mlsanityData to 14 Oct 2026

A Typed Tensor Language for Shared-State Federated Computation

arXiv 2605.21103 ↗First posted 20 May 2026cs.LGcited by 0

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Abstract (arXiv)

Shared-state federated computations combine client-local tensor computation, mergeable aggregation into shared state, and shared-only post-processing. We introduce a typed tensor language for this class of computations. Its two tensor sorts separate client-partitioned data from globally available values, and typing tracks the partitioned axis. A virtual global tensor serves as a semantic reference for centralized evaluation. We show that typed one-round programs factor through shared tensors whose shapes depend on the program but are independent of client and sample counts. The converse applies to typed-realizable factorizations: each encoder component is represented by an allowed aggregation or contraction with its valid merge, and the decoder is shared-only. The construction extends round by round to programs whose persistent state is shared. For a loss supplied with a client-local per-sample gradient expression, summation represents the empirical gradient. This gives typed programs for server-side first-order updates and, with shared linear algebra, curvature-block updates. The language covers federated analytics and FedSGD. General multi-local-step FedAvg and persistent private client state are outside its scope.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 25 of its 55 references that are in the map. First posted on arXiv 20 May 2026.

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25 of 55 references.

References · 25

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,669
  2. 2019Advances and Open Problems in Federated Learningcited by 3,046
  3. 2018Federated Optimization in Heterogeneous Networkscited by 2,987
  4. 2019Towards Federated Learning at Scale: System Designcited by 832
  5. 2020The Future of Digital Health with Federated Learningcited by 633
  6. 2021FedBN: Federated Learning on Non-IID Features via Local Batch Normalizationcited by 571
  7. 2021Federated Learning Based on Dynamic Regularizationcited by 562
  8. 2020Flower: A Friendly Federated Learning Research Frameworkcited by 455
  9. 2021Federated Learning for Internet of Things: A Comprehensive Surveycited by 252
  10. 2019Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processescited by 151
  11. 2021Federated Learning for Open Bankingcited by 141
  12. 2019Federated Learning for Wireless Communications: Motivation, Opportunities and Challengescited by 129
13 more
  1. 2022NVIDIA FLARE: Federated Learning from Simulation to Real-Worldcited by 80
  2. 2021OpenFL: An open-source framework for Federated Learningcited by 58
  3. 2015Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequalitycited by 50
  4. 2019SystemDS: A Declarative Machine Learning System for the End-to-End Data Science Lifecyclecited by 20
  5. 2021Applications of Federated Learning in Smart Cities: Recent Advances, Taxonomy, and Open Challengescited by 17
  6. 2020Tensor Relational Algebra for Machine Learning System Designcited by 11
  7. 2021Getting to the Point. Index Sets and Parallelism-Preserving Autodiff for Pointful Array Programmingcited by 10
  8. 2024DrJAX: Scalable and Differentiable MapReduce Primitives in JAXcited by 9
  9. 2024Empowering Federated Learning for Massive Models with NVIDIA FLAREcited by 5
  10. 2025FBFL: A Field-Based Coordination Approach for Data Heterogeneity in Federated Learningcited by 5
  11. 2023Federated Automatic Differentiationcited by 2
  12. 2025GRACEFUL: A Learned Cost Estimator For UDFscited by 2
  13. 2023Domain-Specific Tensor Languagescited by 1

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