Computation Over Gaussian Networks With Orthogonal Components

Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.Comment: 30 pages, 12 figures, submitted to IEEE Transactions on Information Theor

Analyzing the Performance of Multilayer Neural Networks for Object Recognition

In the last two years, convolutional neural networks (CNNs) have achieved an impressive suite of results on standard recognition datasets and tasks. CNN-based features seem poised to quickly replace engineered representations, such as SIFT and HOG. However, compared to SIFT and HOG, we understand much less about the nature of the features learned by large CNNs. In this paper, we experimentally probe several aspects of CNN feature learning in an attempt to help practitioners gain useful, evidence-backed intuitions about how to apply CNNs to computer vision problems.Comment: Published in European Conference on Computer Vision 2014 (ECCV-2014

Computation in Multicast Networks: Function Alignment and Converse Theorems

The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks is considered: each receiver decodes an identical function of the original messages. For a countably infinite class of two-transmitter two-receiver single-hop linear deterministic networks, the computing capacity is characterized for a linear function (modulo-2 sum) of Bernoulli sources. Inspired by the geometric concept of interference alignment in networks, a new achievable coding scheme called function alignment is introduced. A new converse theorem is established that is tighter than cut-set based and genie-aided bounds. Computation (vs. communication) over multicast networks requires additional analysis to account for multiple receivers sharing a network's computational resources. We also develop a network decomposition theorem which identifies elementary parallel subnetworks that can constitute an original network without loss of optimality. The decomposition theorem provides a conceptually-simpler algebraic proof of achievability that generalizes to $L$-transmitter $L$-receiver networks.Comment: to appear in the IEEE Transactions on Information Theor

A Relation Between Network Computation and Functional Index Coding Problems

In contrast to the network coding problem wherein the sinks in a network demand subsets of the source messages, in a network computation problem the sinks demand functions of the source messages. Similarly, in the functional index coding problem, the side information and demands of the clients include disjoint sets of functions of the information messages held by the transmitter instead of disjoint subsets of the messages, as is the case in the conventional index coding problem. It is known that any network coding problem can be transformed into an index coding problem and vice versa. In this work, we establish a similar relationship between network computation problems and a class of functional index coding problems, viz., those in which only the demands of the clients include functions of messages. We show that any network computation problem can be converted into a functional index coding problem wherein some clients demand functions of messages and vice versa. We prove that a solution for a network computation problem exists if and only if a functional index code (of a specific length determined by the network computation problem) for a suitably constructed functional index coding problem exists. And, that a functional index coding problem admits a solution of a specified length if and only if a suitably constructed network computation problem admits a solution.Comment: 3 figures, 7 tables and 9 page