Learning Macro Variables with Auto-encoders

Most causal variables that we reason over, in both science and everyday life, are coarse abstractions of low-level data. However, despite their importance, the field of causality lacks a precise theory of abstract "macro" variables and their relation to low-level "micro" variables that can account for our intuitions. Here, we define a macro variable as something that (a) is simpler than its micro variable, (b) shares mutual information with its micro variable, and (c) is related to other macro variables via simple mechanisms. From this definition, we propose DeepCFL: a simple self-supervised method that learns macro variables and their relations. We empirically validate DeepCFL on synthetic tasks where the underlying macro variables are known, and find that they can be recovered with high fidelity. Given that the individual components of DeepCFL leverage standard and scalable techniques in deep learning, our preliminary results are encouraging signs that it can be successfully applied to real-world data.