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Active learning of neural population dynamics using two-photon holographic optogenetics
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Develops an active learning procedure that chooses two-photon holographic photostimulation patterns to efficiently estimate low-rank neural population dynamics (causal connectivity), with a nuclear-norm estimation error analysis for non-isotropic measurements.
Problem
Choosing which neurons to photostimulate so that the resulting responses most efficiently inform a dynamical model (and causal connectivity matrix) of mouse motor cortex population activity, under limited experimental data.
Approach
Model neural dynamics as a low-rank (diagonal plus low-rank) autoregressive system and adaptively choose photostimulus inputs via A-optimal design that targets the top right singular directions of the current estimate, mixed with uniform exploration; supported by new error bounds for nuclear-norm-constrained regression with non-isotropic inputs.
Key results
- On simulators fit to mouse data, active design achieves roughly 1.5-2x fewer samples than random or uniform stimulation to reach a given connectivity estimation error.
- On real held-out trials, active ordering reaches up to 2x sample efficiency over random ordering in many splits and matches random in the worst case.
- Low-rank AR-4 models (rank 35) perform almost indistinguishably from full-rank AR-4 models in predicting neural responses.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use active stimulation design instead of random or uniform stimulation | low-rank AR-k neural dynamics simulators · Mouse 1 and Mouse 3 FoV A/B | samples required for a given connectivity estimation error: 1.5-2× fewer samples | Helped |
| adaptively rank real-data trials instead of choosing trials randomly | neural dynamics model · Mouse photostimulation datasets, held-out trials | samples required for prediction performance: up to a factor of $2\times$ | Helped |
| adaptively rank real-data trials instead of choosing trials randomly | neural dynamics model · Mouse photostimulation datasets, worst-case train-test splits | prediction MSE | No clear effect |
| use a low-rank AR-k model with rank r=35 instead of a full-rank AR-k model (ablation) | AR-k neural dynamics model · Mouse motor cortex photostimulation datasets | prediction performance | No clear effect |
| use a GRU instead of an AR-k model (ablation) | neural dynamics prediction · Mouse motor cortex photostimulation datasets | prediction performance | Hurt |
| vary the input rank parameter (ablation) | active low-rank matrix estimation · Mouse photostimulation datasets | estimation error | No clear effect |
Surprising findings
- A GRU network did not perform as well as the linear AR-k models on the photostimulation data, possibly due to hyperparameter tuning difficulty.
- Active learning gives no substantial gain in all real-data cases; in the worst case it only matches random.
Limitations
- Experiments on real data are offline, restricted to 100 candidate stimulation patterns per dataset.
- Linear dynamics assumed; applicability to nonlinear dynamics is untested.
- Targets uniform prediction/connectivity error across all neurons rather than specific subspaces or learning-induced connectivity changes.
Experimental setup
Datasets: two-photon holographic photostimulation recordings from mouse motor cortex (four datasets, Ai229 x Vglut1-cre mice)
Benchmarks: photostimulation recordings from mouse motor cortex (held-out trials)
Metrics: relative Frobenius error of off-diagonal causal connectivity mean squared error of roll-out predictions AUROC for response detection
Baselines: Random stimulation Uniform stimulation full-rank AR-k model GRU network
Builds on: nuclear norm regularization A-optimal experiment design Frank-Wolfe algorithm Suite2p
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