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Anamnesic Neural Differential Equations with Orthogonal Polynomial Projections
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use orthogonal-polynomial coefficient dynamics as memory banks in a Neural ODE | Neural ODE time-series representations · Lorenz63 | reconstruction MSE: 0.428 \pm 0.040 -> 0.034 \pm 0.008 | Helped |
| Use orthogonal-polynomial coefficient dynamics as memory banks in a Neural ODE | Neural ODE time-series representations · Lorenz63 | classification ROC-AUC: 0.911 \pm 0.005 -> 0.992 \pm 0.000 | Helped |
| Use orthogonal-polynomial coefficient dynamics as memory banks in a Neural ODE | Neural ODE time-series representations · MIMIC-III | reconstruction MSE: 0.775 \pm 0.000 -> 0.187 \pm 0.005 | Helped |
| Replace the learned auxiliary dynamics with constant interpolation (ablation) | PolyODE · Lorenz | reconstruction MSE: 0.034 \pm 0.008 -> 0.785 \pm 0.074 | Hurt |
| Replace the learned auxiliary dynamics with linear interpolation (ablation) | PolyODE · Lorenz | reconstruction MSE: 0.034 \pm 0.008 -> 0.787 \pm 0.066 | Hurt |
| Replace the learned auxiliary dynamics with Hermite spline interpolation (ablation) | PolyODE · Lorenz | classification ROC-AUC: 0.992 \pm 0.000 -> 0.976 \pm 0.000 | No clear effect |
| Replace the learned auxiliary dynamics with Hermite spline interpolation (ablation) | PolyODE · Lorenz | reconstruction MSE: 0.034 \pm 0.008 -> 0.135 \pm 0.007 | Hurt |
| Use orthogonal-polynomial projections to retain global history | PolyODE · MIMIC-III | classification ROC-AUC: 0.800 \pm 0.004 -> 0.778 \pm 0.005 | Hurt |
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