# Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs

arXiv: https://arxiv.org/abs/2506.01404 · HTML: https://mlsanity.com/paper/2506.01404/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 71 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 30 of 34)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [On Biased Compression for Distributed Learning](https://mlsanity.com/paper/2002.12410/) (2020)
- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Graph Neural Networks in Network Neuroscience](https://mlsanity.com/paper/2106.03535/) (2021)
- [Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classification](https://mlsanity.com/paper/2406.08993/) (2024)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Momentum Provably Improves Error Feedback!](https://mlsanity.com/paper/2305.15155/) (2023)
- [Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning](https://mlsanity.com/paper/2001.02112/) (2020)
- [Finite-Bit Quantization For Distributed Algorithms With Linear Convergence](https://mlsanity.com/paper/2107.11304/) (2021)
- [Advances in Distributed Graph Filtering](https://mlsanity.com/paper/1808.03004/) (2018)
- [Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)](https://mlsanity.com/paper/2006.11220/) (2020)
- [Compressive Spectral Clustering](https://mlsanity.com/paper/1602.02018/) (2016)
- [Learning over Multitask Graphs -- Part I: Stability Analysis](https://mlsanity.com/paper/1805.08535/) (2018)
- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [Filtering Random Graph Processes Over Random Time-Varying Graphs](https://mlsanity.com/paper/1705.00442/) (2017)
- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [Learning over Multitask Graphs -- Part II: Performance Analysis](https://mlsanity.com/paper/1805.08547/) (2018)
- [Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data](https://mlsanity.com/paper/2406.00621/) (2024)

## Abstract (arXiv)

This paper introduces an innovative error feedback framework designed to mitigate quantization noise in distributed graph filtering, where communications are constrained to quantized messages. It comes from error spectrum shaping techniques from state-space digital filters, and therefore establishes connections between quantized filtering processes over different domains. In contrast to existing error compensation methods, our framework quantitatively feeds back the quantization noise for exact compensation. We examine the framework under three key scenarios: (i) deterministic graph filtering, (ii) graph filtering over random graphs, and (iii) graph filtering with random node-asynchronous updates. Rigorous theoretical analysis demonstrates that the proposed framework significantly reduces the effect of quantization noise, and we provide closed-form solutions for the optimal error feedback coefficients. Moreover, this quantitative error feedback mechanism can be seamlessly integrated into communication-efficient decentralized optimization frameworks, enabling lower error floors. Numerical experiments validate the theoretical results, consistently showing that our method outperforms conventional quantization strategies in terms of both accuracy and robustness.