Predictive processing is reasoning about dynamic systems by predicting what to expect and then reconciling the errors.

Scruff allows users to represent hierarchical dynamic models in which each layer of the model predicts the layer below and then processes errors to the layer above. The models have many layers of abstraction, with a chain of predictions down the hierarchy and a chain of error processing up the hierarchy.

Scruff also allows the flexible instantiation of variables at different time points. Users do not have to model everything in lockstep at the same discrete time step. Instead, users can instantiate variables whenever they need to. In predictive processing, higher-level variables in the hierarchy will tend to evolve more slowly and lower-level variables will tend to do so more quickly.

Implicit representation means that every model component is interpreted as a generative probabilistic model, even if it is not one. Under this approach we stipulate that the components support various operations that relate to each other in the same way they would if actually using a generative probabilistic model.

The principles work for all kinds of models. For example, a physics space model that uses differential equations can be interpreted as probabilistic by looking at the propagation of the differential equations. Given the final state, we can perform back inference of the initial state through these differential equations. A data-driven model like a neural network is yet another example, where we need to be able to take an output and get a probability distribution of the inputs. Constraint models with hard and soft constraints can also conform to this methodology.

Such an approach corrals all models under one umbrella and breaks down components into more readily manipulated units with predictable behaviors.

Every model component using implicit representation is represented as a stochastic function, which means that it takes inputs and probabilistically or stochastically generates an output. The approach is based on principles derived from probabilistic programming, where you describe basic functions and use them to build more complex models.

Stochastic functions just describe model components. Variables actually associate these model components with things in the real world, especially ones that vary over time and space. An instantiation is a particular instance of the variable at a particular point in time and space. A number of these instantiations can be used to fully describe a situation.

The advantage of such flexibility, especially compared with fixed time interval models, is that you can base your instantiation of variables only when you access evidence. Since different variables evolve at different rates, the instantiation can be made granular: You can instantiate frequently changing variables frequently and slowly changing variables more rarely.