A fine-grained look at causal effects in causal spaces

ArXi:2512.11919v3 Announce Type: replace-cross The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a patient's blood pressure (Y). However, in many modern data domains, the raw variables-such as pixels in an image or tokens in a language model-do not have the semantic structure needed to formulate meaningful causal questions.