Hamiltonian Generative Networks

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time. These properties are important for many machine learning problems - from sequence prediction to reinforcement learning and density modelling - but are not typically provided out of the box by standard tools such as recurrent neural networks. In this paper, we introduce the Hamiltonian Generative Network (HGN), the first approach capable of consistently learning Hamiltonian dynamics from high-dimensional observations (such as images) without restrictive domain assumptions. Once trained, we can use HGN to sample new trajectories, perform rollouts both forward and backward in time and even speed up or slow down the learned dynamics. We demonstrate how a simple modification of the network architecture turns HGN into a powerful normalising flow model, called Neural Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive densities. We hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to deep learning.

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Reproducibility Reports


Jan 31 2021
[Re] Hamiltonian Generative Networks

We found the modelʼs input-output data slightly unclear in the original paper. First, it seems that the model reconstructs the same sequence that has been inputted. Nevertheless, further discussion with the authors seems to indicate that they input the first few frames to the network and reconstructed the rest of the rollout. We test both approaches and analyze the results. We generally obtain comparable results to those of the original authors when just reconstructing the input sequence (30% average absolute relative error w.r.t. to their reported values) and worse results when trying to reconstruct unseen frames (107% error). In this report, we include our intuition on possible reasons that would explain these observations.

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