DICE: Data Influence Cascade in Decentralized Learning

Authors: Tongtian Zhu, Wenhao Li, Can Wang, Fengxiang He
Primary area: interpretability and explainable AI
Keywords: Decentralized Learning, Data Influence, Data Valuation, Contribution Attribution, Incentive Mechanism

Abstract:
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.

Decision: accept (poster)
Reviewer scores: 6, 6, 6

Reviews and discussion:
<thread>
creation date:
1730029602063

thread_type:
official_review

<thread_object>
creator: reviewer_4yzv

<content>
summary:
The paper proposes DICE as a framework for measuring data influence cascades in decentralized environments. The framework explains how data influence propagates through the communication network, emphasizing the interaction between the original data and the network structure in shaping data influence within decentralized learning. The experimental results show that the first-order approximation of the “gold standard” for evaluating data influence in decentralized environment can approaching the truth, and this framework can used for detecting mislabeled anomalies.

strengths:
1. This paper summarizes previous work on measuring data influence and highlights the gaps in applying these methods to distributed scenarios.
2. This paper proposes a sound “gold standard” and its first-order approximation to quantify individual contributions in decentralized learning.

weaknesses:
1. The experiments are weak, and Section 5.3 is unfinished.
2. The notation η^t in Theorem 1 is previously appears as η_t in Algorithm 1.

questions:
Please see weaknesses.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730692651763

thread_type:
official_review

<thread_object>
creator: reviewer_f3r7

<content>
summary:
The paper proposes a method for quantifying the impact of data points in decentralized machine learning settings. The influence is measured not only at immediate neighbors but the entire network. This method can be useful for machine unlearning  or to develop new incentive mechanisms.

strengths:
-  The paper is well-organized, with clear definitions, figures, and explanations that make the methods and results easy to follow.
- The paper provides a solid theoretical framework, supported by rigorous proofs and analyses.

weaknesses:
- Need for more details about the practical use of this technique: While the authors use LLMs as one of the examples in the introduction, it might not be the best example to use in this case. It hard to see how this research addresses a practical problem or application that has real-world significance, or how this framework would be relevant for practitioners.
- Link with other papers that use gradient to cluster clients should be added, particularly interesting and relevant in the collaborator choice part.  
- Experiments seem non-exhaustive and many details are missing to replicate the experiments. For instance, no indication on what the anomaly is vs normal client. This is particularly important when using gradients. I expect that the framework would perform differently if the anomaly is label flipping vs if it was noisy features. Additionally, evaluation of the impact of batch size would be particularly important for both scalability and compatibility among clients.

questions:
1) Please motivate the approach with practical use-cases. 
2) Please discuss link with clustered federated learning, in particular techniques that use gradients to cluster clients. 
3) Please provide all necessary details to replicate the results.
4) Please evaluate the impact of batch size (smaller and larger values), to show the scalability of the technique and its robustness in showing the compatibility among clients.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730812252661

thread_type:
official_review

<thread_object>
creator: reviewer_kses

<content>
summary:
This paper proposes the DICE framework for measuring the cascading propagation of data influence
in decentralized learning networks. Decentralized learning enables large-scale model training
through distributed computation, yet the lack of effective incentive mechanisms can lead to unfair
contributions and malicious behavior among nodes. The DICE framework introduces data influence
cascades (DICE-GT and DICE-E), which respectively measure the direct and indirect influence of data
within the network, addressing the limitations of existing data influence measurement methods in
decentralized environments. Experiments validate the consistency and accuracy of DICE across
various network topologies and demonstrate its potential in practical applications like anomaly
detection and collaborator selection

strengths:
1. The DICE framework is the first to systematically measure the cascading propagation of data
influence in decentralized learning environments, providing an effective method to assess data
contributions among nodes and filling a gap in data influence evaluation within decentralized
networks.
2. The experiments cover different network topologies (such as ring and exponential graphs) and
datasets (such as MNIST, CIFAR-10, and CIFAR-100), validating the applicability and consistency
of the DICE framework across various scenarios.
3. The DICE framework provides accurate contribution measurement, laying the foundation for
designing fair and effective incentive mechanisms in decentralized learning systems, with the
potential to foster equitable collaboration within decentralized networks.

weaknesses:
1. Figure 1 lacks legend information, making it difficult to understand.
2. The performance differences of the DICE framework under different parameters (such as learning
rate, batch size, etc.) have not been thoroughly discussed. It is recommended to add parameter
sensitivity experiments to demonstrate the impact of different parameter selections on the
performance of the DICE framework, thereby enhancing its practicality.

questions:
See weaknesses
</content>
</thread_object>

</thread>
<thread>
creation date:
1732297663172

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response (Part 2/2)

comment:
**Clarifications of Challenges and Contributions**
- **Major challenges**. Decentralized learning emerges as a promising paradigm to accommodate the growing demand for distributed computation, while also introduces distinct and unparallel challenges in quantifying and understanding data influence. In a centralized learning system, data influence is typically confined to a single model and can be statically analyzed after training. In decentralized learning, the influence of a single data instance propagates from directly connected neighbors to neighbors faraway. This put major challenge:  **`measuring multi-hop influence beyond one-hop influence, which is determined not only by the stem node, but also the nodes on the way.`** The challenge invalidate the existing influence measure techniques. This phenomenon is termed as the **cascading effect** in our paper. 
- **Major contributions**. Our **DICE (Data Influence CascadE)** method is the first work in the literature that can address this challenge. DICE introduces the concept of ground-truth data influence for decentralized learning, seamlessly integrating direct and indirect contributions to capture influence propagation across multiple hops during training. By transforming data-level influence into model-level influence and tracing the model-level influence of multi-hop neighbors, we developed a theoretical framework to derive tractable approximations for influence cascades. **`We uncover, for the first time, that data influence in decentralized learning is shaped by a synergistic interplay of  original data, the topological importance of the data owner, and the curvature information of intermediate nodes mediating propagation.`** These theoretical insights enable a systematic and interpretable understanding of decentralized data influence, laying the groundwork for incentivized collaboration, anomaly detection, and scalable decentralized learning ecosystems.
</content>
</thread_object>

</thread>
<thread>
creation date:
1732297731011

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response (Part 1/2)

comment:
Dear AC and Reviewers: 

We sincerely thank the reviewers for their helpful comments. We appreciate that reviewers recognize the solidity of our theoretical framework (Reviewers kSES and f3R7), especially for proposing the  “gold standard” data influence measures in decentralized learning and its first-order approximation (Reviewer 4yzV). 

We have carefully revised our manuscript accordingly. The main revisions and contributions are highlighted below: 

**Highlight for Revision** 
1. We conducted **additional experiments** following reviewers’ feedback: 
    - Comprehensive sensitivity analysis on hyperparameters (including batch size, learning rate, training epoch, communication topology and the number of participants) to evaluate the robustness of DICE (to address Reviewers kSES and f3R7). 
    - Additional experiments on Tiny ImageNet (to address Reviewer 4yzV). To secure the reproducibility, we have also provided detailed replication instructions in our revised manuscript, including the definition of anomalies methodologies(to address Reviewer f3R7). 
2. We discussed **practical use cases of DICE** (to address Reviewer f3R7). 
    - **Efficient collaboration between decentralized participants:** DICE enables estimation of the contributions between neighboring participants. Leveraging this, DICE make dynamic reweighting strategies possible, which adaptively prioritizes interactions with more influential peers. This mechanism can significantly improve both convergence speed and validation accuracy, as validated by experiments on CIFAR-10 and CIFAR-100. These results demonstrate the effectiveness of DICE in heterogeneous and decentralized learning environments. 
    - **Anomaly Detection:** DICE strengthens the robustness of decentralized networks by identifying anomalies, such as label-flipping attacks or feature perturbations, by observing the deviations in proximal influence values. This capability is critical for detecting free riders, mitigating malicious behaviors, and maintaining system reliability, even under constraints of limited communication. 
3. We added a comprehensive **discussion of related works on clustered federated learning** (to address Reviewer f3R7).  
    - There are shared aspects between gradient-based Clustered Federated Learning (CFL) and the one-hop DICE approximation, with DICE-E potentially serving as a more advanced high-order gradient similarity metric for clustering participants in decentralized federated learning—a promising direction for future work.  We have carefully discussed and compared them. We also note that there are **key differences** between DICE and gradient-based CFL. While CFL is confined to  peer-level clustering, which is in **one-hop**, DICE non-trivially extend the influence to measuring the **multi-hop influence propagation** to whole decentralized networks.   Specifically, the r-hop DICE-E influence $I_{DICE-E}^{(r)}(z_j^t, z^{\prime})$ is given by:
$
I_{DICE-E}^{(r)}\(z_j^t, z^{\prime}\) = 
-\sum_{\rho=0}^{r} \sum_{ \(k_1, \dots, k_{\rho}\) \in P_j^{\(\rho\)} }  
\eta^{t} q_{k_\rho} \prod_{s=1}^{\rho} W_{k_s, k_{s-1}}^{t+s-1} 
\nabla L\(\theta_{k_{\rho}}^{t+\rho}; z^{\prime}\)^\top 
\prod_{s=2}^{\rho}  
\(I - \eta^{t+s-1} H\(\theta_{k_s}^{t+s-1}; z_{k_s}^{t+s-1}\)\) 
\nabla L\(\theta_{j}^{t}; z_j^t\), 
$
where $k_0 = j$, $P_j^{(\rho)}$ denotes the set of all sequences $k_1, \dots, k_{\rho}$ such that $k_s \in N_{out}^{(1)}(k_{s-1})$ for $s = 1, \dots, \rho$, and $H(\theta_{k_s}^{t+s}; z_{k_s}^{t+s})$ is the Hessian matrix of $L$ with respect to $\theta$, evaluated at $\theta_{k_s}^{t+s}$ and data $z_{k_s}^{t+s}$.  
For further details, please refer to Proposition 3. This formulation highlights a key distinction: **DICE evaluates influence across multiple hops and characterizes the interplay between data, curvature, and communication topology**—factors beyond the scope of CFL frameworks., which primarily aims to cluster clients based on their similarity. 

For your convenience, we provide an anonymous link summarizing our additional experimental results: 

**https://anonymous.4open.science/r/Anonymous-Repo-for-Rebuttal-793D/README.md**

We have uploaded a revised version of our paper, which can be accessed via the official link provided below:

**https://openreview.net/pdf?id=2TIYkqieKw**

Best regards,

The Authors
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</thread_object>

</thread>


Metareview:
metareview:
This paper introduces the DICE framework, a systematic approach to measure cascading data influence in decentralized learning networks, addressing a critical gap in data contribution evaluation. With rigorous theoretical foundations and diverse experimental validations, it lays the groundwork for equitable incentive mechanisms and effective collaboration in decentralized systems. There were concerns in the paper on practical use cases, experiments, and related work in the original reviews which seem to have been addressed in the rebuttal. Further, given that all the reviews are positive after rebuttal, I recommend acceptance of this work.