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Discovering Symbolic Models from Deep Learning with Inductive Biases
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply L1 message regularization instead of standard GN training (ablation) | Graph Network · Newtonian dynamics, most force-law simulations | message-force correlation R^2: Standard values 0.000–0.036; L1 values 0.002–1.000 | Helped |
| Use a dimensionality-matched bottleneck instead of 100 message components (ablation) | Graph Network · Newtonian dynamics, force-law simulations | message-force correlation R^2: Standard values 0.000–0.036; Bottleneck values 0.947–1.000 | Helped |
| Use KL message regularization instead of standard GN training (ablation) | Graph Network · Newtonian dynamics, force-law simulations | test prediction loss: Charge-3: 1.2 -> 4.2; Damped-3: 0.41 -> 3.3; Disc.-2: 0.064 -> 1.8 | Hurt |
| Use FlatHGN rather than L1-regularized GN (ablation) | Graph Network · Newtonian dynamics | test prediction loss: FlatHGN is lower on r^-1-2 (0.079 -> 0.05), but higher on Charge-3 (0.94 -> 3.5) | Mixed |
| Extract an analytic formula with mass using the symbolic model | Dark matter overdensity prediction · Dark matter halos | mean absolute error: 0.121 -> 0.0882 | Helped |
| Distill the trained GN into a symbolic expression | L1-regularized GN · Dark matter halos, masked OOD data | mean absolute error: 0.142 -> 0.0892 | Helped |
| Distill the trained GN into a symbolic expression | L1-regularized GN · Dark matter halos, masked training data | mean absolute error: 0.0634 -> 0.0811 | Hurt |
| Use L1 regularization instead of standard GN training (ablation) | Graph Network · Newtonian dynamics, prediction performance | test prediction loss: L1 is lower on Disc.-2 (0.064 -> 0.044), but higher on Charge-2 (49 -> 52) | Mixed |
| Use the Hamiltonian pairwise-and-self energy decomposition (FlatHGN) (ablation) | Hamiltonian Graph Network · Newtonian dynamics | test prediction loss: Lower on Spring-3 (0.090 -> 0.010), higher on Charge-3 (0.94 -> 3.5) | Mixed |
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