What jacobians are returned when optimizing on a manifold?

[Michael]

When doing manifold optimization, what jacobians end up being returned by evaluate? In general is there a way to access the jacobians in the local parametrization? Googles AI says the jacobians returned are with respect to global coordinates but that doesn't really make sense to me.

[Sameer Agarwal]

Evaluate is supposed to return the jacobians in the ambient space, then ceres will combine them with the jacobian of the Manifold at that point to compute a net jacobian which is on the manifold.

On Tue, Jan 6, 2026 at 9:26 PM Michael <lowel...@gmail.com> wrote:

When doing manifold optimization, what jacobians end up being returned by evaluate? In general is there a way to access the jacobians in the local parametrization? Googles AI says the jacobians returned are with respect to global coordinates but that doesn't really make sense to me.

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