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Breaking the Quadratic Barrier for Matroid Intersection
Combining this with previous exact and approximation algorithms leads to our results.
Data Structures and Algorithms Discrete Mathematics
Minimum Cost Flows, MDPs, and $\ell_1$-Regression in Nearly Linear Time for Dense Instances
In the special case of the minimum cost flow problem on $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities we obtain a randomized method which solves the problem in $\tilde{O}(m+n^{1. 5})$ time.
Data Structures and Algorithms Optimization and Control
Training (Overparametrized) Neural Networks in Near-Linear Time
The slow convergence rate and pathological curvature issues of first-order gradient methods for training deep neural networks, initiated an ongoing effort for developing faster $\mathit{second}$-$\mathit{order}$ optimization algorithms beyond SGD, without compromising the generalization error.
