arXiv Machine Learning June 9, 2026 By Basile Plus-Gourdon, Frank Nielsen

Neural Legendre-Fenchel transform with Hessian Preconditioning

Read the original on arXiv Machine Learning →

arXiv:2606. 09077v1 Announce Type: new Abstract: 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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

benchmarks

arXiv Machine Learning

Aug 4

Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients

arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.

By John Chiang

arXiv Machine Learning

Sep 15

A family of spectral conjugate gradient algorithms derived by least-squares approximations based on a modified quasi--Newton update with application to a revised robust binary classification model

arXiv:2609.13526v1 Announce Type: cross Abstract: We develop a spectral three-term modification of the classic Hestenes--Stiefel conjugate gradient algorithm, preserving its anti-jamming characterist...

By Saman Babaie-Kafaki, Maryam Khoshsimaye-Bargard, Ahmad Mousavi

arXiv Machine Learning

Jul 16

Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning

arXiv:2605. 07914v2 Announce Type: replace Abstract: Sharpness-aware and gradient-alignment methods have been shown to improve generalization, however each family of methods targets a single geometric property of the loss landscape, while ignoring the other.

By Aristotelis Ballas, Christos Diou

benchmarks safety

arXiv Machine Learning

Aug 11

Generalized Convexity and Smoothness via Conjugate Duality: Optimization Theory for Deep Neural Networks

arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.

By Binchuan Qi

safety

Hugging Face Trending Papers

Jul 7

On the Condition Number Upper Bound of the L-BFGS Inverse Hessian Approximation Matrix with a Two-Sided Geometric Envelope Safeguarding Mechanism

The limited-memory BFGS (L-BFGS) algorithm is a cornerstone of large-scale optimization due to its linear memory and computational costs. However, in ill-conditioned or non-convex landscapes, the implicit inverse Hessian approximation can suffer from an exploding condition number, leading to numerical instability and degraded convergence.

benchmarks

arXiv Machine Learning

Jul 8

On the Condition Number Upper Bound of the L-BFGS Inverse Hessian Approximation Matrix with a Two-Sided Geometric Envelope Safeguarding Mechanism

arXiv:2607. 05836v1 Announce Type: cross Abstract: The limited-memory BFGS (L-BFGS) algorithm is a cornerstone of large-scale optimization due to its linear memory and computational costs.

By Don Li

benchmarks

One email a morning, machine-written

Related stories

Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients

A family of spectral conjugate gradient algorithms derived by least-squares approximations based on a modified quasi--Newton update with application to a revised robust binary classification model

Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning

Generalized Convexity and Smoothness via Conjugate Duality: Optimization Theory for Deep Neural Networks

On the Condition Number Upper Bound of the L-BFGS Inverse Hessian Approximation Matrix with a Two-Sided Geometric Envelope Safeguarding Mechanism

On the Condition Number Upper Bound of the L-BFGS Inverse Hessian Approximation Matrix with a Two-Sided Geometric Envelope Safeguarding Mechanism