Structured Sparsity Promoting Functions

Shen, Lixin; Suter, Bruce W.; Tripp, Erin E.

doi:10.48550/arxiv.1809.06777

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…In functional compression, functions themselves can also be exploited. There exist functions with special structures, such as sparsity promoting functions [28], symmetric functions, type sensitive and threshold functions [29]. One can also exploit a function's surjectivity.…”

Section: B Related Workmentioning

confidence: 99%

Function Load Balancing Over Networks

Malak

Médard²

2021

IEEE J. Sel. Areas Inf. Theory

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Using networks as a means of computing can reduce the communication flow or the total number of bits transmitted over the networks. In this paper, we propose to distribute the computation load in stationary networks, and formulate a flow-based delay minimization problem that jointly captures the aspects of communications and computation. We exploit the distributed compression scheme of Slepian-Wolf that is applicable under any protocol information where nodes can do compression independently using different codebooks. We introduce the notion of entropic surjectivity as a measure to determine how sparse the function is and to understand the limits of functional compression for computation. We leverage Little's Law for stationary systems to provide a connection between surjectivity and the computation processing factor that reflects the proportion of flow that requires communications. This connection gives us an understanding of how much a node (in isolation) should compute to communicate the desired function within the network without putting any assumptions on the topology. Our results suggest that to effectively compute different function classes that have different entropic surjectivities, the networks can be re-structured with the transition probabilities being tailored for functions, i.e., task-based link reservations, which can enable mixing versus separately processing of a diverse function classes. They also imply that most of the available resources are reserved for computing low complexity functions versus fewer resources for processing of high complexity ones. We numerically evaluate our technique for search, MapReduce, and classification functions, and infer how sensitive the processing factor for each computation task to the entropic surjectivity is. Slepian-Wolf Achievable rate region 𝐻 ! !" 𝑋 " 𝑋 # ) 𝐻 ! !# 𝑋 # 𝑋 " ) 𝐻(𝑋 " ) 𝐻(𝑋 # ) 𝐻 ! ! " , ! ! # ( 𝑋 " , 𝑋 # ) 𝐻(𝑋 " , 𝑋 # ) 𝐻 𝑋 " 𝑋 # ) 𝐻 𝑋 # 𝑋 " ) 𝑅 & # 𝑅 &"

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Section: B Related Workmentioning

confidence: 99%

Function Load Balancing Over Networks

Malak

Médard²

2021

IEEE J. Sel. Areas Inf. Theory

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“…In functional compression, functions themselves can also be exploited. There exist functions with special structures, such as sparsity promoting functions [31], symmetric functions, type sensitive and threshold functions [32]. One can also exploit a function's surjectivity.…”

Section: Related Workmentioning

confidence: 99%

How to Distribute Computation in Networks

Malak¹,

Cohen²,

Médard³

2019

Preprint

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In network function computation is as a means to reduce the required communication flow in terms of number of bits transmitted per source symbol. However, the rate region for the function computation problem in general topologies is an open problem, and has only been considered under certain restrictive assumptions (e.g. tree networks, linear functions, etc.). In this paper, we propose a new perspective for distributing computation, and formulate a flow-based delay cost minimization problem that jointly captures the costs of communications and computation. We introduce the notion of entropic surjectivity as a measure to determine how sparse the function is and to understand the limits of computation. Exploiting Little's law for stationary systems, we provide a connection between this new notion and the computation processing factor that reflects the proportion of flow that requires communications. This connection gives us an understanding of how much a node (in isolation) should compute to communicate the desired function within the network without putting any assumptions on the topology. Our analysis characterizes the functions only via their entropic surjectivity, and provides insight into how to distribute computation. We numerically test our technique for search, MapReduce, and classification tasks, and infer for each task how sensitive the processing factor to the entropic surjectivity is.

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Structured Sparsity Promoting Functions

Cited by 2 publications

References 12 publications

Function Load Balancing Over Networks

Function Load Balancing Over Networks

How to Distribute Computation in Networks

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