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Adding Latent SDE #104

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0378b23
+ small change in KL divergence computation
anh-tong May 11, 2022
dbed128
minor fix
anh-tong May 11, 2022
71e3ccc
fix description
anh-tong May 11, 2022
47c87ec
check out the original notebook and make small doc change
anh-tong May 28, 2022
1513384
kl divergence via abstractions of control term
anh-tong May 29, 2022
9217c06
minor fix
anh-tong May 30, 2022
a59a111
neural vae lorenz data (in progress)
anh-tong Jun 3, 2022
7ab9bb0
remove used imports and refactor test
anh-tong Jun 4, 2022
92a1842
complete test neural sde vae
anh-tong Jun 13, 2022
da636e5
sde KL with block diagonal diffusion
anh-tong Sep 21, 2022
d8a68b2
sync fork and rename jax.tree_util
anh-tong Sep 21, 2022
dc5fde4
fix typo
anh-tong Sep 21, 2022
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11 changes: 8 additions & 3 deletions diffrax/misc/sde_kl_divergence.py
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Original file line number Diff line number Diff line change
Expand Up @@ -9,8 +9,11 @@


def _kl(drift1, drift2, diffusion):
inv_diffusion = jnp.linalg.pinv(diffusion)
scale = inv_diffusion @ (drift1 - drift2)
if diffusion.ndim == 1:
scale = (drift1 - drift2) / diffusion
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@patrick-kidger patrick-kidger May 13, 2022

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So my original code here in sde_kl_divergence was pretty hacky and not library-ready, and I think it'll still need some more work to get ready.

In particular I think it would make most sense to operate the level of terms. This would allow for abstracting over the kind of diffusion used -- e.g. ControlTerm versus WeaklyDiagonalControlTerm etc. -- rather than the current vector-field-based approach.

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@anh-tong anh-tong Jun 13, 2022

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I think we may need to bump the version number. Here, I have changed sde_kl_divergence API from taking drift functions, a diffusion function ... into taking two MultiTerm. Although there is a duplication in control terms as they share the same, this sounds more natural as we compare two SDEs.

else:
inv_diffusion = jnp.linalg.pinv(diffusion)
scale = inv_diffusion @ (drift1 - drift2)
return 0.5 * jnp.sum(scale**2)


Expand All @@ -23,7 +26,7 @@ class _AugDrift(eqx.Module):
def __call__(self, t, y, args):
y, _ = y
context = self.context(t)
aug_y = jnp.concatenate([y, context], axis=-1)
aug_y = jnp.concatenate([y, context], axis=-1) if context is not None else y
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@patrick-kidger patrick-kidger May 13, 2022

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Nit: flipping the if and else branches allows for switching if context is not None down toj ust if context is None.

drift1 = self.drift1(t, aug_y, args)
drift2 = self.drift2(t, y, args)
diffusion = self.diffusion(t, y, args)
Expand Down Expand Up @@ -66,6 +69,8 @@ def sde_kl_divergence(
bm: AbstractBrownianPath,
):
aug_y0 = (y0, 0.0)
if context is None:
context = lambda t: None
return (
_AugDrift(drift1, drift2, diffusion, context),
_AugDiffusion(diffusion),
Expand Down
13 changes: 8 additions & 5 deletions examples/neural_sde.ipynb → examples/neural_sde_gan.ipynb
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