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BRAID: Input-driven Nonlinear Dynamical Modeling of Neural-Behavioral Data
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Introduces BRAID, an input-driven nonlinear RNN framework that uses multi-step-ahead forecasting and a multi-stage optimization to disentangle intrinsic behaviorally relevant neural dynamics from measured inputs.
Problem
Neural population models usually ignore measured external inputs (sensory stimuli, stimulation, upstream areas) and do not prioritize behaviorally relevant dynamics, so intrinsic and input-driven dynamics get conflated; nonlinear models also lack interpretable intrinsic dynamics.
Approach
Pairs a predictor-form RNN with a generative-form RNN trained jointly on m-step-ahead neural-behavioral forecasts with measured inputs, and learns behaviorally relevant states first in a separate optimization stage (plus optional stages for residual neural and behavior-specific dynamics).
Key results
- In simulations with sinusoidal behavior mapping, BRAID with nonlinear behavior decoder reached behavior decoding CC 0.8696 ± 0.0487, matching the true model's 0.8737.
- On the NHP dataset at 4-step-ahead (200 ms), BRAID achieved behavior forecasting CC 0.8042 at n_x=16, above linear BRAID (0.7453), DPAD (0.6706), and U-BRAID (0.7663).
- BRAID outperformed input-driven mmPLRNN in forecasting behavior and neural activity across horizons, except 2-step-ahead neural prediction.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add nonlinear behavior decoder (C_z) to input-driven model (ablation) | BRAID · Simulation, sinusoidal behavior mapping | behavior decoding CC: 0.8696 vs 0.4558 for linear BRAID | Helped |
| add forecasting-based multi-step objective and separate generative model (ablation) | BRAID · Simulation, intrinsic dynamics eigenvalues | eigenvalue error | Helped |
| remove behavior prioritization (unsupervised U-BRAID) | BRAID · NHP reaching, n_x=16, 4-step forecasting | behavior forecasting CC: 0.8042 vs 0.7663 | Helped |
| remove behavior prioritization (unsupervised U-BRAID) | BRAID · NHP reaching, n_x=16, 4-step forecasting | neural forecasting CC: 0.3274 vs 0.4089 | Hurt |
| include measured sensory inputs and multi-step forecasting (BRAID vs DPAD) | BRAID · NHP reaching, n_x=64, 4-step forecasting | behavior forecasting CC: 0.7970 vs 0.7352 | Helped |
| nonlinear model vs linear (BRAID vs linear BRAID) | BRAID · NHP reaching, n_x=16, 4-step forecasting | behavior forecasting CC: 0.8042 vs 0.7453 | Helped |
| nonlinear encoder, recursion, or neural decoder only, vs nonlinear behavior decoder (ablation) | BRAID · Simulation, sinusoidal behavior mapping | behavior decoding CC: Nonlin K 0.7680; Nonlin A 0.4735; Nonlin C_y 0.4558 | Mixed |
| add sensory inputs to TNDM | TNDM · NHP reaching, behavior decoding | behavior decoding | Helped |
Surprising findings
- Nonlinear behavior decoders gave the best fit in the NHP data, while the paper notes this may not hold for other datasets.
- U-BRAID matched or exceeded BRAID on neural forecasting at n_x=64, despite BRAID being better at behavior forecasting.
Limitations
- Single-session setting; cross-session generalization not addressed.
- Assumes measured inputs are available; unmeasured inputs are not modeled explicitly.
- Nonlinear models may admit many equally good alternative models, making learned dynamics hard to evaluate.
Experimental setup
Datasets: Sabes lab NHP motor cortex reaching dataset (publicly available) simulated nonlinear input-driven systems
Benchmarks: Sabes NHP reaching dataset nonlinear simulations
Metrics: Pearson correlation coefficient R^2 m-step-ahead forecasting accuracy normalized eigenvalue error
Baselines: IPSID linear BRAID DPAD U-BRAID mmPLRNN TNDM LFADS CEBRA
Builds on: IPSID DPAD TNDM mmPLRNN LFADS
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