SPIRE: Shared-Private Representation Learning for Continuous Multi-Region LFP under Perturbation

Learning shared and region-specific representations from continuous multi-region neural signals is challenging when observations are nonlinear, autocorrelated, spectrally structured, and temporally misaligned. These challenges are particularly pronounced in local field potentials (LFPs), where separating activity that is coordinated across regions from activity specific to individual regions is important for studying distributed neural systems and their response to intervention. We introduce **SPIRE** (Shared-Private Inter-Regional Encoder), a nonlinear, time-resolved framework for learning shared and private representations from continuous multi-region LFP. SPIRE combines region-specific sequence encoders with constrained temporal correspondence, shared-only reconstruction, and variance regularization for shared/private separation. On LFP-oriented synthetic benchmarks with known ground-truth factors, SPIRE preferentially assigns shared and private information to the intended latent spaces under nonlinear observation mappings, time-varying delays, and spectral confounding. On held-out human GPi-STN LFP, nonlinear prediction reveals strong transfer of shared representations across regions, whereas cross-region prediction from private representations remains at a structured temporal null, supporting functional rather than strict statistical separation. We then freeze representations learned from off-stimulation recordings and apply them to intracranial deep brain stimulation (DBS) data. Stimulation induces larger changes and carries more condition information in shared than private representations. A matched CTAE analysis reproduces the qualitative shared-over-private effect while retaining substantially less stimulation information. Together, these results establish SPIRE as a shared/private representation-learning framework for continuous multi-region LFP and show that DBS-related changes are preferentially expressed in representations shared across the recorded regions.