Federated learning (FL) must serve devices with varying computational capabilities. A fixed model cannot suit all devices, while training one model per deployment limit is costly. Federated supernet training instead learns one elastic model with differently sized subnetworks, then deploys a suitable one to each device. When client inference budgets differ, however, parameters exclusive to high-cost subnetworks are reachable by fewer clients. We propose FEAST, a federated shared-space training framework that counters this imbalance by jointly training multiple subnetworks within each client's limit. Budget-tailored sub-supernet routing sends only the relevant supernet portion, and sparse aggregation merges the returned parameter slices. The trained supernet directly serves the subnetworks used during federation and supports post-hoc extraction of additional subnetworks without federated retraining. We further show that independently assigning clients' training-data volumes and inference budgets can distort accuracy--inference-cost comparisons in heterogeneous FL simulations, and introduce a one-parameter $γ$-allocation protocol to control this coupling. In our experimental setup, the SuperFedNAS and DeepFedNAS supernet training procedures remain near chance at 25M and reach at most $17.09\%$ at $596$M inference MACs; FEAST reaches $71.06\%$ at $596$M, $2.4$ points above the strongest model-heterogeneous weight-sharing baseline at its largest tier. Across CIFAR-100, CINIC-10, and TinyImageNet-200, FEAST achieves the highest population-averaged accuracy among the evaluated weight-sharing methods when each client receives its largest affordable subnetwork. Sub-supernet routing reduces aggregate model-parameter traffic by $6.8\times$ relative to full-supernet transmission.
Heterogeneous Large Language Model (LLM) systems increasingly rely on shared contexts, retrieved evidence, and multi-agent dialogue histories, yet their internal key-value (KV) caches remain model-specific and cannot be reused across architectures. Consequently, each model must repeatedly prefill or store caches for the same context, limiting the scalability of multi-model reasoning and long-context generation. We propose Mixture-of-Translators(MoT), a cache translation framework that maps context KV caches from a source LLM into the cache space of a target LLM. Unlike prior approaches that depend on a single projection path or global shared latent space, MoT uses multiple translator modules to capture diverse source--target mappings. To further reduce residual translation error, we introduce a Context Correction Loss that aligns the replayed target trajectory with the native target trajectory. We reveal two competing failure modes in cache translation: propagated translation shift from early injection and last-state shift from late injection. MoT addresses them through translator mixtures and target-side correction. Across homogeneous and heterogeneous translations among Qwen2.5, GPT-2, and OPT models, MoT preserves downstream QA performance, including Qwen2.5-7B-scale translation with 51.0% average closed-set QA accuracy and 0.43 average extractive QA F1. In practical case studies, MoT enables quality-preserving memory reuse for multi-agent reasoning and retains 96.3% of direct-context quality in long-context cache-augmented generation, demonstrating scalable KV cache reuse across heterogeneous LLMs.
Federated learning (FL) enables collaborative learning over decentralized data silos without centralizing raw data. However, heterogeneous local architectures often induce non-aligned representation spaces, making it difficult to transfer global knowledge across silos. Existing paradigms share this knowledge as model parameters, distilled predictions, or class prototypes, yet all encode it in an absolute space that must be aligned across clients. Heterogeneous backbones break this alignment, so the shared knowledge becomes unreliable and misleads local training. We propose FedTopo, a relation-level framework that encodes global knowledge as class relation topology, capturing how classes relate within each client rather than where they lie in feature space. Each client builds its relation topology from local prototypes and uploads it with class statistics. The server then aggregates these relations in a reliability-aware manner that down-weights weakly supported ones, and broadcasts the global topology to clients. The global topology guides local training by emphasizing topology-similar negative classes. Experiments on three datasets under eight heterogeneous backbones show that FedTopo consistently outperforms parameter-, distillation-, and prototype-sharing baselines, with low communication and no inference overhead. Our code is available at https://github.com/Zhaoyang-Ma/FedTopo.