Data-driven oscillatory network modeling with condition-dependent coupling laws: Identifying directed neural interactions in working memory attention dynamics

Learning new information in the presence of distracters and changing conditions requires the ability to adapt. In the brain, this adaptive capability has been linked to dynamic interactions between attention and working memory, which enable the selective filtering of irrelevant input while preserving behaviorally relevant information. Specific neural oscillations have been implicated in this process. Here, we introduce a phenomenological data-driven framework for oscillatory network modeling that learns condition-dependent coupling laws directly from neural recordings and enables inference of condition-dependent directed pathways. We apply our approach to magnetoen-cephalography (MEG) data collected while participants performed a working-memory task with and without distracters. Recall dynamics in the non-distracter condition are first modeled using a linear oscillatory network in which each region of interest is represented by two alpha-band harmonic oscillators. We use universal differential equations (UDE), an extension of neural differential equations, to capture distracter-induced changes in coupling laws. Symbolic regression is then used to interpret the modifications identified by UDE as nonlinear functions, and an additional method is proposed to identify the directed pathway from the newly emerging nonlinear terms in the dynamics of brain regions of interest. Despite inter-subject variability, working memory recall data from all four participants examined under distraction showed the emergence of a pathway from the dorsolateral prefrontal cortex (dlPFC) to the primary visual cortex (V1). This finding is consistent with the established role of the dlPFC in cognitive control and suggests that distracter processing recruits a directed interaction from prefrontal to visual regions. More broadly, our results illustrate that combining linear models whose parameters are learned from the data with universal differential equations augmented by interpretability methods enables the identification of condition-dependent coupling laws, their representation as interpretable mathematical functions, and the discovery of candidate directed pathways underlying adaptive changes in oscillatory networks without requiring strong prior assumptions about the underlying mechanisms.