretic objects and network (co)sheaves. This takes us beyond the familiar Vect/Hilb categories into convex spaces of probability measures. A full cohomology theory and an algebraic description of these cellular sheaves still need to be developed, ultimately leading to a spectral theory for relative causal knowledge.

And if you’re an AI/ML researcher, there’s plenty for you too. Our work lays the foundation for network sheaf inference and discovery in the context of relative causal knowledge, definitely novel and nontrivial research directions. Plus, reinforcement learning looks like a promising approach given our framework.