节点 n19

Now I'll write the solution. Let me set up `run.py` implementing the manifold_ode PLAN.

lty may over-regularize and erase real change (all cells stay near input) → check that std of displacement > 5% of std of target-source difference. 4) proxy10 fallback means ~1/3 of score is copy_last-level → X3 must gain ≥3 points to beat overall baseline. Engineer should check after first vec-score: if X3 < 49, abort parameter sweep and report failure.",
  "family_id": "manifold_ode",
  "mechanism": "A small non-autonomous neural ODE in 30-dim PCA space transports E8.5 cells toward E9.5 distribution (Sinkhorn loss), with a kNN manifold penalty keeping trajectories near observed data; extrapolation to the target time uses damped velocity (γ=0.5).",
  "vs_constant_shift": "The velocity field is state-dependent (MLP on x,t): cells in different PCA regions follow different curved paths, whereas constant shift applies one uniform vector. The manifold penalty further bends paths along data density, preventing straight-line traversal through empty expression space.",
  "mechanism_evidence": "1) Compare per-cell displacement vectors: compute cosine similarity between each cell's displacement and the global mean displacement; manifold ODE should show lower mean cosine (< 0.9) vs constant shift (≈1.0). 2) Report PCA trajectory snapshots at t=0.5, 1.0, 1.5, 2.0: paths should curve, not be straight lines. 3) Report 4-group score breakdown separately for λ_man=0 vs λ_man>0 to isolate manifold effect. 4) Check that zero-fraction and variance of output match input within 10%.",
  "mechanism_off_control": "Set λ_man=0 (remove kNN manifold penalty); same ODE architecture, same Sinkhorn training, same damping, same number of epochs. Run once on X3. Expected difference: without manifold constraint, trajectories are straighter (higher mean cosine to global shift), may overshoot into low-density regions, yielding worse mmd_u/variogram. If λ_man=0 and λ_man>0 give identical outputs (bitwise), the manifold penalty never activated and the mechanism is not running.",
  "sources": []
}
```