Related papers: An Encoder-Decoder Approach for Packing Circles
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
Semantic segmentation, which refers to pixel-wise classification of an image, is a fundamental topic in computer vision owing to its growing importance in robot vision and autonomous driving industries. It provides rich information about…
We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. Multiple packing is a natural generalization of the sphere packing problem. For any $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $, a multiple…
We propose a deep learning framework based on an encoder-decoder architecture for the design and evaluation of cloaking devices, demonstrated in this work for two-dimensional wave propagation governed by the Helmholtz equation. The cloaks…
Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user's local cache memory, even without knowledge of user's later demands. Maddah-Ali and Niesen proposed a two-phase…
The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of disks in a rectangle without overlapping.) We consider the following algorithmic…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
Recently, Transformer-based encoder-decoder models have demonstrated strong performance in multilingual speech recognition. However, the decoder's autoregressive nature and large size introduce significant bottlenecks during inference.…
We propose a novel decoding approach for neural machine translation (NMT) based on continuous optimisation. We convert decoding - basically a discrete optimization problem - into a continuous optimization problem. The resulting constrained…
Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular…
In this work, we present Detective - an attentive object detector that identifies objects in images in a sequential manner. Our network is based on an encoder-decoder architecture, where the encoder is a convolutional neural network, and…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
We present an optimal method for encoding cluster assignments of arbitrary data sets. Our method, Random Cycle Coding (RCC), encodes data sequentially and sends assignment information as cycles of the permutation defined by the order of…
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
Modern 3D printing technologies and the upcoming mass-customization paradigm call for efficient methods to produce and distribute arbitrarily-shaped 3D objects. This paper introduces an original algorithm to split a 3D model in parts that…
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
Encoder-decoder networks with attention have proven to be a powerful way to solve many sequence-to-sequence tasks. In these networks, attention aligns encoder and decoder states and is often used for visualizing network behavior. However,…
In this paper we describe a method for packing tubes and boxes in containers. Each container is divided into parts (holders) which are allocated to subsets of objects. The method consists of a recursive procedure which, based on a…
In this paper, we propose a general approach to optimize anchor boxes for object detection. Nowadays, anchor boxes are widely adopted in state-of-the-art detection frameworks. However, these frameworks usually pre-define anchor box shapes…