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Meta-Dynamical State Space Models for Integrative Neural Data Analysis
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Proposes meta-learning a low-dimensional dynamical embedding that conditions low-rank hypernetwork changes to a shared latent SSM, enabling few-shot reconstruction and forecasting of neural dynamics across recordings.
Problem
Inferring latent dynamics from heterogeneous neural recordings across sessions and subjects, where neurons are non-overlapping and dynamics vary across datasets, so single-dataset or naive shared-dynamics models generalize poorly.
Approach
Encode dataset-level variation of dynamics in a low-dimensional embedding e that a hypernetwork maps to low-rank changes of a shared nonlinear dynamics network, with dataset-specific read-in networks and likelihoods; new recordings are aligned by inferring only their read-in, likelihood and embedding.
Key results
- On Duffing/Hopf held-out datasets with n_s=16 trials, few-shot 30-step forecasting r^2 of 0.87 ± 0.037 vs 0.79 for Single Session and 0.74 for Linear-Adapter.
- Shared Dynamics baseline gave negative forecasting r^2 (-0.31 at n_s=1), showing that naive joint training fails under dynamical variation.
- On motor cortex held-out sessions, the method outperformed all multi-session baselines on forecasting in low-sample regimes while matching reconstruction performance.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use embedding-conditioned low-rank dynamics instead of the Linear-Adapter | Few-shot dynamical forecasting · Held-out Duffing/Hopf datasets, n_s=16 | forecasting r² (k=30): 0.74 $\pm$ 0.039 -> 0.87 $\pm$ 0.037 | Helped |
| Use embedding-conditioned low-rank dynamics instead of the Linear-Adapter | Few-shot dynamical forecasting · Held-out Duffing/Hopf datasets, n_s=1 and n_s=8 | forecasting r² (k=30): 0.68 $\pm$ 0.08 vs 0.69 $\pm$ 0.072; 0.79 $\pm$ 0.026 vs 0.78 $\pm$ 0.051 | No clear effect |
| Use embedding-conditioned low-rank dynamics instead of the Linear-Adapter | Few-shot dynamical forecasting · Held-out Hopf datasets, n_s=1 and n_s=8 | forecasting r² (k-step=20): -0.1 $\pm$ 0.34 -> 0.64 $\pm$ 0.1; 0.55 $\pm$ 0.08 -> 0.69 $\pm$ 0.07 | Mixed |
| Vary the low-rank adaptation rank (ablation) | Meta-Dynamical State Space Model · Motor Cortex Recordings | behavior reconstruction and prediction r² | No clear effect |
| Use VSMC or DVBF inference instead of DKF inference (ablation) | Proposed generative model · Motor Cortex Recordings, few-shot forecasting | behavior forecasting | No clear effect |
| Pretrain on a smaller collection of recordings (ablation) | Proposed generative model · Motor Cortex Recordings, new sessions | few-shot forecasting | Hurt |
Surprising findings
- Shared dynamics model with dataset-specific likelihoods yields negative forecasting r^2 on synthetic data, and Multi-Session CEBRA produced poor generative forecasts on motor cortex.
- Single-session seqVAE achieved the best forecasting on motor cortex, outperforming the proposed multi-session approach overall.
Limitations
- Relies on event-aligned neural observations (movement onset), limiting use for unstructured tasks.
- Generalization depends on accurate embedding inference from few trials.
- Assumes shared structure across related tasks; may not apply to unrelated recordings.
Experimental setup
Datasets: synthetic Hopf, Duffing, and limit-cycle dynamical systems motor cortex recordings (Centre-Out and Maze reaching tasks)
Benchmarks: synthetic dynamical systems few-shot reconstruction and forecasting motor cortex hand velocity decoding from reconstructed and forecasted neural activity
Metrics: r^2 k-step forecasting r^2
Baselines: Single Session Shared Dynamics Embedding-Input Linear-Adapter LFADS Multi-Session CEBRA VSMC DVBF
Builds on: Deep Kalman Filter LFADS CoDA CEBRA hierarchical Bayesian state-space models
Closest papers by meaning
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- A scalable generative model for dynamical system reconstruction from neuroimaging data (NeurIPS 2024 · similarity 0.88)
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