General Coded Computing: Adversarial Settings

TL;DR

This paper introduces a foundational framework for general coded computing that extends beyond structured tasks, effectively managing adversarial servers and ensuring robustness across a wide range of computations, including neural network inference.

Contribution

It develops a novel scheme for general coded computing capable of handling adversarial servers, achieving optimal robustness and broad applicability beyond traditional algebraic tasks.

Findings

Error decay rate of $N^{rac{6}{5}(a-1)}$ with adversarial fraction $a$

Achieves optimal adversarial robustness in general coded computing

Validated effectiveness on neural network inference tasks

Abstract

Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to improve the reliability of distributed systems in the presence of stragglers and adversarial servers. This paper lays the foundation for general coded computing, which extends the applicability of coded computing to handle a wide class of computations. In addition, it particularly addresses the challenging problem of managing adversarial servers. We demonstrate that, in the proposed scheme, for a system with $N$ servers, where $\mathcal{O}(N^a)$, $a \in [0,1)$, are adversarial, the supremum of the average approximation error over all adversarial strategies decays at a rate of $N^{\frac{6}{5}(a-1)}$, under minimal assumptions on the computing tasks. Furthermore, we show that within a general framework, the proposed scheme achieves optimal adversarial robustness, in terms of maximum number of adversarial servers it can tolerate. This marks a significant step toward practical and reliable general coded computing. Implementation results further validate the effectiveness of the proposed method in handling various computations, including inference in deep neural networks.