Representational Reorganization of Multi-Region Neural Dynamics under Deep Brain Stimulation

Separating cross-regional from region-specific structure in continuous local field potentials (LFPs) is challenging because these signals can exhibit nonlinear regional mixing, temporal misalignment, autocorrelation, and strong spectral structure. We evaluate spire (shared-private Inter-Regional Encoder), a general nonlinear, time-resolved shared-private representation model, in this setting. On LFP-oriented synthetic benchmarks with known latent factors, spire recovers shared and private processes more accurately than CTAE and, outside the linear control regime, generally more accurately than DLAG, including under nonlinear mixing, time-varying delay, and spectral confounding. In held-out human GPi-STN recordings, the learned shared representations show stronger cross-region correspondence than private representations and stronger shared GPi-STN correspondence than CTAE. We then use these representations to examine how deep brain stimulation (DBS) reorganizes shared and private latent structure. Shared trajectories exhibit larger Off-to-On centroid shifts during both GPi and STN stimulation, and GPi stimulation condition is decoded more accurately from shared than private representations. A matched CTAE analysis reproduces the direction of the decoding effect but retains substantially less stimulation information. These results indicate that, within the recorded GPi-STN network, DBS-related changes are expressed more strongly in shared than region-private latent structure.