Table 2. Mechanistic principles of the compositional theory of flexible cognitive control.

These principles differ from those presented in Table 1 in that these are less abstract, such that we consider these to be readily implementable in computational models.

Principle	Description
Multi-system global connectivity	LPFC connectivity with many content-specific systems throughout the brain, giving access to many potentially task-relevant representations.
Rapid updating	A fast change of active content within LPFC, likely via a mechanism (basal ganglia) that gates instruction information (from posterior cortex).
Within-LPFC global connectivity	Extensive connectivity between neurons within LPFC, allowing for complex processing and latent connectivity (see below).
Latent connectivity	Unused connections and connectivity patterns that can become used as necessary by novel tasks during RITL.
Coarse-coded conjunctive representations	A large set of neurons with broad receptive fields that receive inputs from (potentially random) combinations of each other to produce many conjunctive receptive fields. This allows for representational binding, general processing (see below), and other principles considered here.
Synchrony/co-activation	Binding via synchronous co-activation of multiple representations, allowing for rapid selection (see below) of sets of representations to achieve massive combinatorics during RITL.
Incremental selection	Slow, multi-trial selection and tuning of task-representing neurons and connections for optimizing task performance from practice. Transfer of subsets of these neurons and connections to new tasks facilitates RITL.
Rapid selection	Fast selection of novel and (previously incrementally selected) representations from practiced tasks during RITL.
General processing hierarchy	Specific instantiations of a “compositional hierarchy” (Table 1). It consists of many connected neural populations building a wide variety of representations via conjunctions, unions, and other set theory operations, ultimately based on primitives in primary sensory-motor cortices. Due to wiring costs promoting short-distance connectivity, this results in multiple hierarchies of processing starting from primary cortices and going outward anatomically in terms of complexity and abstraction. We focus on the general processing hierarchy within LPFC.
Hierarchical conservation	A bias to incrementally select and strengthen more posterior (lower-level) representations of a task during practice.
Population adaptive coding	The ability of LPFC as a whole to represent a wide variety of possible tasks. This is accomplished by compositionally selecting sets of individual neurons, each with relatively static and coarse coding, that together specify processes necessary to implement each specific task.