Neural Legendre-Fenchel transform with Hessian Preconditioning
The Legendre-Fenchel (LF) transform is a fundamental tool in convex analysis and machine learning that maps lower semi-continuous functions to their convex conjugates. In practice, when closed-form formula are not available for expressing convex conjugates of given functions, one must approximate them using various techniques. One recent such versatile numerical method is the deep Legendre transform method which relies on neural networks although it remains challenging particularly for tackling ill-conditioned functions. This work builds on the reformulation of the LF transform as a projective polarity. A notable property of this framework is its affine invariance. We leverage this affine...
| Authors | Basile Plus-Gourdon, Frank Nielsen |
|---|---|
| Primary category | cs.LG |
| Published | 8 June 2026 |
| Last updated at source | 8 June 2026 |
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