# Toward Understanding the Influence of Individual Clients in Federated Learning

arXiv: https://arxiv.org/abs/2012.10936 · HTML: https://mlsanity.com/paper/2012.10936/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2020.

## Built on by (most cited first, 16 of 16)

- [Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective](https://mlsanity.com/paper/2111.11850/) (2021)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [Towards Interpretable Federated Learning](https://mlsanity.com/paper/2302.13473/) (2023)
- [Influence-Oriented Personalized Federated Learning](https://mlsanity.com/paper/2410.03315/) (2024)
- [LIA: Privacy-Preserving Data Quality Evaluation in Federated Learning Using a Lazy Influence Approximation](https://mlsanity.com/paper/2205.11518/) (2022)
- [Incentivising the federation: gradient-based metrics for data selection and valuation in private decentralised training](https://mlsanity.com/paper/2305.02942/) (2023)
- [FedMobile: Enabling Knowledge Contribution-aware Multi-modal Federated Learning with Incomplete Modalities](https://mlsanity.com/paper/2502.15839/) (2025)
- [Keep It Simple: Fault Tolerance Evaluation of Federated Learning with Unreliable Clients](https://mlsanity.com/paper/2305.09856/) (2023)
- [Suppressing Noise from Built Environment Datasets to Reduce Communication Rounds for Convergence of Federated Learning](https://mlsanity.com/paper/2209.01417/) (2022)
- [Decentralized Hyper-Gradient Computation over Time-Varying Directed Networks](https://mlsanity.com/paper/2210.02129/) (2022)
- [Evaluating the Impact of Local Differential Privacy on Utility Loss via Influence Functions](https://mlsanity.com/paper/2309.08678/) (2023)
- [SoK: Memorisation in machine learning](https://mlsanity.com/paper/2311.03075/) (2023)
- [Adaptive incentive for cross-silo federated learning: A multi-agent reinforcement learning approach](https://mlsanity.com/paper/2302.07493/) (2023)
- [Lazy But Effective: Collaborative Personalized Federated Learning with Heterogeneous Data](https://mlsanity.com/paper/2505.02540/) (2025)
- [How to Evaluate Participant Contributions in Decentralized Federated Learning](https://mlsanity.com/paper/2505.23246/) (2025)
- [Beyond Non-IID: Learner--Client Distribution Mismatch in Federated Learning](https://mlsanity.com/paper/2608.27715/) (2026)

## Abstract (arXiv)

Federated learning allows mobile clients to jointly train a global model without sending their private data to a central server. Extensive works have studied the performance guarantee of the global model, however, it is still unclear how each individual client influences the collaborative training process. In this work, we defined a new notion, called em Fed-Influence, to quantify this influence over the model parameters, and proposed an effective and efficient algorithm to estimate this metric. In particular, our design satisfies several desirable properties: (1) it requires neither retraining nor retracing, adding only linear computational overhead to clients and the server; (2) it strictly maintains the tenets of federated learning, without revealing any client's local private data; and (3) it works well on both convex and non-convex loss functions, and does not require the final model to be optimal. Empirical results on a synthetic dataset and the FEMNIST dataset demonstrate that our estimation method can approximate Fed-Influence with small bias. Further, we show an application of Fed-Influence in model debugging.