NeuralODEs - A journey

Project of course Computational Statistics @ PoliMi - Second Edition, A.A. 2021/2022, First Semester

Team

• Luca Caivano
• Paulina Moskwa
• Manfred Nesti

Topic

Investigation on NeuralOde's: a new innovative approach that combines Neural Networks and Ordinary Differential Equations.

Notebooks

Half moons

In notebooks/2D_Half_Moons.ipynb a NeuralODE is used to classify points of the half moons dataset.

Concentric Annuli

In notebooks/2D_Concentric_Annuli.ipynb a NeuralODE is used to classify points of the concentric annuli dataset.

Concentric Spirals

• In notebooks/2D_Spirals_Augmented.ipynb a vanilla NeuralODE is used to classify points of the concentric spirals dataset.

• In notebooks/2D_Spirals.ipynb a NeuralODE with augmentation technique is used to improve performance on concentric spirals dataset.

MNIST dataset

In notebooks/MNIST.ipynb a NeuralODE is used to classify MNIST dataset's images, providing the accuracy on the test set and visualizing the trajectories of the images in their space. The trained model can be saved and upload using the from the file notebooks/MNIST_model.pt.

Media

Al media (GIF and images) used in the slides.

References

• Ricky T. Q. Chen, et al. | “Neural Ordinary Differential Equations” | 32nd Conference on NeurIPS, 2019
• Stefano Massaroli, Michael Poli, et al. | “Dissecting NeuralODEs” | 34th Conference on NeurIPS, 2021
• Software: TorchDyn: Implicit Models and Neural Numerical Methods in PyTorch | S. Massaroli, M. Poli, et. al | (doc)
• Repository: Dissecting NeuralODEs | S. Massaroli, M. Poli, et. al | (repo)
• Repository: torchdyn/tutorials/ | S. Massaroli, M. Poli, et. al | (repo)