SPIRE: Learning Shared–Private Neural Structure for Perturbation Analysis

Learning useful representations of multi-region neural activity requires separating structure that is shared across regions from dynamics that remain region-specific, while remaining robust to nonlinear observation mappings, temporal misalignment, and strong spectral structure. We present SPIRE (Shared-Private Inter-Regional Encoder), a nonlinear, time-resolved representation model that learns shared and private latent trajectories from multivariate time series. Shared structure is defined operationally by cross-region transfer after limited temporal and latent-space alignment; private structure captures predominantly nontransferable regional information. On controlled LFP-oriented simulations with known latent factors, SPIRE recovers shared and private processes more accurately than CTAE and, outside a linear control regime, generally more accurately than DLAG. In held-out human GPi-STN recordings, shared representations show stronger cross-region correspondence and transfer than private representations. We then freeze the representation learned from Off-stimulation activity and use it to study deep brain stimulation (DBS). Stimulation produces larger geometric shifts in shared than private latent structure, and stimulation condition is decoded more accurately from shared representations. These effects persist across stimulation sites and are reproduced in direction by CTAE, while the defining shared-over-private organization remains intact under stimulation. Together, the results support shared-private representation learning as a framework for analyzing how perturbations reorganize distributed neural systems.