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Preconditioned subgradient method for composite optimization: overparameterization and fast convergence
Mateo Díaz, Liwei Jiang, Abdel Ghani Labassi
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing appl…
Beyond Scores: Proximal Diffusion Models
Zhenghan Fang, Mateo Díaz, Sam Buchanan +1
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the reali…
On Transferring Transferability: Towards a Theory for Size Generalization
Eitan Levin, Yuxin Ma, Mateo Díaz +1
Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs a…
Invariant Kernels: Rank Stabilization and Generalization Across Dimensions
Mateo Díaz, Dmitriy Drusvyatskiy, Jack Kendrick +1
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary appli…
PDLP: A Practical First-Order Method for Large-Scale Linear Programming
David Applegate, Mateo Díaz, Oliver Hinder +4
We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) metho…