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Stable Neural Flows
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We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on asymptotic stability of the depth-flows, leading to robustness against input perturbations and low computational burden for the numerical solver. The learning procedure is cast as an optimal control problem, and an approximate solution is proposed based on adjoint sensivity analysis. We further introduce novel regularizers designed to ease the optimization process and speed up convergence. The proposed model class is evaluated on non-linear classification and function approximation tasks.
Forward citations
Cited by 3 Pith papers
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Robust Convolution Neural ODEs via Contractivity-promoting regularization
Regularizing convolutional NODE weights to promote contractivity improves robustness to noise and adversarial attacks by up to 34 percentage points.
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ICODE: Modeling Dynamical Systems with Extrinsic Input Information
ICODE, a control-affine neural ODE that feeds external inputs directly into the dynamics, predicts trajectories better than NODE, ANODE, and CDE on simulated physical benchmarks, but its contraction guarantee is not e...
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Deep Neural Networks Inspired by Differential Equations
A review of differential-equation-inspired neural networks that compiles known results into a taxonomy, with no new experiments or theory.
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