Modular mathematical model connects perception, thinking, and decisions for adaptive systems
This paper proposes a clear, “white-box” model that links what people sense to what they do by passing information through three stages: perception, cognition, and decision-making. Instead of treating human behavior as a black box, the authors build a state-space framework that represents hidden internal variables such as attention, beliefs, goals, and intentions. The model is meant to be both psychologically interpretable and suitable for mathematical analysis and control.
Perception is split into two parts. The first part picks which sensory cues matter now using a competitive weighting rule (divisive normalization). The second part is predictive inference: the model keeps a latent perceptual estimate that is updated when new sensory evidence disagrees with prior expectation. The size of each update depends on factors like sensory confidence, prior confidence, and attention gain. The cognition module then lets these perceptual estimates drive interacting latent cognitive variables. The authors borrow a state-space coupling style from Dynamic Causal Modelling (DCM) to describe directed influences among beliefs, goals, emotions, and biases. The decision-making module forms intentions from those cognitive states and then turns intentions into actions.
The paper does not stop at describing the architecture. The authors prove mathematical properties of the model under certain parameter conditions. These include boundedness (states do not blow up), Lipschitz regularity (small changes in input give small changes in state), forward invariance (states stay in lawful ranges), contraction of the perceptual inference when input is constant (estimates settle), and input-to-state stability (ISS) of the cognitive dynamics, which informally means cognitive states react in a controlled way to inputs. These results give formal conditions under which the model behaves predictably.