124 citations · 566 across the 52 of their papers we have counts for
64 papers
Representing MAX functions using two-hidden-layer ReLU networks
Zhimao Wang, Amitabh Basu
We study exact representations of using two-hidden-layer ReLU neural networks. This problem has been studied in recent years in an attempt…
Information Complexity of Mixed-integer Convex Optimization
Amitabh Basu, Hongyi Jiang, Phillip Kerger +1
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle,…
On the power of graph neural networks and the role of the activation function
Sammy Khalife, Amitabh Basu
In this article we present new results about the expressivity of Graph Neural Networks (GNNs). We prove that for any GNN with piecewise polynomial activations, whose architecture s…
Globally optimal and scalable -way matching of astronomy catalogs
Tu Nguyen, Amitabh Basu, Támas Budavári
Building on previous Bayesian approaches, we introduce a novel formulation of probabilistic cross-identification, where detections are directly associated to (hypothesized) astrono…
Neural networks with linear threshold activations: structure and algorithms
Sammy Khalife, Hongyu Cheng, Amitabh Basu
In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by suc…
Helly systems and certificates in optimization
Amitabh Basu, Tongtong Chen, Michele Conforti +1
Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof complexity, we develop a general approach via Hoffman's Helly systems. This helps to d…