FAX: Scalable and Differentiable Federated Primitives in JAX

We present FAX, a JAX-based library designed to support large-scale distributed and federated computations in both data center and cross-device applications. FAX leverages JAX's sharding mechanisms to enable native targeting of TPUs and state-of-the-art JAX runtimes, including Pathways. FAX embeds building blocks for federated computations as primitives in JAX. This enables three key benefits. First, FAX computations can be translated to XLA HLO. Second, FAX provides a full implementation of federated automatic differentiation, greatly simplifying the expression of federated computations. Last, FAX computations can be interpreted out to existing production cross-device federated compute systems. We show that FAX provides an easily programmable, performant, and scalable framework for federated computations in the data center. FAX is available at https://github.com/google-research/google-research/tree/master/fax .

Leveraging Function Space Aggregation for Federated Learning at Scale

The federated learning paradigm has motivated the development of methods for aggregating multiple client updates into a global server model, without sharing client data. Many federated learning algorithms, including the canonical Federated Averaging (FedAvg), take a direct (possibly weighted) average of the client parameter updates, motivated by results in distributed optimization. In this work, we adopt a function space perspective and propose a new algorithm, FedFish, that aggregates local approximations to the functions learned by clients, using an estimate based on their Fisher information. We evaluate FedFish on realistic, large-scale cross-device benchmarks. While the performance of FedAvg can suffer as client models drift further apart, we demonstrate that FedFish is more robust to longer local training. Our evaluation across several settings in image and language benchmarks shows that FedFish outperforms FedAvg as local training epochs increase. Further, FedFish results in global networks that are more amenable to efficient personalization via local fine-tuning on the same or shifted data distributions. For instance, federated pretraining on the C4 dataset, followed by few-shot personalization on Stack Overflow, results in a 7% improvement in next-token prediction by FedFish over FedAvg.

Towards Federated Foundation Models: Scalable Dataset Pipelines for Group-Structured Learning

We introduce a library, Dataset Grouper, to create large-scale group-structured (e.g., federated) datasets, enabling federated learning simulation at the scale of foundation models. This library allows the creation of group-structured versions of existing datasets based on user-specified partitions, and directly leads to a variety of useful heterogeneous datasets that can be plugged into existing software frameworks. Dataset Grouper offers three key advantages. First, it scales to settings where even a single group's dataset is too large to fit in memory. Second, it provides flexibility, both in choosing the base (non-partitioned) dataset and in defining partitions. Finally, it is framework-agnostic. We empirically demonstrate that Dataset Grouper allows for large-scale federated language modeling simulations on datasets that are orders of magnitude larger than in previous work. Our experimental results show that algorithms like FedAvg operate more as meta-learning methods than as empirical risk minimization methods at this scale, suggesting their utility in downstream personalization and task-specific adaptation.

Convergence of Gradient Descent with Linearly Correlated Noise and Applications to Differentially Private Learning

We study stochastic optimization with linearly correlated noise. Our study is motivated by recent methods for optimization with differential privacy (DP), such as DP-FTRL, which inject noise via matrix factorization mechanisms. We propose an optimization problem that distils key facets of these DP methods and that involves perturbing gradients by linearly correlated noise. We derive improved convergence rates for gradient descent in this framework for convex and non-convex loss functions. Our theoretical analysis is novel and might be of independent interest. We use these convergence rates to develop new, effective matrix factorizations for differentially private optimization, and highlight the benefits of these factorizations theoretically and empirically.

Federated Automatic Differentiation

Federated learning (FL) is a general framework for learning across heterogeneous clients while preserving data privacy, under the orchestration of a central server. FL methods often compute gradients of loss functions purely locally (ie. entirely at each client, or entirely at the server), typically using automatic differentiation (AD) techniques. We propose a federated automatic differentiation (FAD) framework that 1) enables computing derivatives of functions involving client and server computation as well as communication between them and 2) operates in a manner compatible with existing federated technology. In other words, FAD computes derivatives across communication boundaries. We show, in analogy with traditional AD, that FAD may be implemented using various accumulation modes, which introduce distinct computation-communication trade-offs and systems requirements. Further, we show that a broad class of federated computations is closed under these various modes of FAD, implying in particular that if the original computation can be implemented using privacy-preserving primitives, its derivative may be computed using only these same primitives. We then show how FAD can be used to create algorithms that dynamically learn components of the algorithm itself. In particular, we show that FedAvg-style algorithms can exhibit significantly improved performance by using FAD to adjust the server optimization step automatically, or by using FAD to learn weighting schemes for computing weighted averages across clients.

Federated Select: A Primitive for Communication- and Memory-Efficient Federated Learning

Federated learning (FL) is a framework for machine learning across heterogeneous client devices in a privacy-preserving fashion. To date, most FL algorithms learn a "global" server model across multiple rounds. At each round, the same server model is broadcast to all participating clients, updated locally, and then aggregated across clients. In this work, we propose a more general procedure in which clients "select" what values are sent to them. Notably, this allows clients to operate on smaller, data-dependent slices. In order to make this practical, we outline a primitive, federated select, which enables client-specific selection in realistic FL systems. We discuss how to use federated select for model training and show that it can lead to drastic reductions in communication and client memory usage, potentially enabling the training of models too large to fit on-device. We also discuss the implications of federated select on privacy and trust, which in turn affect possible system constraints and design. Finally, we discuss open questions concerning model architectures, privacy-preserving technologies, and practical FL systems.

Motley: Benchmarking Heterogeneity and Personalization in Federated Learning

Personalized federated learning considers learning models unique to each client in a heterogeneous network. The resulting client-specific models have been purported to improve metrics such as accuracy, fairness, and robustness in federated networks. However, despite a plethora of work in this area, it remains unclear: (1) which personalization techniques are most effective in various settings, and (2) how important personalization truly is for realistic federated applications. To better answer these questions, we propose Motley, a benchmark for personalized federated learning. Motley consists of a suite of cross-device and cross-silo federated datasets from varied problem domains, as well as thorough evaluation metrics for better understanding the possible impacts of personalization. We establish baselines on the benchmark by comparing a number of representative personalized federated learning methods. These initial results highlight strengths and weaknesses of existing approaches, and raise several open questions for the community. Motley aims to provide a reproducible means with which to advance developments in personalized and heterogeneity-aware federated learning, as well as the related areas of transfer learning, meta-learning, and multi-task learning.

Optimizing the Communication-Accuracy Trade-off in Federated Learning with Rate-Distortion Theory

A significant bottleneck in federated learning is the network communication cost of sending model updates from client devices to the central server. We propose a method to reduce this cost. Our method encodes quantized updates with an appropriate universal code, taking into account their empirical distribution. Because quantization introduces error, we select quantization levels by optimizing for the desired trade-off in average total bitrate and gradient distortion. We demonstrate empirically that in spite of the non-i.i.d. nature of federated learning, the rate-distortion frontier is consistent across datasets, optimizers, clients and training rounds, and within each setting, distortion reliably predicts model performance. This allows for a remarkably simple compression scheme that is near-optimal in many use cases, and outperforms Top-K, DRIVE, 3LC and QSGD on the Stack Overflow next-word prediction benchmark.

Iterated Vector Fields and Conservatism, with Applications to Federated Learning

We study iterated vector fields and investigate whether they are conservative, in the sense that they are the gradient of some scalar-valued function. We analyze the conservatism of various iterated vector fields, including gradient vector fields associated to loss functions of generalized linear models. We relate this study to optimization and derive novel convergence results for federated learning algorithms. In particular, we show that for certain classes of functions (including non-convex functions), federated averaging is equivalent to gradient descent on a surrogate loss function. Finally, we discuss a variety of open questions spanning topics in geometry, dynamical systems, and optimization.

A Field Guide to Federated Optimization

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.