Double Momentum and Error Feedback for Clipping with Fast Rates and Differential Privacy

Strong Differential Privacy (DP) and Optimization guarantees are two desirable properties for a method in Federated Learning (FL). However, existing algorithms do not achieve both properties at once: they either have optimal DP guarantees but rely on restrictive assumptions such as bounded gradients/bounded data heterogeneity, or they ensure strong optimization performance but lack DP guarantees. To address this gap in the literature, we propose and analyze a new method called Clip21-SGD2M based on a novel combination of clipping, heavy-ball momentum, and Error Feedback. In particular, for non-convex smooth distributed problems with clients having arbitrarily heterogeneous data, we prove that Clip21-SGD2M has optimal convergence rate and also near optimal (local-)DP neighborhood. Our numerical experiments on non-convex logistic regression and training of neural networks highlight the superiority of Clip21-SGD2M over baselines in terms of the optimization performance for a given DP-budget.

Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks

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.

CYCle: Choosing Your Collaborators Wisely to Enhance Collaborative Fairness in Decentralized Learning

Collaborative learning (CL) enables multiple participants to jointly train machine learning (ML) models on decentralized data sources without raw data sharing. While the primary goal of CL is to maximize the expected accuracy gain for each participant, it is also important to ensure that the gains are fairly distributed. Specifically, no client should be negatively impacted by the collaboration, and the individual gains must ideally be commensurate with the contributions. Most existing CL algorithms require central coordination and focus on the gain maximization objective while ignoring collaborative fairness. In this work, we first show that the existing measure of collaborative fairness based on the correlation between accuracy values without and with collaboration has drawbacks because it does not account for negative collaboration gain. We argue that maximizing mean collaboration gain (MCG) while simultaneously minimizing the collaboration gain spread (CGS) is a fairer alternative. Next, we propose the CYCle protocol that enables individual participants in a private decentralized learning (PDL) framework to achieve this objective through a novel reputation scoring method based on gradient alignment between the local cross-entropy and distillation losses. Experiments on the CIFAR-10, CIFAR-100, and Fed-ISIC2019 datasets empirically demonstrate the effectiveness of the CYCle protocol to ensure positive and fair collaboration gain for all participants, even in cases where the data distributions of participants are highly skewed. For the simple mean estimation problem with two participants, we also theoretically show that CYCle performs better than standard FedAvg, especially when there is large statistical heterogeneity.

Initialization using Update Approximation is a Silver Bullet for Extremely Efficient Low-Rank Fine-Tuning

Low-rank adapters have become a standard approach for efficiently fine-tuning large language models (LLMs), but they often fall short of achieving the performance of full fine-tuning. We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces using a carefully designed initialization strategy. We theoretically demonstrate that the architecture of LoRA-XS, which inserts a trainable (r x r) matrix between B and A while keeping other matrices fixed, provides the precise conditions needed for this approximation. We leverage its constrained update space to achieve optimal scaling for high-rank gradient updates while removing the need for hyperparameter tuning. We prove that our initialization offers an optimal low-rank approximation of the initial gradient and preserves update directions throughout training. Extensive experiments across mathematical reasoning, commonsense reasoning, and language understanding tasks demonstrate that our approach exceeds the performance of standard LoRA while using 27-90x fewer parameters, and comprehensively outperforms LoRA-XS. Our findings establish that it is possible to simulate full fine-tuning in low-rank subspaces, and achieve significant efficiency gains without sacrificing performance. Our code is publicly available at https://github.com/RaghavSinghal10/lora-sb.

FedPeWS: Personalized Warmup via Subnetworks for Enhanced Heterogeneous Federated Learning

Statistical data heterogeneity is a significant barrier to convergence in federated learning (FL). While prior work has advanced heterogeneous FL through better optimization objectives, these methods fall short when there is extreme data heterogeneity among collaborating participants. We hypothesize that convergence under extreme data heterogeneity is primarily hindered due to the aggregation of conflicting updates from the participants in the initial collaboration rounds. To overcome this problem, we propose a warmup phase where each participant learns a personalized mask and updates only a subnetwork of the full model. This personalized warmup allows the participants to focus initially on learning specific subnetworks tailored to the heterogeneity of their data. After the warmup phase, the participants revert to standard federated optimization, where all parameters are communicated. We empirically demonstrate that the proposed personalized warmup via subnetworks (FedPeWS) approach improves accuracy and convergence speed over standard federated optimization methods.

Redefining Contributions: Shapley-Driven Federated Learning

Federated learning (FL) has emerged as a pivotal approach in machine learning, enabling multiple participants to collaboratively train a global model without sharing raw data. While FL finds applications in various domains such as healthcare and finance, it is challenging to ensure global model convergence when participants do not contribute equally and/or honestly. To overcome this challenge, principled mechanisms are required to evaluate the contributions made by individual participants in the FL setting. Existing solutions for contribution assessment rely on general accuracy evaluation, often failing to capture nuanced dynamics and class-specific influences. This paper proposes a novel contribution assessment method called ShapFed for fine-grained evaluation of participant contributions in FL. Our approach uses Shapley values from cooperative game theory to provide a granular understanding of class-specific influences. Based on ShapFed, we introduce a weighted aggregation method called ShapFed-WA, which outperforms conventional federated averaging, especially in class-imbalanced scenarios. Personalizing participant updates based on their contributions further enhances collaborative fairness by delivering differentiated models commensurate with the participant contributions. Experiments on CIFAR-10, Chest X-Ray, and Fed-ISIC2019 datasets demonstrate the effectiveness of our approach in improving utility, efficiency, and fairness in FL systems. The code can be found at https://github.com/tnurbek/shapfed.

Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad

Adaptive methods are extremely popular in machine learning as they make learning rate tuning less expensive. This paper introduces a novel optimization algorithm named KATE, which presents a scale-invariant adaptation of the well-known AdaGrad algorithm. We prove the scale-invariance of KATE for the case of Generalized Linear Models. Moreover, for general smooth non-convex problems, we establish a convergence rate of $O \left(\frac{\log T}{\sqrt{T}} \right)$ for KATE, matching the best-known ones for AdaGrad and Adam. We also compare KATE to other state-of-the-art adaptive algorithms Adam and AdaGrad in numerical experiments with different problems, including complex machine learning tasks like image classification and text classification on real data. The results indicate that KATE consistently outperforms AdaGrad and matches/surpasses the performance of Adam in all considered scenarios.

Rethink Model Re-Basin and the Linear Mode Connectivity

Recent studies suggest that with sufficiently wide models, most SGD solutions can, up to permutation, converge into the same basin. This phenomenon, known as the model re-basin regime, has significant implications for model averaging. However, current re-basin strategies are limited in effectiveness due to a lack of comprehensive understanding of underlying mechanisms. Addressing this gap, our work revisits standard practices and uncovers the frequent inadequacies of existing matching algorithms, which we show can be mitigated through proper re-normalization. By introducing a more direct analytical approach, we expose the interaction between matching algorithms and re-normalization processes. This perspective not only clarifies and refines previous findings but also facilitates novel insights. For instance, it connects the linear mode connectivity to pruning, motivating a lightweight yet effective post-pruning plug-in that can be directly merged with any existing pruning techniques. Our implementation is available at https://github.com/XingyuQu/rethink-re-basin.

Efficient Conformal Prediction under Data Heterogeneity

Conformal Prediction (CP) stands out as a robust framework for uncertainty quantification, which is crucial for ensuring the reliability of predictions. However, common CP methods heavily rely on data exchangeability, a condition often violated in practice. Existing approaches for tackling non-exchangeability lead to methods that are not computable beyond the simplest examples. This work introduces a new efficient approach to CP that produces provably valid confidence sets for fairly general non-exchangeable data distributions. We illustrate the general theory with applications to the challenging setting of federated learning under data heterogeneity between agents. Our method allows constructing provably valid personalized prediction sets for agents in a fully federated way. The effectiveness of the proposed method is demonstrated in a series of experiments on real-world datasets.

Handling Data Heterogeneity via Architectural Design for Federated Visual Recognition

Federated Learning (FL) is a promising research paradigm that enables the collaborative training of machine learning models among various parties without the need for sensitive information exchange. Nonetheless, retaining data in individual clients introduces fundamental challenges to achieving performance on par with centrally trained models. Our study provides an extensive review of federated learning applied to visual recognition. It underscores the critical role of thoughtful architectural design choices in achieving optimal performance, a factor often neglected in the FL literature. Many existing FL solutions are tested on shallow or simple networks, which may not accurately reflect real-world applications. This practice restricts the transferability of research findings to large-scale visual recognition models. Through an in-depth analysis of diverse cutting-edge architectures such as convolutional neural networks, transformers, and MLP-mixers, we experimentally demonstrate that architectural choices can substantially enhance FL systems' performance, particularly when handling heterogeneous data. We study 19 visual recognition models from five different architectural families on four challenging FL datasets. We also re-investigate the inferior performance of convolution-based architectures in the FL setting and analyze the influence of normalization layers on the FL performance. Our findings emphasize the importance of architectural design for computer vision tasks in practical scenarios, effectively narrowing the performance gap between federated and centralized learning. Our source code is available at https://github.com/sarapieri/fed_het.git.