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A scalable generative model for dynamical system reconstruction from neuroimaging data
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Proposes convSSM, a state-space DSR model trained with generalized teacher forcing via Wiener deconvolution of BOLD signals, enabling scalable reconstruction of dynamical systems from short fMRI time series.
Problem
Dynamical systems reconstruction via control-based teacher forcing requires an invertible observation model, which fails for signals that are convolved with a filter over a history of latent states, such as BOLD fMRI and calcium imaging.
Approach
Incorporate the hemodynamic response function into the observation model and invert it once via Wiener deconvolution of the observations (exploiting linearity so deconvolution is done only once before training), then use the pseudo-inverse of the decoder to generate generalized teacher forcing signals for a cshPLRNN latent model.
Key results
- On LEMON rsfMRI (51 participants), convSSM achieved mean D_stsp 2.73 ± 1.09 versus 2.77 ± 0.93 for standard SSM, 3.77 for no-GTF, and 6.79 for MINDy.
- convSSM significantly outperformed the standard SSM in latent space on ALN pseudo-empirical data (rank-sum Z = 11.50, p ≤ .001).
- Per-epoch runtime increased approximately linearly with latent dimension M, hidden dimension L, and observation dimension N (R² ≈ 0.99), and did not depend significantly on TR.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the convolutional observation model instead of a standard observation model | convSSM · Lorenz63, hrf_0.2, σ=0.01 | PE_20: 0.0418 ± 0.0099 -> 0.0023 ± 0.0001 | Helped |
| use the convolutional observation model instead of a standard observation model | convSSM · Lorenz63, hrf_0.2, σ=0.1 | D_stsp: 2.79 ± 0.90 -> 0.70 ± 0.08 | Helped |
| use the convolutional observation model instead of a standard observation model | convSSM · Lorenz63, hrf_0.5, σ=0.01 | D_stsp: 0.42 ± 0.55 -> 0.09 ± 0.02 | Helped |
| use the convolutional observation model instead of a standard observation model | convSSM · Lorenz63, hrf_1.2, σ=0.01 | D_stsp: 0.15 ± 0.32 -> 0.16 ± 0.46 | No clear effect |
| remove GTF (ablation) | convSSM · LEMON | D_stsp: 2.73 ± 1.09 -> 3.77 ± 1.22 | Hurt |
| remove GTF (ablation) | convSSM · LEMON | D_PSE: 0.14 ± 0.03 -> 0.34 ± 0.11 | Hurt |
| remove GTF (ablation) | convSSM · LEMON | 10-step PE: 1.78 ± 0.38 -> 1.43 ± 0.61 | Helped |
| use the convolutional observation model instead of a standard observation model | convSSM · LEMON | D_stsp: 2.77 ± 0.93 -> 2.73 ± 1.09 | No clear effect |
| use the convolutional observation model instead of a standard observation model | convSSM · LEMON | 10-step PE: 2.00 ± 0.44 -> 1.78 ± 0.38 | Helped |
| use the convolutional observation model instead of a standard observation model | convSSM · LEMON | D_PSE: 0.15 ± 0.03 -> 0.14 ± 0.03 | Helped |
Surprising findings
- Most recovered LEMON fMRI systems had positive maximal Lyapunov exponents, suggesting chaotic attractors in resting-state data.
- On LEMON data, convSSM's D_stsp was not clearly better than the standard SSM, despite the claimed advantage in simulations.
Limitations
- Data-driven approach lacks detailed biophysical mechanisms, limiting pharmacological or receptor-level questions.
- Open issues on non-stationarity in data, combining data from many subjects, and generalization to out-of-domain data.
- Latent model is deterministic; noise in the latent process is not modeled.
Experimental setup
Datasets: Lorenz63 (simulated) ALN model simulations via neurolib LEMON rsfMRI
Benchmarks: Lorenz63 convolved and noised benchmarks ALN pseudo-empirical simulations LEMON rsfMRI
Metrics: D_stsp D_PSE PE_20 10-step PE maximum Lyapunov exponent rank-sum test
Baselines: standard SSM MINDy rSLDS LFADS convSSM without GTF
Builds on: generalized teacher forcing shallow PLRNN clipped shallow PLRNN sparse teacher forcing VisuShrink
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