# Internal Cross-layer Gradients for Extending Homogeneity to Heterogeneity in Federated Learning

arXiv: https://arxiv.org/abs/2308.11464 · HTML: https://mlsanity.com/paper/2308.11464/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 66 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 30 of 47)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [FedMD: Heterogenous Federated Learning via Model Distillation](https://mlsanity.com/paper/1910.03581/) (2019)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Data-Free Knowledge Distillation for Heterogeneous Federated Learning](https://mlsanity.com/paper/2105.10056/) (2021)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients](https://mlsanity.com/paper/2010.01264/) (2020)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Asynchronous Federated Optimization](https://mlsanity.com/paper/1903.03934/) (2019)
- [No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2106.05001/) (2021)
- [Universally Slimmable Networks and Improved Training Techniques](https://mlsanity.com/paper/1903.05134/) (2019)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)

## Built on by (most cited first, 5 of 5)

- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [Federated Model Heterogeneous Matryoshka Representation Learning](https://mlsanity.com/paper/2406.00488/) (2024)
- [Federated Learning with Sample-level Client Drift Mitigation](https://mlsanity.com/paper/2501.11360/) (2025)
- [TACO: Tackling Over-correction in Federated Learning with Tailored Adaptive Correction](https://mlsanity.com/paper/2504.17528/) (2025)
- [SpecGradFilter: A Spectral Gradient Filtering Framework for Taming Federated Heterogeneity](https://mlsanity.com/paper/2607.04189/) (2026)

## Abstract (arXiv)

Federated learning (FL) inevitably confronts the challenge of system heterogeneity in practical scenarios. To enhance the capabilities of most model-homogeneous FL methods in handling system heterogeneity, we propose a training scheme that can extend their capabilities to cope with this challenge. In this paper, we commence our study with a detailed exploration of homogeneous and heterogeneous FL settings and discover three key observations: (1) a positive correlation between client performance and layer similarities, (2) higher similarities in the shallow layers in contrast to the deep layers, and (3) the smoother gradients distributions indicate the higher layer similarities. Building upon these observations, we propose InCo Aggregation that leverages internal cross-layer gradients, a mixture of gradients from shallow and deep layers within a server model, to augment the similarity in the deep layers without requiring additional communication between clients. Furthermore, our methods can be tailored to accommodate model-homogeneous FL methods such as FedAvg, FedProx, FedNova, Scaffold, and MOON, to expand their capabilities to handle the system heterogeneity. Copious experimental results validate the effectiveness of InCo Aggregation, spotlighting internal cross-layer gradients as a promising avenue to enhance the performance in heterogeneous FL.