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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.21103 |
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| _version_ | 1866917516394102784 |
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| author | Mailis, Theofilos Despotidou, Kalliopi-Christina Filippopolitis, Konstantinos Foufoulas, Yannis Karampatsis, Thanasis-Michail Ktenidis, Andreas Mailli, Evdokia Papamarkou, Theodore Ioannidis, Yannis |
| author_facet | Mailis, Theofilos Despotidou, Kalliopi-Christina Filippopolitis, Konstantinos Foufoulas, Yannis Karampatsis, Thanasis-Michail Ktenidis, Andreas Mailli, Evdokia Papamarkou, Theodore Ioannidis, Yannis |
| contents | Federated learning and analytics are often described as collections of separate protocols, even when they share the same mathematical form: client-local tensor computation, mergeable aggregation into shared state, and shared-only post-processing. We introduce a typed tensor language that formalizes this structure. The language distinguishes federated tensors, whose records are partitioned across clients along a tracked record axis, from shared tensors, which are available globally. Its semantics are defined by comparison with a virtual global tensor, used only as a reference object. The main result is a shared-state factorization theory. We show that typed one-round programs factor through fixed-dimensional shared state whose size is independent of the number of clients and records, computed from client-local tensor expressions and merged across clients. We also prove a converse representability result; factorizations whose encoders and decoders are expressible in the language are realized by typed one-round programs, and the correspondence extends to iterative programs whose cross-round state is shared. This gives a formal account of the computations in the language that can be expressed as encode, merge, and decode procedures. We then develop a differentiable fragment for learning. If a per-record loss and its per-record gradient are represented by client-local tensor expressions, the global gradient is represented by record-axis summation of the federated gradient tensor. This yields typed iterative programs for server-side gradient descent and shared-linear-algebra second-order updates. The framework characterizes a broad class of federated learning computations whose communication passes through fixed-dimensional shared state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Typed Tensor Language for Federated Learning Mailis, Theofilos Despotidou, Kalliopi-Christina Filippopolitis, Konstantinos Foufoulas, Yannis Karampatsis, Thanasis-Michail Ktenidis, Andreas Mailli, Evdokia Papamarkou, Theodore Ioannidis, Yannis Machine Learning Federated learning and analytics are often described as collections of separate protocols, even when they share the same mathematical form: client-local tensor computation, mergeable aggregation into shared state, and shared-only post-processing. We introduce a typed tensor language that formalizes this structure. The language distinguishes federated tensors, whose records are partitioned across clients along a tracked record axis, from shared tensors, which are available globally. Its semantics are defined by comparison with a virtual global tensor, used only as a reference object. The main result is a shared-state factorization theory. We show that typed one-round programs factor through fixed-dimensional shared state whose size is independent of the number of clients and records, computed from client-local tensor expressions and merged across clients. We also prove a converse representability result; factorizations whose encoders and decoders are expressible in the language are realized by typed one-round programs, and the correspondence extends to iterative programs whose cross-round state is shared. This gives a formal account of the computations in the language that can be expressed as encode, merge, and decode procedures. We then develop a differentiable fragment for learning. If a per-record loss and its per-record gradient are represented by client-local tensor expressions, the global gradient is represented by record-axis summation of the federated gradient tensor. This yields typed iterative programs for server-side gradient descent and shared-linear-algebra second-order updates. The framework characterizes a broad class of federated learning computations whose communication passes through fixed-dimensional shared state. |
| title | A Typed Tensor Language for Federated Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.21103 |