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

Rahil Soroushmojdehi; Sina Javadzadeh; Mehrnaz Asadi; Terence D. Sanger

cs.LGOct 28, 2025

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

Authors: Rahil Soroushmojdehi, Sina Javadzadeh, Mehrnaz Asadi, Terence D. Sanger

Organizations: Department of Electrical Engineering and Computer Science · Department of Biomedical Engineering, University of California, Irvine, CA, USA · Department of Neurology, Children’s Health Orange County, Orange, CA, USA

Abstract

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.

Figures & tables

Figure 1: SPIRE separates each region into time-resolved shared and private latent trajectories. Shared trajectories are aligned across regions through constrained temporal and linear mappings, while shared/private separation and reconstruction objectives preserve complementary information.

Regime	SPIRE	DLAG	CTAE
D0 linear	0.72 / 0.64	0.89 / 0.83	0.29 / 0.31
D1 nonlinear	0.76 / 0.60	0.64 / 0.48	0.14 / 0.17
D2 + delay	0.75 / 0.58	0.57 / 0.48	0.12 / 0.16
D3 spectral confound	0.54 / 0.55	0.42 / 0.46	0.17 / 0.35

Table 1: Nonlinear recovery of known ground-truth factors. Each cell reports intended shared/private recovery,

R^{2}(Z_{\mathrm{sh}}\!\rightarrow\!S_{\mathrm{GT}})\,/\,R^{2}(Z_{\mathrm{pr}}\!\rightarrow\!P_{\mathrm{GT}})

, averaged across four matched seeds. Higher values indicate stronger recovery of the corresponding ground-truth factors. Full means and standard deviations are reported in Appendix A.4.1 .

Panel of Figure 2 — Figure 2: Representative latent recovery in the challenging D3 synthetic regime. Recovered trajectories (solid red) are compared with ground-truth trajectories (dashed teal) after CCA-based alignment for visualization. D3 combines nonlinear observation mappings with strong low-frequency private structure and higher-frequency shared factors, producing substantial spectral confounding. Shaded regions denote SEM across trials. Quantitative nonlinear recovery is reported in Table 1 , and branch specificity in Table 2 .

Regime	SPIRE	DLAG	CTAE
D0 linear	0.48 / 0.40	0.81 / 0.68	0.07 / -0.01
D1 nonlinear	0.44 / 0.39	0.43 / 0.20	0.02 / -0.01
D2 + delay	0.42 / 0.38	0.37 / 0.16	0.04 / -0.01
D3 spectral confound	0.42 / 0.27	0.15 / 0.13	-0.06 / 0.14

Table 2: Nonlinear shared/private specificity. Each cell reports

\Delta_{\mathrm{sh}}/\Delta_{\mathrm{pr}}

(mean across four matched seeds), where

\Delta_{\mathrm{sh}}=SS-SP

and

\Delta_{\mathrm{pr}}=PP-PS

. Positive values indicate preferential assignment of information to the intended latent branch.

Prediction category	Excess $R^{2}$	95% CI
Shared across regions	0.636	[0.507, 0.764]
Shared $\rightarrow$ private, within region	0.504	[0.376, 0.633]
Private $\rightarrow$ shared, within region	0.312	[0.183, 0.440]
Private across regions	0.009	[-0.120, 0.138]

Table 3: Held-out nonlinear organization of human GPi-STN LFP. Cross-region shared prediction is strongly above the structured temporal null, whereas cross-region private prediction is approximately at the null. Values are hemisphere-level mean excess

R^{2}

with 95% confidence intervals.

Panel of Figure 3 — Figure 3: Functional organization and DBS-induced changes in SPIRE representations. (a) Shared and private latent trajectories exhibit distinct spectral structure, with shared latents showing lower spectral centroids in human GPi-STN LFP. (b) DBS produces larger off-to-on displacement in shared than private representations. (c,d) Shared representations encode stimulation condition more strongly than private representations under both GPi and STN stimulation. Statistical significance: $*:p<0.05$ , $**:p<0.01$ , $***:p<0.001$ ; ns, not significant.

Latent class	CTAE	SPIRE	Difference
Private	31.0%	53.6%	+22.6 points
Shared	38.4%	67.7%	+29.3 points

Table 4: Matched GPi-stimulation decoding comparison. Accuracies are averaged across regions after first averaging stimulation-contact settings within hemisphere. Both SPIRE-CTAE differences have Holm-adjusted

p<0.0001

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1: Synthetic benchmark datasets. Each trial is 0.5 s, with a 0.3 s segment shown for visualization. Left: example observed channels from region 1 and region 2. Middle: example shared and private latent trajectories. Right: diagnostic plots showing nonlinear cross-region relationships, time-varying delay structure, and spectral separation between shared and private dynamics.

Loss component	Pre (0-80)	Ramp (80-140)	Post (140-500)
$\mathcal{L}_{\text{rec}}$ (reconstruction)	1.00	1.00	1.00
$\mathcal{L}_{\text{align}}$ (shared alignment)	0.22	0.10	0.08
$\mathcal{L}_{\text{cross}}$ (cross recon)	0.03	0.05	0.07
$\mathcal{L}_{\text{self}}$ (self recon)	0.02	0.04	0.03
$\mathcal{L}_{\text{orth}}$ (shared $\perp$ private)	0.008	0.015	0.025
$\mathcal{L}_{\text{mapid}}$ (mapper identity)	0.010	0.005	0.000

Appendix

Table A.1: Loss weights for synthetic training across phases.

\alpha_{p}

ramps from 0 to 1 between epochs 80-140.

Panel of Figure 10 — Figure A.2: Ablation results for shared latents with statistical comparison. Mean $\pm$ SD CCA across four seeds, faceted by dataset regime. Dunnett-adjusted contrasts are shown relative to the full SPIRE model ( SPIRE_synth ).

Dataset	Metric	SPIRE	DLAG	CTAE
D0	Shared latent recovery	0.72 (0.03)	0.91 (0.03) ∗∗∗	0.26 (0.04) ∗∗∗
D0	Private latent recovery	0.71 (0.08)	0.87 (0.05) ∗∗∗	0.38 (0.02) ∗∗∗
D1	Shared latent recovery	0.82 (0.02)	0.75 (0.01) ⋅	0.25 (0.09) ∗∗∗
D1	Private latent recovery	0.63 (0.03)	0.55 (0.02) ∗	0.27 (0.06) ∗∗∗
D2	Shared latent recovery	0.82 (0.00)	0.71 (0.01) ∗∗	0.22 (0.09) ∗∗∗
D2	Private latent recovery	0.61 (0.01)	0.55 (0.01) ∗	0.28 (0.05) ∗∗∗

Appendix

Table A.2: CCA-based synthetic latent recovery across benchmark regimes. Values report mean canonical correlation (SD) between learned and corresponding ground-truth latent subspaces across four matched random seeds. Bold indicates the highest recovery within each regime and latent class. Significance was assessed using regime-wise Dunnett-adjusted contrasts comparing each baseline against SPIRE (

{}^{\cdot}p<0.1

{}^{*}p<0.05

{}^{**}p<0.01

{}^{***}p<0.001

Panel of Figure 12 — Figure A.3: Representative latent recovery in the D0 synthetic regime. Recovered trajectories (solid red) are compared with ground-truth trajectories (dashed teal) after CCA-based alignment for visualization. Shaded regions denote SEM across trials.

Panel of Figure 13 — Figure A.4: Representative latent recovery in the D1 synthetic regime. Recovered trajectories (solid red) are compared with ground-truth trajectories (dashed teal) after CCA-based alignment for visualization. Shaded regions denote SEM across trials.

Panel of Figure 14 — Figure A.5: Representative latent recovery in the D2 synthetic regime. Recovered trajectories (solid red) are compared with ground-truth trajectories (dashed teal) after CCA-based alignment for visualization. Shaded regions denote SEM across trials.

Subject	Etiology	Hemisphere	GPi rec.	STN rec.	VO rec.	VA rec.	GPi stim.	STN stim.
S1	MEPAN	Left	18	3	4	4	3	1
		Right	12	6	2	3	2	1
S2	GA1	Left	6	6	1	6	2	1
		Right	9	1	1	4	2	1
S3	Atypical PKAN	Left	11	4	1	0	4	1
		Right	8	4	1	0	3	1

Appendix

Table A.3: Participant demographics and number of stimulation and recording contacts per hemisphere. The table includes each subject’s etiology, the number of usable microelectrode recording contacts per region (GPi, STN), and whether GPi or STN stimulation was applied in each hemisphere. Abbreviations: MEPAN = Mitochondrial Enoyl CoA Reductase Protein-Associated Neurodegeneration Heimer et al. (2019) , KMT2B = Lysine Methyltransferase-2B Abela and Kurian (1993) , GA1 = Glutaric aciduria type 1 Boy (2017) , PKAN = Pantothenate Kinase-Associated Neurodegeneration Gregory and Hayflick (2017) , HIE = Hypoxic-ischemic encephalopathy Vannucci (2000) , MYH2 = Myosin heavy chain IIa mutation Tajsharghi et al. (2005) , CP = Cerebral palsy Krigger (2006) , BG = Basal ganglia.

Figure A.6: Subject-specific variance partition of GPi vs. STN. For each subject-hemisphere, two adjacent bars (GPi, STN) show the fraction of variance explained by the unique shared , unique private , and redundant components. Labels include the selected latent sizes

(d_{s},d_{p})

per hemisphere chosen via the appendix rule A.3.2 ). Cohort heterogeneity is evident: several hemispheres are dominated by private variance (weak GPi–STN shared structure), whereas others show a more balanced decomposition consistent with stronger cross-regional coordination. Full dimension sweeps (per hemisphere and region) are in Appendix Fig. A.9 .

Panel of Figure 17 — Figure A.7: Representative held-out shared/private latent organization. Shared GPi and STN trajectories overlap more strongly than their private counterparts.

Panel of Figure 18 — Figure A.8: Representative shared and private latent organization. (a) 3D UMAPs of shared and private GPi/STN latent spaces. (b) Corresponding latent trajectories across time. Shared GPi/STN trajectories are phase-aligned but have very low amplitude and primarily reflect slow baseline co-modulation , whereas private trajectories carry larger, region-specific dynamics that dominate the variance.

Panel of Figure 19 — Figure A.9: Variance partition across latent dimensionalities. For each subject–hemisphere, we trained SPIRE with shared dimension $d_{s}\in\{3,4,5\}$ and private dimension $d_{p}\in\{2,3,4\}$ . Each bar shows the fraction of explained variance in the observed signal that is uniquely attributable to shared latents, uniquely attributable to private latents, or redundantly captured by both. (a) GPi recordings. (b) STN recordings. These sweeps were used to select the final $(d_{s},d_{p})$ configuration per subject–hemisphere, as reported in the main text (Fig. A.6 ).

Loss component	Epoch ( $<60$ )	(60-100)	(100-140)	( $\geq 140$ )
Reconstruction ( $\mathcal{L}_{\text{rec}}$ )	1.00	1.00	1.00	1.00
Alignment ( $\mathcal{L}_{\text{align}}$ )	0.30	0.30	0.38	0.45
Orthogonality ( $\mathcal{L}_{\text{orth}}$ )	0.012	0.012	0.015	0.015
Self recon. ( $\mathcal{L}_{\text{self}}$ )	0.03	0.05	0.05	0.05
Cross recon. ( $\mathcal{L}_{\text{cross}}$ )	0.00	0.05	0.06	0.06
Mapper identity ( $\mathcal{L}_{\text{mapid}}$ )	0.005	0.005	0.003	0.000

Appendix

Table A.4: Loss weight schedule for real DBS training. Values are weight multipliers in the objective.

Loss component	Epoch ( $<60$ )	(60-110)	(110-150)	( $\geq 150$ )
Reconstruction ( $\mathcal{L}_{\text{rec}}$ )	1.00	1.00	1.00	1.00
Alignment ( $\mathcal{L}_{\text{align}}$ )	0.22	0.24	0.30	0.36
Orthogonality ( $\mathcal{L}_{\text{orth}}$ )	0.012	0.012	0.015	0.015
Self recon. ( $\mathcal{L}_{\text{self}}$ )	0.03	0.04	0.05	0.05
Cross recon. ( $\mathcal{L}_{\text{cross}}$ )	0.00	0.025	0.04	0.05
Mapper identity ( $\mathcal{L}_{\text{mapid}}$ )	0.005	0.005	0.003	0.000

Appendix

Table A.5: Loss weight schedule for three-region SPIRE training on real DBS recordings. Values are weight multipliers in the objective.

Figure A.10: Subject-specific variance partition of GPi vs. STN vs. Thalamus For each subject-hemisphere, three adjacent bars (GPi, STN, Thal) show the fraction of variance explained by the unique shared , unique private , and redundant components. Labels include the selected latent sizes

(d_{s},d_{p})

per hemisphere chosen via the appendix rule A.3.2 ). Cohort heterogeneity is evident. Full dimension sweeps (per hemisphere and region) are in Appendix Fig. A.11 .

Panel of Figure 23 — Figure A.11: Variance partition across latent dimensionalities. For each subject–hemisphere, we trained SPIRE with shared dimension $d_{s}\in\{3,4,5\}$ and private dimension $d_{p}\in\{2,3,4\}$ . Each bar shows the fraction of explained variance in the observed signal that is uniquely attributable to shared latents, uniquely attributable to private latents, or redundantly captured by both. (a) GPi recordings. (b) STN recordings. (c) Thalamus recording. These sweeps were used to select the final $(d_{s},d_{p})$ configuration per subject–hemisphere.

Figure A.12: Three-region latent similarity analysis. CCA similarity was computed among grouped latent pairs across GPi, STN, and thalamus. Shared cross-region latents showed the highest similarity, indicating recovery of a common multi-region latent manifold. Shared-private similarities were lower, reflecting limited within-region leakage, while private cross-region similarities were lowest, consistent with private latents capturing region-specific dynamics.

Figure A.13: Three-region decoding of GPi stimulation frequency from SPIRE latents. Random Forest classifiers were trained to decode stimulation frequency (off, 85, 185, and 250 Hz) from private and shared latent subsets of GPi, STN, and thalamus. Shared latents across all three regions achieved higher decoding accuracy than private latents, indicating that GPi stimulation induces structured changes in the shared multi-region latent manifold. Private latents showed lower and more variable accuracy, consistent with region-specific residual activity. Boxplots show median and interquartile range, whiskers extend to 1.5

\times

IQR, and black dots denote means. Statistical comparisons are shown with conventional significance notation: ns, not significant;

{}^{***}p<0.001

Model	Params (M)	Seq length $T$	Inference (ms / seq)
SPIRE (ours)	0.116	247	4.45
CTAE	0.860	247	4.84

Appendix

Table A.6: Compute comparison under matched batch size (

B{=}8

), channels

(36,12)

, and AMP (fp16). Latencies are wall-clock forward-pass times averaged over 50 runs following 10 warm-up iterations.

Regime	Model	$SS$	$SP$	$PP$	$PS$	$SS-SP$	$PP-PS$
D0	SPIRE	0.72 (.02)	0.24 (.15)	0.64 (.11)	0.24 (.01)	0.48 (.16)	0.40 (.11)
	DLAG	0.89 (.03)	0.09 (.02)	0.83 (.06)	0.15 (.03)	0.81 (.04)	0.68 (.09)
	CTAE	0.29 (.10)	0.22 (.05)	0.31 (.02)	0.32 (.06)	0.07 (.12)	-0.01 (.07)
D1	SPIRE	0.76 (.01)	0.31 (.03)	0.60 (.01)	0.20 (.01)	0.44 (.02)	0.39 (.02)
	DLAG	0.64 (.01)	0.21 (.01)	0.48 (.03)	0.28 (.01)	0.43 (.01)	0.20 (.02)
	CTAE	0.14 (.05)	0.12 (.02)	0.17 (.04)	0.18 (.04)	0.02 (.05)	-0.01 (.02)

Appendix

Table A.7: Complete nonlinear intended-versus-crossed recovery matrix. Specificity margins are

SS-SP

and

PP-PS

Latent pair	Lag	No lag
Shared GPi-STN	0.987	0.750
Shared-private GPi	0.610	0.571
Shared-private STN	0.568	0.626
Private GPi-STN	0.390	0.406

Appendix

Table A.8: Median CCA organization with and without lag augmentation across 16 matched hemispheres.

Regime	Original	Private 0.01	Private 0.005
D0	0.360 / 0.397	0.455 / 0.446	0.454 / 0.455
D1	0.644 / 0.548	0.647 / 0.526	0.645 / 0.548
D2	0.607 / 0.539	0.610 / 0.524	0.606 / 0.540
D3	0.472 / 0.463	0.482 / 0.475	0.478 / 0.480

Appendix

Table A.9: CCA shared/private specificity margins for the original objective and two lower-weight private-only reconstruction variants.

Panel of Figure 30 — Figure A.14: Secondary held-out human-LFP diagnostics. (a) Reconstruction error when decoding GPi and STN activity from full, shared-only, and private-only representations. (b) CCA similarity between shared and private latent spaces for SPIRE and CTAE. These analyses provide complementary characterization of representation quality and organization; the primary evidence for functional segregation is the nonlinear cross-region prediction analysis in the main text.

Cohort	GPi target	STN target
GPi stimulation	0.888	0.952
STN stimulation	0.853	0.905

Appendix

Table A.10: Mean Test-On full-reconstruction

R^{2}

Cohort	Shared CCA	Private CCA	Shared $>$ private
GPi stimulation	0.588	0.189	17/17
STN stimulation	0.516	0.197	13/13

Appendix

Table A.11: Functional organization of the frozen representation on unseen stimulation data.

Rat	Shared CCA	Private CCA	Within-region sh-pr CCA
T1	0.987	0.064	0.135-0.190
S2	0.995	0.022	0.038-0.122
Q1	0.997	0.067	0.033-0.052
R1	0.660	0.049	0.213-0.230

Appendix

Table A.12: Held-out CA1-PFC latent organization in four rats.

Rat	Shared-shared $R^{2}$	Shared-to-private $R^{2}$	Private-private $R^{2}$
T1	0.978	0.323	-0.008
S2	0.990	0.461	-0.018
Q1	0.997	0.345	-0.013
R1	0.620	0.154	-0.016

Appendix

Table A.13: Nonlinear held-out cross-predictability in the CA1-PFC transfer example.

Rat	CA1	PFC
T1	0.0044 / 0.158 / 0.863	0.0358 / 0.182 / 1.120
S2	0.0008 / 0.036 / 0.276	0.0245 / 0.267 / 1.074
Q1	0.0017 / 0.059 / 0.686	0.0260 / 0.196 / 2.566
R1	0.0025 / 0.175 / 0.809	0.0361 / 0.171 / 0.965

Appendix

Table A.14: Held-out reconstruction MSE in the external LFP transfer example; each cell is full/shared-only/private-only.

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