neurojax-sleep-flow

name: neurojax_sleep_flow description: Model Wake-NREM transitions as a continuous Neural ODE flow.

Skill: Continuous Sleep Flow Modeling

Context

Sleep stages (N1, N2, N3) are artificial discretizations of a continuous biological process. Your goal is to model the "Sleep Manifold" using Neural ODEs on the OpenNeuro/Bitbrain sleep datasets.

Strategy

Instead of classification (State $\in {0,1,2}$), we learn a velocity field $\dot{x} = f_\theta(x, t)$ that describes the flow of brain dynamics on a manifold defined by band powers.

Pipeline steps

1. Preprocessing & Feature Extraction

• Input: BIDS-formatted EEG (e.g., OpenNeuro).
• Resample: 100 Hz.
• Features: Compute relative band powers in log-space ($\log P_\delta, \log P_\theta, \dots$) for every 30s epoch (or finer 5s resolution for continuity).
• Manifold: Treat this 5D vector as the state $x(t)$.

2. Neural ODE Training

• Model: Define a diffrax.NeuralODE using equinox.

  class VectorField(eqx.Module):
      mlp: eqx.nn.MLP
      def __call__(self, t, y, args):
          return self.mlp(y)
  

• Training:
  • Use diffrax.diffeqsolve to predict $x(t+\Delta t)$ from $x(t)$.
  • Loss: MSE between predicted band power trajectory and actual future trajectory.
  • Advanced: Use "Multiple Shooting" for long sequences to stabilize training.

3. Analysis: Flow Visualization

• Streamplot: Visualize the learned vector field $f_\theta(x)$ in the $(\delta, \alpha)$ plane.
• Attractors: Identify fixed points ($\dot{x} \approx 0$).
  • Expected: A "Wake" attractor (High $\alpha$, Low $\delta$) and a "Deep Sleep" attractor (High $\delta$, Low $\alpha$).
• Success: The vector field shows a clear "river" or trajectory connecting Wake to Sleep, with N1/N2 as transient states along the flow.

Critical Instructions

• Normalization: Log-band powers must be z-scored per subject before training.
• Stiffness: Sleep dynamics can be stiff (fast spindles vs slow waves). Use diffrax.Tsit5 or diffrax.Kvaerno5 with adaptive stepping.