Authors: Theofilos Mailis, Kalliopi-Christina Despotidou, Konstantinos Filippopolitis, Yannis Foufoulas, Thanasis-Michail Karampatsis, Andreas Ktenidis, Evdokia Mailli, Theodore Papamarkou, +1 more
Organizations: Athena Research Center · National and Kapodistrian University of Athens · National Technical University of Athens
Abstract
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.
Federated learning (FL) aggregation on serverless platforms faces a hard scalability ceiling: existing architectures (lambda-FL, LIFL) partition clients across aggregators, but every aggregator must hold the complete model gradient in memory. When gradients exceed the per-function memory limit (e.g., 10 GB on AWS Lambda), aggregation becomes infeasible regardless of tree depth or branching factor. We propose GradsSharding, which instead partitions the gradient tensor into M shards, each averaged independently by a serverless function that receives contributions from all clients. Because FedAvg averaging is element-wise, this produces bit-identical results to tree-based approaches, so model accuracy is invariant by construction. Per-function memory is bounded at O(|θ|/M), independent of client count, enabling aggregation of arbitrarily large models. We evaluate GradsSharding against lambda-FL and LIFL through HPC experiments and real AWS Lambda deployments across model sizes from 43 MB to 5 GB. Results show a cost crossover at approximately 500 MB gradient size, 2.7x cost reduction at VGG-16 scale, and that GradsSharding is the only architecture that remains deployable beyond the serverless memory ceiling.
Federated learning is bandwidth-bound on two orthogonal axes: model size, which limits how often parameter-averaging methods can afford to merge, and class count, which makes per-probe soft-label distillation prohibitive at large vocabularies. Both ceilings tighten as modern systems scale. We collapse the class-count axis to ⌈log2C⌉ bits per probe by transmitting only each peer's argmax class index, where C is the number of output classes. The resulting protocol, TallyTrain, is not merely compressed: under non-IID training it can be preferable to soft-label distillation, because under-trained peers are confidently wrong and majority voting filters this noise where soft-label averaging amplifies it. Across standard benchmarks, TallyTrain matches or beats soft-label distillation at up to three orders of magnitude less communication. We also relax the model-size axis: we compose the cheap hard-label consensus with sparse parameter merges to obtain a bandwidth-bridge variant, which Pareto-dominates every tested operating point of the standard FedAvg, FedProx and FedDF baselines.
Federated LoRA enables parameter-efficient adaptation of large language models under decentralized data and limited client resources.However, directly averaging LoRA factors is representation-dependent: the same intrinsic update admits infinitely many gauge-equivalent factorizations, so factor-level aggregation can change under arbitrary coordinate choices while the underlying update remains unchanged. This reveals a semantic mismatch in existing federated LoRA aggregation rules. We propose \textbf{GLoRA}, a gauge-aware server representation for federated LoRA.Instead of aggregating raw factors, GLoRA estimates a consensus update subspace from client projectors and aggregates client updates in shared reference coordinates, thereby representing semantic update aggregation entirely in low-rank form. To support heterogeneous client capacities, GLoRA further provides a rank-compatible readout that instantiates adapters of different ranks from the same server state without dense update reconstruction. Experiments on GLUE and SuperNI show that GLoRA consistently outperforms federated LoRA baselines under data, resource, and task heterogeneity, including heterogeneous client ranks, sparse participation, larger backbones, and unseen-task evaluation. GLoRA also achieves a favorable efficiency--performance trade-off, suggesting that effective federated LoRA requires not merely averaging low-rank factors, but defining a semantically meaningful server-side representation for aggregation.