Related papers: Optimal-Depth Sorting Networks
Automatically determining knot number and positions is a fundamental and challenging problem in B-spline approximation. In this paper, the knot placement is abstracted as a mapping from initial knots to the optimal knots. We innovatively…
Previous work identifying depth-optimal $n$-channel sorting networks for $9\leq n \leq 16$ is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper…
We consider the problem of sorting elements on a series of stacks, introduced by Tarjan and Knuth. We improve the asymptotic lower bound for the number of stacks necessary to sort $n$ elements to $0.561 \log_2 n + O(1)$. This is the first…
In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of…
This paper studies properties of the back end of a sorting network and illustrates the utility of these in the search for networks of optimal size or depth. All previous works focus on properties of the front end of networks and on how to…
A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n->infinity the space-time process of swaps converges to the…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
The paper is divided in to two parts. In the first part we present some new results for the \textit{routing via matching} model introduced by Alon et al\cite{5}. This model can be viewed as a communication scheme on a distributed network.…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…
Deep neural networks (DNNs) have provided brilliant performance across various tasks. However, this success often comes at the cost of unnecessarily large model sizes, high computational demands, and substantial memory footprints.…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
In recent years, deeper and wider neural networks have shown excellent performance in computer vision tasks, while their enormous amount of parameters results in increased computational cost and overfitting. Several methods have been…
It is well-known that the training of Deep Neural Networks (DNN) can be formalized in the language of optimal control. In this context, this paper leverages classical turnpike properties of optimal control problems to attempt a quantifiable…
The problem of searchability in decentralized complex networks is of great importance in computer science, economy and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion…
Network compression reduces the computational complexity and memory consumption of deep neural networks by reducing the number of parameters. In SVD-based network compression, the right rank needs to be decided for every layer of the…
We develop a fast end-to-end method for training lightweight neural networks using multiple classifier heads. By allowing the model to determine the importance of each head and rewarding the choice of a single shallow classifier, we are…
Existing high-performance deep learning models require very intensive computing. For this reason, it is difficult to embed a deep learning model into a system with limited resources. In this paper, we propose the novel idea of the network…
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
This mini-course was given in the First Yaroslavl Summer School on Discrete and Computational Geometry in August 2012, organized by International Delaunay Laboratory "Discrete and Computational Geometry" of Demidov Yaroslavl State…