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

Didrik Bergström; Onur Günlü

cs.ITMar 11, 2026

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

Authors: Didrik Bergström, Onur Günlü

Organizations: Information Theory and Security Laboratory (ITSL), Linköping University, Sweden

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.

Figures & tables

Panel of Figure 1 — Fig. 1: Distributed channel simulation system model, implemented using our AE designs.

#	Layer	In-Layer	Output Dim.
1	Input $\underaccent{\bar}{x}$	—	$2^{n}$
2	Input $\underaccent{\bar}{k}$	—	$nR_{0}$
3	Concatenate	1,2	$4(2^{n}+nR_{0})$
4-6	Dense + ReLU	3	$4(2^{n}+nR_{0})$
7	Dense + Sigmoid	6	$n-1$
8	Vector Quantizer	7	$n-1$

TABLE I: General layout of AE, where for cases without common randomness, we set

nR_{0}=0

and remove layer 2.

$n$	$nR_{0}$	$nR_{L}$	$nR$	$p$	$\text{TVD}_{T}$	$\text{TVD}_{G}$
$8$	–	$12$	$7$	$0.11$	$0.575393$	$0.575175$
$8$	–	$12$	$7$	$0.25$	$0.349378$	$0.348698$
$10$	–	$15$	$9$	$0.11$	$0.553410$	$0.551960$
$10$	–	$15$	$9$	$0.25$	$0.370869$	$0.366169$
$8$	–	$16$	$7$	$0.11$	$0.558904$	$0.558633$
$8$	–	$16$	$7$	$0.25$	$0.346572$	$0.346019$

TABLE II: TVD hyper-parameter data in LR-case and LR+CR-case.

$n$	$nR_{0}$	$nR_{L}$	$T$	$N_{s}/T$
$8$	–	$12$	$2^{28}$	$25.000$ %
$10$	–	$15$	$2^{35}$	$0.1953$ %
$8$	–	$16$	$2^{32}$	$1.5620$ %
$10$	–	$20$	$2^{40}$	$0.0061$ %
$8$	$16$	$12$	$2^{44}$	$0.0004$ %
$10$	$20$	$15$	$2^{55}$	$1.863\cdot 10^{-7}$ %

TABLE III: Sample sizes in relation to total number of combinations.

Panel of Figure 5 — Fig. 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 $\text{TVD}_{T}\approx 0.35$ ; and (c) is $P_{\underaccent{\bar}{X}\underaccent{\bar}{Y}}$ with $nR_{L}\!=\!16$ , $nR_{0}\!=\!16$ , and $\text{TVD}_{T}\approx 0.04$ . The x- and y-axis correspond to $\underaccent{\bar}{x}$ and $\underaccent{\bar}{y}$ , respectively.

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Scalable Discrete-to-Continuous Channel Simulation for Compression and Privacy

Joseph Rowan, Buu Phan, Ashish J. Khisti

Department of Electrical and Computer Engineering, University of Toronto

Open paper AskPDF arXiv

Channel simulation has recently emerged as a useful component in machine learning systems where samples from a prescribed probability distribution are to be compressed. Yet, general channel simulation algorithms often suffer from high computational costs, random stopping times or, in the worst case, can require generating an infinite number of shared random samples. We introduce a scheme for both exact and approximate simulation of discrete-to-continuous channels which conversely uses a fixed number of random samples, and therefore has a runtime independent of the channel and the input. Unlike existing channel simulation schemes which generate a sequence of independent samples from a proposal distribution, our approach generates one sample, or alternatively a fixed number of samples, from each potential target distribution. We then apply a latent permutation to the samples before performing sample selection using an exponential race. Our scheme provides a flexible tradeoff between the number of generated samples and the compression rate. Using polar and multilevel coding, we scale our approach to handle long blocklengths in

O(n \log n)

time in order to benefit from reduced per-symbol overhead. We conclude by demonstrating applications to variable-rate compression with stochastic VQ-VAEs and communication-efficient differentially private distributed mean estimation via exact simulation of the Gaussian mechanism.

Abstract

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