Scaling Abstract Representations Across Domains and Modalities
AI Track ResearchLower ratio = better abstraction (irrelevant sensitivity / relevant sensitivity)
Relevant vs. irrelevant sensitivity per method
| Domain | Method | Rel. Sens. | Irr. Sens. | Ratio |
|---|---|---|---|---|
| Linear Dynamics | CBWM (Ours) | 2.554 | 4.370 | 1.711 |
| Reconstruction | 2.524 | 2.829 | 1.121 | |
| Forward-Only | 0.671 | 0.511 | 0.762 | |
| Nonlinear Pendulum | CBWM (Ours) | 2.864 | 2.668 | 0.931 |
| Reconstruction | 2.696 | 5.098 | 1.891 | |
| Forward-Only | 0.386 | 0.274 | 0.710 | |
| Grid Navigation | CBWM (Ours) | 4.687 | 4.627 | 0.987 |
| Reconstruction | 1.604 | 2.954 | 1.841 | |
| Forward-Only | 0.555 | 0.405 | 0.730 |
Latent L2 error over prediction horizon
Adaptation curves with frozen encoder (20 gradient steps)
| Transfer Pair | Initial Error | Final Error | Improvement |
|---|---|---|---|
| Linear Dyn. → Pendulum | 4.701 | 2.597 | 1.810x |
| Linear Dyn. → Grid | 4.819 | 2.794 | 1.725x |
| Pendulum → Grid | 3.603 | 2.051 | 1.757x |
Abstraction ratio and prediction error vs. latent dim
Exponential entropy of normalized singular values
| Method | Linear Dynamics | Nonlinear Pendulum | Grid Navigation |
|---|---|---|---|
| CBWM (Ours) | 6.248 | 6.299 | 6.085 |
| Reconstruction | 7.740 | 7.751 | 7.746 |
| Forward-Only | 7.478 | 7.217 | 6.797 |
| Dim | Abstraction Ratio | Rel. Sensitivity | Irr. Sensitivity | Avg Fwd Error |
|---|---|---|---|---|
| 2 | 5.970 | 0.523 | 3.125 | 1.395 |
| 4 | 2.188 | 1.338 | 2.929 | 2.109 |
| 8 | 2.026 | 1.961 | 3.973 | 2.670 |
| 16 | 1.429 | 2.223 | 3.176 | 3.177 |
| 32 | 0.366 | 2.521 | 0.923 | 3.034 |