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Modeling Neural Activity with Conditionally Linear Dynamical Systems
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Proposes Conditionally Linear Dynamical Systems (CLDS), an LDS whose parameters vary as GP-prior functions of observed task/behavioral covariates, enabling closed-form EM inference under Gaussian noise.
Problem
Modeling nonlinear neural population dynamics that vary with observed task and behavioral conditions, especially in data-limited regimes with few trials per condition.
Approach
Place approximate GP priors (Fourier/basis-function expansions) on the parameters (A, b, C, d, m) of a linear dynamical system as functions of observed conditions, so the system is linear conditioned on covariates; MAP inference reduces to Bayesian linear regression in an expanded feature space, giving closed-form EM with Kalman smoothing.
Key results
- On macaque reaching data, CLDS outperformed LDS, gpSLDS and LFADS in co-smoothing R^2, with the largest gap at 1 training trial per reach angle.
- On the synthetic head-direction ring attractor, CLDS recovered the true A(theta) and b(theta) and achieved co-smoothing R^2 = 0.86 on a held-out neuron.
- Closed-form EM with Kalman smoothing gives exact marginal likelihood and monotonic ascent under Gaussian observations.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CLDS instead of the compared baselines | Macaque center-out reaching task · Macaque center-out reaching task, especially 1 training trial per reach angle | co-smoothing R² | Helped |
| Increase the number of training trials per reach angle | gpSLDS · Macaque center-out reaching task | co-smoothing R² | Helped |
| Use LFADS instead of CLDS in the low-data regime | Macaque center-out reaching task · Macaque center-out reaching task | co-smoothing R² | Hurt |
| Fit CLDS to the synthetic head-direction ring attractor | CLDS · Synthetic head-direction ring attractor test set | co-smoothing R²: R² = 0.86 | Helped |
Limitations
- Requires observed condition covariates over time; performance degrades with corrupted or partially observed covariates.
- Assumes conditionally linear dynamics; may struggle when covariates are loosely correlated with latent state (e.g. cognitive tasks).
- Only Gaussian observation model implemented in closed form; Poisson extension not implemented, and MAP rather than full posterior inference.
Experimental setup
Datasets: synthetic head-direction ring attractor synthetic neural circuit ring attractor model mouse ADn head-direction recordings (Peyrache et al.) macaque PMd center-out reaching recordings
Benchmarks: co-smoothing on mouse ADn recordings co-smoothing on macaque PMd reaching data
Metrics: co-smoothing R^2 parameter recovery reconstruction accuracy
Baselines: LDS gpSLDS LFADS
Builds on: Gaussian Process Factor Analysis gpSLDS recurrent SLDS LFADS Wishart process models
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