1 code implementation • 22 May 2024 • Hongyu Cheng, Amitabh Basu
Recent advances have employed a data-driven approach to select optimal cutting planes from a parameterized family, aimed at reducing the branch-and-bound tree size (in expectation) for a given distribution of integer programming instances.
no code implementations • 4 Feb 2024 • Hongyu Cheng, Sammy Khalife, Barbara Fiedorowicz, Amitabh Basu
We build upon recent work in this line of research by considering the setup where, instead of selecting a single algorithm that has the best performance, we allow the possibility of selecting an algorithm based on the instance to be solved, using neural networks.
no code implementations • 10 Jul 2023 • Sammy Khalife, Amitabh Basu
In contrast, it was already known that unbounded GNNs (those whose size is allowed to change with the graph sizes) with piecewise polynomial activations can distinguish these vertices in only two iterations.
no code implementations • 15 Nov 2021 • Sammy Khalife, Hongyu Cheng, Amitabh Basu
We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are necessary and sufficient to represent any function representable in the class.
no code implementations • 23 Jun 2021 • Hayden S. Helm, Marah Abdin, Benjamin D. Pedigo, Shweti Mahajan, Vince Lyzinski, Youngser Park, Amitabh Basu, Piali~Choudhury, Christopher M. White, Weiwei Yang, Carey E. Priebe
In modern ranking problems, different and disparate representations of the items to be ranked are often available.
1 code implementation • NeurIPS 2021 • Christoph Hertrich, Amitabh Basu, Marco Di Summa, Martin Skutella
We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture.
no code implementations • 19 Feb 2021 • Amitabh Basu, Hongyi Jiang
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope.
Combinatorics Optimization and Control 90C10, 90C57, 90C60
2 code implementations • 20 May 2020 • Hayden S. Helm, Amitabh Basu, Avanti Athreya, Youngser Park, Joshua T. Vogelstein, Carey E. Priebe, Michael Winding, Marta Zlatic, Albert Cardona, Patrick Bourke, Jonathan Larson, Marah Abdin, Piali Choudhury, Weiwei Yang, Christopher W. White
Learning to rank -- producing a ranked list of items specific to a query and with respect to a set of supervisory items -- is a problem of general interest.
no code implementations • 8 Nov 2017 • Anirbit Mukherjee, Amitabh Basu
We use the method of sign-rank to show exponential in dimension lower bounds for ReLU circuits ending in a LTF gate and of depths upto $O(n^{\xi})$ with $\xi < \frac{1}{8}$ with some restrictions on the weights in the bottom most layer.
no code implementations • 12 Aug 2017 • Akshay Rangamani, Anirbit Mukherjee, Amitabh Basu, Tejaswini Ganapathy, Ashish Arora, Sang Chin, Trac. D. Tran
This property holds independent of the loss function.
no code implementations • ICLR 2018 • Raman Arora, Amitabh Basu, Poorya Mianjy, Anirbit Mukherjee
In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU).