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We consider distributed computation of a sequence of $J$ gradients $\{\mathbf {g}(0), \ldots,\mathbf {g}(J-1)\}$ . Each worker node computes a fraction of $\mathbf {g}(t)$ in round- $t$ and attempts to communicate the result to a master. Master is required to obtain the full gradient $\mathbf {g}(t)$ by the end of round- $(t+T)$ . The goal here is to finish all the $J$ gradient computations, keeping the cumulative processing time as short as possible. Delayed availability of results from individual workers causes bottlenecks in this setting.

Zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) allows a party, known as the prover, to convince another party, known as the verifier, that he knows a private value $v$ , without revealing it, such that $F(u,v)=y$ for some function $F$ and public values $u$ and $y$ . There are various versions of zk-SNARK, among them, Quadratic Arithmetic Program (QAP)-based zk-SNARK has been widely used in practice, especially in Blockchain technology.

The emerging large-scale and data-hungry algorithms require the computations to be delegated from a central server to several worker nodes. One major challenge in the distributed computations is to tackle delays and failures caused by the stragglers. To address this challenge, introducing efficient amount of redundant computations via distributed coded computation has received significant attention. Recent approaches in this area have mainly focused on introducing minimum computational redundancies to tolerate certain number of stragglers.

Using networks as a means of computing can reduce the communication flow over networks. We propose to distribute the computation load in stationary networks and formulate a flow-based delay minimization problem that jointly captures the costs of communications and computation. We exploit the distributed compression scheme of Slepian-Wolf that is applicable under any protocol information. We introduce the notion of entropic surjectivity as a measure of function’s sparsity and to understand the limits of functional compression for computation.

Gradient codes use data replication to mitigate the effect of straggling machines in distributed machine learning. Approximate gradient codes consider codes where the data replication factor is too low to recover the full gradient exactly. Our work is motivated by the challenge of designing approximate gradient codes that simultaneously work well in both the adversarial and random straggler models. We introduce novel approximate gradient codes based on expander graphs.