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State-driven Implicit Modeling for Sparsity and Robustness in Neural Networks
Implicit models are a general class of learning models that forgo the hierarchical layer structure typical in neural networks and instead define the internal states based on an ``equilibrium'' equation, offering competitive performance and reduced memory consumption.
On the convex hull of convex quadratic optimization problems with indicators
We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic number of additional variables consists of a single positive semidefinite constraint (explicitly stated) and linear constraints.
Safe Screening Rules for $\ell_0$-Regression
We give safe screening rules to eliminate variables from regression with $\ell_0$ regularization or cardinality constraint.
