Learning shared and region-specific representations from continuous multi-region local field potentials (LFPs) is challenging because neural signals are nonlinear, autocorrelated, spectrally structured, and temporally misaligned. We introduce SPIRE (Shared-Private Inter-Regional Encoder), a nonlinear, time-resolved framework that separates multi-region LFP into shared and region-specific latent trajectories using region-specific sequence encoders, constrained temporal alignment, shared-only reconstruction, and variance regularization. On synthetic benchmarks with known ground-truth factors, SPIRE preferentially recovers shared and private information despite nonlinear mixing, time-varying delays, and spectral confounding. On held-out human GPi-STN LFP, shared representations strongly predict activity across regions, while cross-region prediction from private representations remains near a structured temporal null, supporting functional rather than strict statistical separation. We then apply representations trained on off-stimulation recordings to deep brain stimulation (DBS) data. Stimulation induces larger changes and more strongly encodes stimulation condition in shared than private representations. A matched CTAE analysis reproduces the shared-over-private effect, while retaining substantially less stimulation information. These findings suggest that DBS-related changes are preferentially expressed in neural representations shared across recorded regions.

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