Bridging Perceptual and Analytic Dynamics via Function Alignment

Human modeling of complex processes often involves multiple representations that capture different aspects of the same underlying reality. While recent approaches mostly unify such representations into a single predictive model, this unification could obscure the distinct functional roles associated with each representation. Inspired by the function alignment framework proposed recently, we study an alternative paradigm in which heterogeneous predictive dynamics are preserved and coupled through bidirectional alignment at the level of functions. We consider a setting with two representations of the same process paired in time: a high-dimensional perceptual sequence and a compact analytic state sequence, each governed by its own autoregressive dynamics. Rather than collapsing them into a unified model, we align their predictive functions using lightweight adapter modules that allow each dynamics to incorporate signals from the other during rollout. We conduct experiments on two physical prediction tasks exhibiting different functional roles of the two dynamic processes, and demonstrate that function alignment significantly improves long-horizon stability during joint rollout in both perceptual and analytic domains. Together, our results provide a concrete instantiation of function alignment between perceptual and analytic dynamics, along with empirical evidence that preserving heterogeneous predictive dynamics can be critical for stable sequential prediction.