节点 n18

α smaller is better monotonically — field underfits (sinkhorn only −10%). One try with larger blur + lr, plus λ=0 control:

m PCA space trained with Sinkhorn divergence to transport E8.5→E9.5, then integrated forward one more day from E9.5; a kNN-based tangent-plane constraint penalizes velocity components leaving the local data manifold, forcing trajectories to bend along observed expression geometry rather than taking straight-line paths.",
 "vs_constant_shift": "Constant per-type displacement (nodes 4/5/13) applies the same vector to all cells of a type regardless of position. This ODE learns a position-dependent velocity field: cells at different locations in PCA space receive different velocities, and the manifold constraint ensures these velocities follow the curved data geometry. The displacement is not a fixed vector but the integral of a state-and-time-dependent field along a curved path.",
 "mechanism_evidence": "Engineer should report: (1) per-cell displacement vectors from ODE vs. straight-line (barycentric) displacement — compute cosine similarity distribution; if all >0.99 the manifold constraint did nothing. (2) Distribution of displacement magnitudes within each cell type — constant shift gives zero variance, ODE gives nonzero. (3) Four group scores separately for λ_manifold>0 vs λ_manifold=0. (4) Fraction of cells whose trajectory (intermediate Euler steps) deviates >1 PCA unit from the straight line connecting start and end points. (5) Sinkhorn loss before/after training to confirm the field learned meaningful transport.",
 "mechanism_off_control": "Same code, same architecture, same training budget, but set λ_manifold=0 (remove the tangent-plane penalty term from the loss). The ODE is then trained purely on Sinkhorn + kinetic energy without any manifold constraint. If outputs are element-wise identical (or cosine sim >0.999 per cell), the manifold constraint mechanism did not operate. Additionally, a second control: set damping α=0, which makes the output equal to stage-2 input (copy_last equivalent), confirming the ODE integration path is active.",
 "sources": []}
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