Fast Fractional Natural Gradient Descent using Learnable Spectral Factorizations
Keywords: natural gradient, Riemannian optimization, positive-definite manifold, Kronecker-facotrized, Shampoo
Abstract: Many popular optimization methods can be united through fractional natural gradient descent (FNGD), which pre-conditions the gradient with a fractional power of the inverse Fisher:
RMSprop and Adam(W) estimate a diagonal Fisher matrix and apply a square root before inversion; other methods like K-FAC and Shampoo employ matrix-valued Fisher estimates and apply the inverse and inverse square root, respectively.
Recently, the question of how fractional power affects optimization has moved into focus, e.g. offering trade-offs between convergence and generalization.
Gaining deeper insights into this phenomenon would require going beyond diagonal estimations and using cheap and flexible matrix-valued Fisher estimators capable of applying any fractional power; however, existing methods are limited by their expensive matrix fraction computation.
To address this, we propose a Riemannian framework to learn eigen-factorized Fisher estimations on the fly, allowing for the cheap application of *arbitrary* fractional powers.
Our approach does not require matrix decompositions and, therefore, is stable in half precision.
We show our framework's efficacy on positive-definite matrix optimization problems and demonstrate its efficiency and flexibility for training neural nets.
Primary Area: optimization
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 12257
Loading