# SpecGradFilter: A Spectral Gradient Filtering Framework for Taming Federated Heterogeneity

arXiv: https://arxiv.org/abs/2607.04189 · HTML: https://mlsanity.com/paper/2607.04189/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [FedDC: Federated Learning with Non-IID Data via Local Drift Decoupling and Correction](https://mlsanity.com/paper/2203.11751/) (2022)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [Federated Learning with Label Distribution Skew via Logits Calibration](https://mlsanity.com/paper/2209.00189/) (2022)
- [Improving Generalization in Federated Learning by Seeking Flat Minima](https://mlsanity.com/paper/2203.11834/) (2022)
- [FedCM: Federated Learning with Client-level Momentum](https://mlsanity.com/paper/2106.10874/) (2021)
- [FedDisco: Federated Learning with Discrepancy-Aware Collaboration](https://mlsanity.com/paper/2305.19229/) (2023)
- [Revisiting Weighted Aggregation in Federated Learning with Neural Networks](https://mlsanity.com/paper/2302.10911/) (2023)
- [Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape](https://mlsanity.com/paper/2305.11584/) (2023)
- [GIANT: Globally Improved Approximate Newton Method for Distributed Optimization](https://mlsanity.com/paper/1709.03528/) (2017)
- [Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization](https://mlsanity.com/paper/2405.18890/) (2024)
- [FireCaffe: near-linear acceleration of deep neural network training on compute clusters](https://mlsanity.com/paper/1511.00175/) (2015)
- [FedAWA: Adaptive Optimization of Aggregation Weights in Federated Learning Using Client Vectors](https://mlsanity.com/paper/2503.15842/) (2025)
- [FedSkip: Combatting Statistical Heterogeneity with Federated Skip Aggregation](https://mlsanity.com/paper/2212.07224/) (2022)
- [FedLWS: Federated Learning with Adaptive Layer-wise Weight Shrinking](https://mlsanity.com/paper/2503.15111/) (2025)
- [Towards the Flatter Landscape and Better Generalization in Federated Learning under Client-level Differential Privacy](https://mlsanity.com/paper/2305.00873/) (2023)
- [Internal Cross-layer Gradients for Extending Homogeneity to Heterogeneity in Federated Learning](https://mlsanity.com/paper/2308.11464/) (2023)
- [Tackling Resource-Constrained and Data-Heterogeneity in Federated Learning with Double-Weight Sparse Pack](https://mlsanity.com/paper/2601.01840/) (2026)

## Abstract (arXiv)

Federated Learning (FL) is fundamentally challenged by statistical heterogeneity, where non-identically distributed (non-IID) data induces client drift that severely hampers global convergence. While existing approaches attempt to mitigate this drift through spatial-domain gradient correction or regularization, they overlook the intrinsic spectral structure of optimization signals. In this work, we revisit client drift from a novel frequency-domain perspective and uncover a critical Spectral Bias of Drift: inter-client gradient divergence is predominantly concentrated in low-frequency components which encode client-specific distributional shifts, while high-frequency components representing fine-grained features remain relatively consistent. Motivated by this, we propose SpecGradFilter, a unified Spectral Gradient Filtering Framework that tames heterogeneity by suppressing discordant low-frequency signals. Crucially, we demonstrate that SpecGradFilter is a generalizable principle, effective not only via precise FFT-based truncation but also through spatial approximations like Gaussian detrending. Extensive experiments on benchmarks such as CIFAR-10/100 and Tiny-ImageNet demonstrate that SpecGradFilter significantly performs better performance in highly Non-IID settings with negligible communication overhead, establishing a new paradigm for robust federated optimization.