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Deep Randomized Distributed Function Computation (DeepRDFC): Neural Distributed Channel Simulation

Didrik Bergström, Onur Günlü

TL;DR

The randomized distributed function computation (RDFC) framework is considered and an autoencoder architecture is proposed to minimize the total variation distance between the probability distribution simulated by the AE outputs and an unknown target distribution, using only data samples.

Abstract

The randomized distributed function computation (RDFC) framework, which unifies many cutting-edge distributed computation and learning applications, is considered. An autoencoder (AE) architecture is proposed to minimize the total variation distance between the probability distribution simulated by the AE outputs and an unknown target distribution, using only data samples. We illustrate significantly high RDFC performance with communication load gains from our AEs compared to data compression methods. Our designs establish deep learning-based RDFC methods and aim to facilitate the use of RDFC methods, especially when the amount of common randomness is limited and strong function computation guarantees are required.

Deep Randomized Distributed Function Computation (DeepRDFC): Neural Distributed Channel Simulation

TL;DR

The randomized distributed function computation (RDFC) framework is considered and an autoencoder architecture is proposed to minimize the total variation distance between the probability distribution simulated by the AE outputs and an unknown target distribution, using only data samples.

Abstract

The randomized distributed function computation (RDFC) framework, which unifies many cutting-edge distributed computation and learning applications, is considered. An autoencoder (AE) architecture is proposed to minimize the total variation distance between the probability distribution simulated by the AE outputs and an unknown target distribution, using only data samples. We illustrate significantly high RDFC performance with communication load gains from our AEs compared to data compression methods. Our designs establish deep learning-based RDFC methods and aim to facilitate the use of RDFC methods, especially when the amount of common randomness is limited and strong function computation guarantees are required.
Paper Structure (11 sections, 1 theorem, 5 equations, 2 figures, 3 tables, 2 algorithms)

This paper contains 11 sections, 1 theorem, 5 equations, 2 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Review of AEs
  3. Distributed Channel Simulation
  4. Review of AEs
  5. AE-based RDFC
  6. Loss Function for TVD Minimization
  7. Training and Testing
  8. Vector Quantizer Layer
  9. Experimental Results
  10. AE Design Insights
  11. Conclusion

Key Result

Theorem 1

The RDFC rate region $\mathcal{R}$ is It suffices to have $|\mathcal{U}| \leq |\mathcal{X}||\mathcal{Y}|+2$.

Figures (2)

  • Figure 1: Distributed channel simulation system model, implemented using our AE designs.
  • Figure 2: Heatmaps for $Q_{\underaccent{\bar{}}{X}\underaccent{\bar{}}{Y}}$ and $P_{\underaccent{\bar{}}{X}\underaccent{\bar{}}{Y}}$ of a $\text{BSC}(p\!=\!0.25)$ and $n\!=\!8$, where (a) is $Q_{\underaccent{\bar{}}{X}\underaccent{\bar{}}{Y}}$; (b) is $P_{\underaccent{\bar{}}{X}\underaccent{\bar{}}{Y}}$ with $nR_L\!=\!16$, $nR_0\!=\!0$, and $\text{TVD}_T\approx0.35$; and (c) is $P_{\underaccent{\bar{}}{X}\underaccent{\bar{}}{Y}}$ with $nR_L\!=\!16$,$nR_0\!=\!16$, and $\text{TVD}_T\approx0.04$. The x- and y-axis correspond to $\underaccent{\bar{}}{x}$ and $\underaccent{\bar{}}{y}$, respectively.

Theorems & Definitions (2)

  • Definition 1
  • Theorem 1: CuffChannelSynthesis