Augmented Neural ODEs
2019-04-02NeurIPS 2019Code Available1· sign in to hype
Emilien Dupont, Arnaud Doucet, Yee Whye Teh
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ReproduceCode
- github.com/EmilienDupont/augmented-neural-odesOfficialIn paperpytorch★ 0
- github.com/mitmath/18S096SciMLnone★ 315
- github.com/locuslab/monotone_op_netpytorch★ 53
- github.com/kfallah/NODE-Denoiserpytorch★ 4
- github.com/Daniel-H-99/ANODEpytorch★ 0
- github.com/mandubian/pytorch-neural-odepytorch★ 0
Abstract
We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these limitations, we introduce Augmented Neural ODEs which, in addition to being more expressive models, are empirically more stable, generalize better and have a lower computational cost than Neural ODEs.
Tasks
Benchmark Results
| Dataset | Model | Metric | Claimed | Verified | Status |
|---|---|---|---|---|---|
| CIFAR-10 | ANODE | Percentage correct | 60.6 | — | Unverified |
| MNIST | Augmented Neural Ordinary Differential Equation | Percentage error | 0.37 | — | Unverified |
| MNIST | ANODE | Percentage error | 1.8 | — | Unverified |
| SVHN | ANODE | Percentage error | 16.5 | — | Unverified |