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Properly implement Ueda and Yamashita's regularized Newton method #136

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Vectornaut wants to merge 2 commits from Vectornaut/dyna3:grad-norm-reg into main

Vectornaut commented

2026-01-30 04:31:46 +00:00

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Goals

Primary

This pull request addresses issue #130.

Secondary

This pull request also:

Switches to regularizing the Hessian after we project out the frozen variables, instead of before. This is probably what we should've been doing all along.
Clarifies the comment about our handling of frozen entries. When we restrict the computation of the Newton step to the subspace where the velocities of the frozen entries are zero, the outcome shouldn't depend on any implicit choice of complement for that subspace. The new comment points this out.

Notes

Uniform regularization of Newton's method depends on a choice of metric on the configuration space. On the branch to be merged, we keep using the Euclidean metric associated with the computational basis. That means this pull request doesn't address issue #131.

I did test some versions of the branch to be merged that use other metrics, including completions of the Gram partial metric described in issue #131. I found that this branch was among the best in terms of realization quality and number of steps before convergence! I also realized that the computational metric is more geometrically meaningful than I'd appreciated at first, as explained in this comment.

## Goals ### Primary This pull request addresses issue #130. ### Secondary This pull request also: - Switches to regularizing the Hessian after we project out the frozen variables, instead of before. This is probably what we should've been doing all along. - Clarifies the comment about our handling of frozen entries. When we restrict the computation of the Newton step to the subspace where the velocities of the frozen entries are zero, the outcome shouldn't depend on any implicit choice of complement for that subspace. The new comment points this out. ## Notes Uniform regularization of Newton's method depends on a choice of metric on the configuration space. On the branch to be merged, we keep using the Euclidean metric associated with the computational basis. That means this pull request doesn't address issue #131. I did test some versions of the branch to be merged that use other metrics, including completions of the Gram partial metric described in issue #131. I found that this branch was among the best in terms of realization quality and number of steps before convergence! I also realized that the computational metric is more geometrically meaningful than I'd appreciated at first, as explained in [this comment](issues/131#issuecomment-3637).

Vectornaut added 2 commits

2026-01-30 04:31:47 +00:00

Add gradient norm regularization 26830f8b26

In the process, switch to regularizing the Hessian after we project out
the frozen variables, instead of before. This is probably what we
should've been doing all along.

Clarify comment on frozen velocity restriction

/ test (pull_request) Successful in 3m42s

Details

7193f13601

Note that the restriction doesn't depend on a choice of complement for
the subspace we're restricting to.

/ test (pull_request) Successful in 3m42s

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