Tootfinder

Generalized Gradient Norm Clipping & Non-Euclidean $(L_0,L_1)$-Smoothness
Thomas Pethick, Wanyun Xie, Mete Erdogan, Kimon Antonakopoulos, Tony Silveti-Falls, Volkan Cevher
https://arxiv.org/abs/2506.01913

Generalized Gradient Norm Clipping & Non-Euclidean $(L_0,L_1)$-Smoothness
This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of ($L_0$,$L_1$)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal $O(n^{-1/4})$ convergence rate b…

Efficient Quadratic Corrections for Frank-Wolfe Algorithms
Jannis Halbey, Seta Rakotomandimby, Mathieu Besan\c{c}on, Sebastian Pokutta
https://arxiv.org/abs/2506.02635

Efficient Quadratic Corrections for Frank-Wolfe Algorithms
We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended pairwise conditional gradients and fully-corrective Frank-Wolfe, and propose a highly efficient corrective algorithm in the case of convex quadratic objectives based on linear optimization or linear system solving, akin to Wolfe's minimum-norm point. Beyond optimization problems that are directly quadratic, we revisit two algorithms, split conditional gradient for the intersection of two…

- We investigate the distribution of the feature variables (corpus frequency, dictionary views, part-of-speech, polysemy) over CEFR levels.
- Variable importance analyses show us how important each variable was for the classification of each level.
We conclude: "Thus, our semi-automatic approach offers a practical solution to the limitations of existing CEFR lists, providing a framework for expanding these lists in a systematic and data-driven manner. However, our findings also reveal the importance of human oversight in the process."
Supplementary material contains an ensemble approach to classification and all used/generated data: https://osf.io/6s9y7/

This https://arxiv.org/abs/2505.08408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A three-term Polak-Ribière-Polyak conjugate gradient method for vector optimization
A three-term Polak-Ribière-Polyak conjugate gradient method is first proposed in this paper for solving vector optimization problems. This method can autonomously generate descent directions independent of line search procedures, while retaining the conjugate property. The global convergence of the proposed scheme is established by the generalized Wolfe line search procedure without self-adjusting strategies, regular restarts and convexity assumptions. Finally, numerical experiments illustrati…

This https://arxiv.org/abs/2505.08408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A three-term Polak-Ribière-Polyak conjugate gradient method for vector optimization
A three-term Polak-Ribière-Polyak conjugate gradient method is first proposed in this paper for solving vector optimization problems. This method can autonomously generate descent directions independent of line search procedures, while retaining the conjugate property. The global convergence of the proposed scheme is established by the generalized Wolfe line search procedure without self-adjusting strategies, regular restarts and convexity assumptions. Finally, numerical experiments illustrati…

This https://arxiv.org/abs/2506.02635 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Efficient Quadratic Corrections for Frank-Wolfe Algorithms
We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended pairwise conditional gradients and fully-corrective Frank-Wolfe, and propose a highly efficient corrective algorithm in the case of convex quadratic objectives based on linear optimization or linear system solving, akin to Wolfe's minimum-norm point. Beyond optimization problems that are directly quadratic, we revisit two algorithms, split conditional gradient for the intersection of two…