Understanding Deep Neural Networks with Rectified Linear Units
1 version
AB
Amitabh Basu
math.OCcs.LGmath.FAcs.CCcs.DMmath.COmath.MGstat.MLastro-ph.IMcs.DS
On Valency
published · living versionsPreprints & journals
67 papers in the corpus · 2011–2026A centerpoint theorem for three planar convex bodies
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Representing MAX functions using two-hidden-layer ReLU networks
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Sample Complexity of Stochastic Optimization with Integer Variables
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Linear Threshold for Oertel's Conjecture on the Mixed-Integer Volume
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Theoretical Challenges in Learning for Branch-and-Cut
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Identifying faulty edges in resistive electrical networks
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Tight Lower Bounds for Binary First-Order Oracles for Convex Optimization
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Generalization Guarantees for Learning Branch-and-Cut Policies in Integer Programming
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A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles
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Learning Cut Generating Functions for Integer Programming
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Sample Complexity of Algorithm Selection Using Neural Networks and Its Applications to Branch-and-Cut
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Information Complexity of Mixed-integer Convex Optimization
3 citations
On the power of graph neural networks and the role of the activation function
1 citation
Globally optimal and scalable -way matching of astronomy catalogs
2 citations
Neural networks with linear threshold activations: structure and algorithms
6 citations
Helly systems and certificates in optimization
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Complexity of optimizing over the integers
8 citations
Leveraging semantically similar queries for ranking via combining representations
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Towards Lower Bounds on the Depth of ReLU Neural Networks
19 citations
Enumerating integer points in polytopes with bounded subdeterminants
6 citations
Complexity of branch-and-bound and cutting planes in mixed-integer optimization -- II
15 citations
Optimal Probabilistic Catalogue Matching for Radio Sources
7 citations
Two-halfspace closure
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Distance-based Positive and Unlabeled Learning for Ranking
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Split cuts in the plane
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Complexity of branch-and-bound and cutting planes in mixed-integer optimization
35 citations
Admissibility of solution estimators for stochastic optimization
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An exposition of special relativity without appeal to "constancy of speed of light" hypotheses
1 citation
Mixed-integer bilevel representability
13 citations
Can cut generating functions be good and efficient?
3 citations
An extreme function which is nonnegative and discontinuous everywhere
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Mixed-integer linear representability, disjunctions, and Chvatal functions --- modeling implications
2 citations
Probabilistic Cross-identification of Multiple Catalogs in Crowded Fields
9 citations
Optimal cutting planes from the group relaxations
7 citations
Approximation of Minimal Functions by Extreme Functions
2 citations
Sparse Coding and Autoencoders
13 citations
Approximation of corner polyhedra with families of intersection cuts
9 citations
A geometric approach to cut-generating functions
29 citations
Minimal cut-generating functions are nearly extreme
7 citations
Extreme functions with an arbitrary number of slopes
9 citations
On the Relative Strength of Split, Triangle and Quadrilateral Cuts
49 citations
Minimal inequalities for an infinite relaxation of integer programs
58 citations
Maximal lattice-free convex sets in linear subspaces
78 citations
Convex Sets and Minimal Sublinear Functions
17 citations
Experiments with two-row cuts from degenerate tableaux
30 citations
Intersection Cuts with Infinite Split Rank
15 citations
A Counterexample to a Conjecture of Gomory and Johnson
29 citations
Characterization of the Split Closure via Geometric Lifting
1 citation
Mixed-integer linear representability, disjunctions, and variable elimination
7 citations
The structure of the infinite models in integer programming
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