The idea underneath: the causal state.

Two histories that lead to the same future are, for every practical purpose, the same situation. That is the whole idea, and it is surprisingly powerful.

An everyday example

Read the letters New Yor. You know the next letter is almost certainly k. It makes no difference whether the text before it was a news report, a recipe or a train timetable. Every history that ends in "New Yor" points to the same next step, so for predicting what comes next they are one state.

Now read the. What follows is wide open, and it depends on what came earlier in the sentence. Those histories do not share a future, so they are different states, even though they end in the same letters.

From the example to a model

Group every history of a process by the future it leads to, and you have its causal states. Record how each state moves to the next, and you have a complete working model of the process: the smallest one that predicts as well as anything can.

It is small

A process with a handful of real situations needs a handful of states, however much data it produced.

It can be read

At any moment the model is in a named state, and the state says what is expected next. A departure from it can be pointed to.

It keeps growing

New observations refine the states, or add one, without starting again.

The idea comes from computational mechanics: Crutchfield and Young, Inferring Statistical Complexity (1989), and Shalizi and Crutchfield, Computational Mechanics: Pattern and Prediction, Structure and Simplicity (2001). How Senua AI learns causal states at scale, and from what, is its own work.