A spectral partial information decomposition framework for quantifying information about cognitive variables in oscillatory brain networks

Neural oscillations are thought to play a central role in encoding and transmitting cognitive information across large-scale brain networks, yet the relative contributions of phase synchrony and amplitude co-modulations to distributed coding remain unclear. A key obstacle is the absence of tools that can simultaneously quantify task-relevant information in the frequency domain and disentangle its phase and amplitude co-modulation components across pairwise and higher order interactions. Here, we introduce a spectral partial information decomposition framework (NeOPID) for quantifying information about cognitive variables in amplitude co-modulation and phase contributions, and to quantify redundant and synergistic information in brain relations, from pairwise to higher-order interactions. We validated the approach on Kuramoto and Stuart- Landau oscillator networks, including a whole-brain model constrained by macaque anatomical connectivity. NeOPID accurately recovers ground-truth encoding schemes and reveals that phase relations and amplitude co-modulations act as complementary coding channels with both redundant and synergistic components. NeOPID further extends this decomposition to higher-order functional interactions enabling the characterization of how cognitive information is collectively distributed across multiple oscillatory edges via redundant and synergistic encoding. To illustrate biological applicability, we applied NeOPID to local field potentials (LFPs) recorded from the macaque fronto-parietal network during a working memory task. In this dataset, NeOPID identified beta-band amplitude co-modulations as the primary carrier of stimulus information, and revealed that higher-order phase interactions exhibit both redundant and synergistic structure during the memory delay. These results establish NeOPID as a principled tool for dissecting the informational architecture about cognitive processes of oscillatory brain networks.Significance Statement Understanding how the brain coordinates large-scale communication to support cognition remains a fundamental challenge in neuroscience. Characterizing the distinct roles of phase synchrony and amplitude co-modulation has been hindered by a lack of computational approaches capable of separating these components across pairwise and higher-order interactions. Here, we introduce NeOPID (neural spectral Partial Information Decomposition), a framework designed to isolate phase and amplitude co-modulation contributions and quantify redundant and synergistic information contained in pair-wise and higher order functional interactions. NeOPID was validated on simulated oscillator models and on macaque local field potentials (LFPs) during a working memory task. Overall, the results establish NeOPID as a principled tool for dissecting the informational architecture underlying cognitive processes in oscillatory brain networks.