# Analog Lagrange Coded Computing

arXiv: https://arxiv.org/abs/2008.08565 · HTML: https://mlsanity.com/paper/2008.08565/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2020.

## Built on by (most cited first, 13 of 13)

- [ApproxIFER: A Model-Agnostic Approach to Resilient and Robust Prediction Serving Systems](https://mlsanity.com/paper/2109.09868/) (2021)
- [Coded Computing for Resilient Distributed Computing: A Learning-Theoretic Framework](https://mlsanity.com/paper/2406.00300/) (2024)
- [List-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier](https://mlsanity.com/paper/2101.11653/) (2021)
- [General Coded Computing: Adversarial Settings](https://mlsanity.com/paper/2502.08058/) (2025)
- [Privacy-aware Berrut Approximated Coded Computing for Federated Learning](https://mlsanity.com/paper/2405.01704/) (2024)
- [Privacy-aware Berrut Approximated Coded Computing applied to general distributed learning](https://mlsanity.com/paper/2505.06759/) (2025)
- [Generalized Lagrange Coded Computing: A Flexible Computation-Communication Tradeoff for Resilient, Secure, and Private Computation](https://mlsanity.com/paper/2204.11168/) (2022)
- [A Learning-Based Approach to Approximate Coded Computation](https://mlsanity.com/paper/2205.09818/) (2022)
- [Differentially Private Secure Multiplication: Hiding Information in the Rubble of Noise](https://mlsanity.com/paper/2309.16105/) (2023)
- [Perfectly-Private Analog Secure Aggregation in Federated Learning](https://mlsanity.com/paper/2509.08683/) (2025)
- [Privacy-Preserving and Verifiable Approximate Distributed Coded Computing](https://mlsanity.com/paper/2607.02187/) (2026)
- [Learning-Theoretic Foundation for General Coded Computing: The Straggler Setting](https://mlsanity.com/paper/2608.28910/) (2026)
- [GenomeOcean Anywhere: Private WebGPU Inference for Genome MoEs](https://mlsanity.com/paper/2609.35882/) (2026)

## Abstract (arXiv)

A distributed computing scenario is considered, where the computational power of a set of worker nodes is used to perform a certain computation task over a dataset that is dispersed among the workers. Lagrange coded computing (LCC), proposed by Yu et al., leverages the well-known Lagrange polynomial to perform polynomial evaluation of the dataset in such a scenario in an efficient parallel fashion while keeping the privacy of data amidst possible collusion of workers. This solution relies on quantizing the data into a finite field, so that Shamir's secret sharing, as one of its main building blocks, can be employed. Such a solution, however, is not properly scalable with the size of dataset, mainly due to computation overflows. To address such a critical issue, we propose a novel extension of LCC to the analog domain, referred to as analog LCC (ALCC). All the operations in the proposed ALCC protocol are done over the infinite fields of R/C but for practical implementations floating-point numbers are used. We characterize the privacy of data in ALCC, against any subset of colluding workers up to a certain size, in terms of the distinguishing security (DS) and the mutual information security (MIS) metrics. Also, the accuracy of outcome is characterized in a practical setting assuming operations are performed using floating-point numbers. Consequently, a fundamental trade-off between the accuracy of the outcome of ALCC and its privacy level is observed and is numerically evaluated. Moreover, we implement the proposed scheme to perform matrix-matrix multiplication over a batch of matrices. It is observed that ALCC is superior compared to the state-of-the-art LCC, implemented using fixed-point numbers, assuming both schemes use an equal number of bits to represent data symbols.