# DICE: Data Influence Cascade in Decentralized Learning

arXiv: https://arxiv.org/abs/2507.06931 · HTML: https://mlsanity.com/paper/2507.06931/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 87 of its 131 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 30 of 87)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [Asynchronous Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06952/) (2017)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [D2: Decentralized Training over Decentralized Data](https://mlsanity.com/paper/1803.07068/) (2018)
- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Dataset Pruning: Reducing Training Data by Examining Generalization Influence](https://mlsanity.com/paper/2205.09329/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)

## Built on by (most cited first, 2 of 2)

- [On the Escaping Efficiency of Distributed Adversarial Training Algorithms](https://mlsanity.com/paper/2509.11337/) (2025)
- [Row-Stochastic Matrices Can Provably Outperform Doubly Stochastic Matrices in Decentralized Learning](https://mlsanity.com/paper/2511.19513/) (2025)

## Abstract (arXiv)

Decentralized learning offers a promising approach to crowdsource data consumptions and computational workloads across geographically distributed compute interconnected through peer-to-peer networks, accommodating the exponentially increasing demands. However, proper incentives are still in absence, considerably discouraging participation. Our vision is that a fair incentive mechanism relies on fair attribution of contributions to participating nodes, which faces non-trivial challenges arising from the localized connections making influence ``cascade'' in a decentralized network. To overcome this, we design the first method to estimate Data Influence CascadE (DICE) in a decentralized environment. Theoretically, the framework derives tractable approximations of influence cascade over arbitrary neighbor hops, suggesting the influence cascade is determined by an interplay of data, communication topology, and the curvature of loss landscape. DICE also lays the foundations for applications including selecting suitable collaborators and identifying malicious behaviors. Project page is available at https://raiden-zhu.github.io/blog/2025/DICE/.