Anytime-Valid Federated Conformal RAG for LLM Swarms
Authors: Prasanjit Dubey, Xiaoming Huo
Organizations: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
Abstract
Federated Conformal RAG (FC-RAG) provides distribution-free coverage for a bandwidth-limited swarm of weak language models, but only at a fixed horizon. We extend it to anytime-valid sequential coverage: validity at every stopping time, preserved under predictable adaptive control (recalibration, per-node bandwidth escalation, distilled-student refresh), at no extra cost in assumptions over fixed-horizon FC-RAG. Naive composition fails because FC-RAG's marginal coverage bound makes the betting e-process a non-supermartingale on adverse calibration draws, and Ville's inequality cannot be invoked. We give Anytime-FC-RAG, a sequential extension built on a summable per-step calibration-deviation budget that converts the marginal bound into a strict conditional bound on a calibration-good event, paired with a truncated betting e-process that is a nonnegative supermartingale on the entire probability space. From these two ingredients, we obtain four guarantees: time-uniform alarm validity P(suptEt≥1/δe)≤δe+δcal, a Hoeffding-stitched cumulative-miscoverage envelope at the same total budget, safety under any predictable controller (recalibration, bandwidth escalation, student refresh), and training-side error propagation across an unbounded sequence of Federated Probe-Logit Distillation (FPLD) refreshes via a summable training budget. As a practical consequence, an adaptive controller that escalates retrieval bandwidth only when the e-process crosses a warning threshold matches the alarm rate of a fixed-high-bandwidth schedule at substantially lower communication cost. Experiments on a GPT-2-small + MiniLM swarm across MMLU, DBpedia, and AG News verify the predicted alarm rate, detection delay, envelope coverage, and 14-57% bandwidth savings; the alarm fires when and only when coverage genuinely breaks.
Training a language model on data scattered across bandwidth-limited nodes that cannot be centralized is a setting that arises in clinical networks, enterprise knowledge bases, and scientific consortia. We study the regime in which data must remain distributed across nodes, and ask what statistical guarantees are in principle achievable under explicit bandwidth budgets; we aim to characterize what is provably possible, not to demonstrate a deployment-ready system. Existing theory treats either training-time consistency or inference-time calibration in isolation, and no prior work makes bandwidth a first-class statistical parameter. We analyze two protocols, Federated Probe-Logit Distillation (FPLD) for training and Federated Conformal RAG (FC-RAG) for inference, as the analytical vehicles for our results. Our first main result is an explicit high-probability KL-consistency rate for FPLD with simultaneous dependence on node count K, per-node sample size n, quantization budget B, probe-set size m, and vocabulary size V; bandwidth enters only through an exponentially vanishing quantization term. Our second main result is a distribution-free marginal-coverage bound for FC-RAG, whose novel retrieval-bandwidth slack ΔRAG=fmaxK−2∑iv(Bi) makes per-node retrieval bandwidth a first-class statistical parameter, with arithmetic aggregation across K nodes shrinking the slack as K−1/2 in the per-node-uniform regime. A Pinsker-type corollary composes the two bounds into an end-to-end coverage guarantee. Synthetic experiments verify the predicted scaling along the bounds' parameters; small-scale experiments on a GPT-2 testbed illustrate that the qualitative bandwidth-accuracy tradeoff survives on a real language model. A deployment-scale empirical evaluation is out of scope.
Retrieval-augmented generation (RAG) has emerged as a paradigm for grounding large language models in external knowledge, yet most existing RAG systems assume centralized knowledge access and ample computation. These assumptions break down in edge environments, where knowledge is fragmented across devices, raw data cannot be shared, and repeated LLM calls are prohibitively expensive. We propose FD-RAG, a federated dual-system RAG framework that decouples lightweight memory access from on-demand LLM reasoning for decentralized deployment. Specifically, FD-RAG learns semantic-aware adaptive hypergraphs over local corpora and distills them into compact QA memories. At inference time, it answers well-covered queries via direct memory matching and invokes LLM-based reasoning only when necessary, while tracing retrieved memories to hypergraph-grounded evidence. To mitigate cross-device knowledge fragmentation, FD-RAG aggregates anonymized memories across devices without exposing raw documents. Experiments on QA benchmarks show that FD-RAG improves accuracy by up to 7.8% while reducing latency by 8.4× compared with strong local and federated baselines. We also provide theoretical analysis establishing an O(1/ε2) convergence rate for the proposed hypergraph learning, supporting its tractable deployment in edge settings.
Large language models (LLMs) exhibit strong reasoning capabilities when guided by high-quality demonstrations, yet such data is often distributed across organizations that cannot centralize it due to regulatory, proprietary, or institutional constraints. We study federated reasoning, where a server improves multi-step reasoning by coordinating with heterogeneous clients holding private demonstrations, without centralized training or raw data sharing. The key challenge is that client reliability is query-dependent, while the server cannot inspect client data to determine which contributions are trustworthy. To address this, we propose Uncertainty-Aware Federated Reasoning (FERA), a training-free framework based on iterative server-client co-refinement. Across communication rounds, clients generate reasoning traces with lightweight uncertainty estimates, and the server synthesizes them into improved reasoning that is redistributed as context for the next round, progressively improving both server outputs and client-side reasoning. Within each round, Uncertainty-Aware Self-Critique Aggregation (UA-SCA) resolves conflicts among heterogeneous client traces through query-dependent trust weighting and structured cross-client verification. Rather than simply discarding low-quality traces, UA-SCA revises flawed reasoning steps to recover useful information. We provide theoretical guarantees showing that the proposed iterative protocol converges and that uncertainty-aware weighting accelerates convergence. Experiments on multiple reasoning benchmarks show that FERA consistently outperforms both federated training and training-free baselines, achieving progressively higher accuracy across rounds while maintaining communication and computational efficiency.