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Optimizing Neural Networks via Koopman Operator Theory
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Koopman training replaces Adam steps for NN DE solver | Koopman training · NN DE solver 1:10:10:2 | speedup: 98x | Helped |
| Koopman training replaces Adagrad steps | Koopman training · NN DE solver 1:10:10:2 | speedup: 132x | Helped |
| Koopman training replaces Adadelta steps | Koopman training · NN DE solver 1:10:10:2 | speedup: 141x | Helped |
| Koopman training replaces stochastic Adadelta steps | Koopman training · MNIST NN 784:20:20:20:10 | speedup: 15x | Helped |
| choose Adam instead of Adadelta as underlying optimizer | Koopman training · NN DE solver | success rate: 100% -> 84% | Hurt |
| choose Adagrad instead of Adadelta as underlying optimizer | Koopman training · NN DE solver | success rate: 100% -> 92% | Hurt |
| choose Adam instead of Adadelta as underlying optimizer | Koopman training · NN DE solver | Teq/T: 1.00 -> 0.85 | Hurt |
| Koopman weight prediction vs true Adadelta weight evolution | Koopman training · NN DE solver, ten best NNs | error / true evolution: median ratio 0.0044 | Helped |
Closest papers by meaning
- Deep-Koopman-KANDy: Dictionary Discovery for Deep-Koopman Operators with Kolmogorov-Arnold Networks for Dynamics (NeurIPS 2026 · similarity 0.90)
- Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems (NeurIPS 2025 · similarity 0.90)
- SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting (ICML 2025 · similarity 0.89)
- ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals (ICML 2025 · similarity 0.88)
- Generalizing across Temporal Domains with Koopman Operators (AAAI 2024 · similarity 0.88)
- Identifying Equivalent Training Dynamics (NeurIPS 2024 · similarity 0.88)
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