# Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks

arXiv: https://arxiv.org/abs/2502.04850 · HTML: https://mlsanity.com/paper/2502.04850/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 30 of 44)

- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Universally Slimmable Networks and Improved Training Techniques](https://mlsanity.com/paper/1903.05134/) (2019)
- [FjORD: Fair and Accurate Federated Learning under heterogeneous targets with Ordered Dropout](https://mlsanity.com/paper/2102.13451/) (2021)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Collaborative Fairness in Federated Learning](https://mlsanity.com/paper/2008.12161/) (2020)
- [Papaya: Practical, Private, and Scalable Federated Learning](https://mlsanity.com/paper/2111.04877/) (2021)
- [Learning Ordered Representations with Nested Dropout](https://mlsanity.com/paper/1402.0915/) (2014)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [Towards Fairness-Aware Federated Learning](https://mlsanity.com/paper/2111.01872/) (2021)
- [Fair Federated Medical Image Segmentation via Client Contribution Estimation](https://mlsanity.com/paper/2303.16520/) (2023)
- [Incentive Design for Efficient Federated Learning in Mobile Networks: A Contract Theory Approach](https://mlsanity.com/paper/1905.07479/) (2019)
- [A Reputation Mechanism Is All You Need: Collaborative Fairness and Adversarial Robustness in Federated Learning](https://mlsanity.com/paper/2011.10464/) (2020)
- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [Hierarchically Fair Federated Learning](https://mlsanity.com/paper/2004.10386/) (2020)
- [ProgFed: Effective, Communication, and Computation Efficient Federated Learning by Progressive Training](https://mlsanity.com/paper/2110.05323/) (2021)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)

## Built on by (most cited first, 6 of 6)

- [Stochastic Self-Organization in Multi-Agent Systems](https://mlsanity.com/paper/2510.00685/) (2025)
- [MoSE: Mixture of Slimmable Experts for Efficient and Adaptive Language Models](https://mlsanity.com/paper/2602.06154/) (2026)
- [Response-Conditioned Parallel-to-Sequential Orchestration for Multi-Agent Systems](https://mlsanity.com/paper/2605.15573/) (2026)
- [Data-Free Contribution Estimation in Federated Learning using Gradient von Neumann Entropy](https://mlsanity.com/paper/2604.22562/) (2026)
- [Class-wise Contribution Estimation via Logit Maximization for Federated Learning](https://mlsanity.com/paper/2605.18892/) (2026)
- [PreLort: Prefix-Nested LoRA for Federated Fine-Tuning under Rank Heterogeneity](https://mlsanity.com/paper/2606.15963/) (2026)

## Abstract (arXiv)

Collaborative learning enables multiple participants to learn a single global model by exchanging focused updates instead of sharing data. One of the core challenges in collaborative learning is ensuring that participants are rewarded fairly for their contributions, which entails two key sub-problems: contribution assessment and reward allocation. This work focuses on fair reward allocation, where the participants are incentivized through model rewards - differentiated final models whose performance is commensurate with the contribution. In this work, we leverage the concept of slimmable neural networks to collaboratively learn a shared global model whose performance degrades gracefully with a reduction in model width. We also propose a post-training fair allocation algorithm that determines the model width for each participant based on their contributions. We theoretically study the convergence of our proposed approach and empirically validate it using extensive experiments on different datasets and architectures. We also extend our approach to enable training-time model reward allocation.