#machinelearning
https://arxiv.org/abs/2007.04504
Learning Differential Equations that are Easy to Solve
Jacob Kelly, Jesse Bettencourt, Matthew James Johnson, David Duvenaud
Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable surrogate for the time cost of standard numerical solvers, using higher-order derivatives of solution trajectories. These derivatives are efficient to compute with Taylor-mode automatic differentiation. Optimizing this additional objective trades model performance against the time cost of solving the learned dynamics. We demonstrate our approach by training substantially faster, while nearly as accurate, models in supervised classification, density estimation, and time-series modelling tasks.
https://arxiv.org/abs/2007.04504
Learning Differential Equations that are Easy to Solve
Jacob Kelly, Jesse Bettencourt, Matthew James Johnson, David Duvenaud
Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable surrogate for the time cost of standard numerical solvers, using higher-order derivatives of solution trajectories. These derivatives are efficient to compute with Taylor-mode automatic differentiation. Optimizing this additional objective trades model performance against the time cost of solving the learned dynamics. We demonstrate our approach by training substantially faster, while nearly as accurate, models in supervised classification, density estimation, and time-series modelling tasks.
https://github.com/volotat/DiffMorph
#machinelearning #opensource
Differentiable Morphing
> Image morphing without reference points by applying warp maps and optimizing over them.
#machinelearning #opensource
Differentiable Morphing
> Image morphing without reference points by applying warp maps and optimizing over them.
GitHub
GitHub - volotat/DiffMorph: Image morphing without reference points by applying warp maps and optimizing over them.
Image morphing without reference points by applying warp maps and optimizing over them. - volotat/DiffMorph
#machinelearning
A nice colloquium paper:
The unreasonable effectiveness of deep learning in artificial intelligence | PNAS
https://www.pnas.org/content/117/48/30033
A nice colloquium paper:
The unreasonable effectiveness of deep learning in artificial intelligence | PNAS
https://www.pnas.org/content/117/48/30033
PNAS
The unreasonable effectiveness of deep learning in artificial intelligence
Deep learning networks have been trained to recognize speech, caption photographs, and translate text between languages at high levels of performance. Although applications of deep learning networks to real-world problems have become ubiquitous, our understanding…