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Doubt regarding the Hamiltonian calculations for RHVAE model.

See original GitHub issue

In the paper, Hamiltonian is defined as follows:

H(z, v) = U(z) + K(v)  = -0.5*log(det(G^-1(z)) + 0.5*v^T*v

But in the code, I see extra terms like addition of a joint probability term and a G inverse multiplied in the term for kinetic energy. Are these 2 equations equivalent?

Issue Analytics

State:
Created 2 years ago
Comments:12 (6 by maintainers)

Top GitHub Comments

1reaction

clementchadebeccommented, Feb 12, 2022

You’re welcome 😃. Not really, you can down-sample a bit your input data to deal with memory issues for instance but, in theory, the VAE can handle any kind of data regardless of the dimension. If you are referring to the paper, we only down-sampled the data by a factor 2 in each dimension when dealing with 3D MRIs.

1reaction

shikhar2333commented, Feb 11, 2022

So are M and G equivalent, since M is also defined as LL^T.

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Doubt regarding the Hamiltonian calculations for RHVAE model. In the paper, Hamiltonian is defined as follows: