FedRP: Communication-efficient Federated Learning

• FedRP is a federated learning method that leverages random projection to compress model updates and enforce consensus in a projected space.
• It uses an ADMM optimization framework to coordinate decentralized training while providing analytic differential privacy guarantees without extra noise.
• Empirical results show that FedRP achieves competitive accuracy with dramatically reduced per-round communication compared to standard methods.

Searching arXiv for papers on “FedRP” and closely related variants to ground the article in current literature. FedRP denotes a federated learning algorithm that combines random projection with an Alternating Direction Method of Multipliers (ADMM) optimization framework in order to address two coupled constraints in decentralized training: user privacy protection and communication cost. In the formulation introduced in "FedRP: A Communication-Efficient Approach for Differentially Private Federated Learning Using Random Projection" (Narimani et al., 12 Sep 2025), each client transmits a low-dimensional projected representation of its model parameters rather than the full parameter vector, and consensus is enforced in the projected space. The method is presented as providing an analytic $(\epsilon,\delta)$-differential privacy guarantee without adding extra noise, while reducing per-round communication from $O(n)$ to $O(m)$ when the original model dimension is $n$ and the projection dimension is $m \ll n$.

1. Definition and optimization objective

FedRP is formulated for federated optimization with $K$ clients, where client $i$ holds dataset $\mathcal{D}_i$ and local loss

$$f_i(w_i)=\sum_{(x,y)\in\mathcal{D}_i} \ell(y,f_{(w_i)}(x)).$$

The optimization goal is

$$\min_{w_1,\dots,w_K} \sum_{i=1}^K f_i(w_i) \qquad \text{subject to } w_i=\bar z,\ \forall i,$$

where $O(n)$0 is the global consensus variable (Narimani et al., 12 Sep 2025).

ADMM is used to convert this constrained problem into an augmented Lagrangian. The paper writes

$O(n)$1

with $O(n)$2, $O(n)$3, $O(n)$4, and penalty parameter $O(n)$5. Within this formulation, FedRP departs from standard consensus FL by moving the agreement constraint into a compressed space generated by a random projection. This suggests that the method is not merely a communication codec layered on top of FedAvg, but a consensus procedure defined directly in the projected domain.

2. Random projection as transmission mechanism

At each round $O(n)$6, clients generate a fresh random matrix

$O(n)$7

independently, using a shared secret seed (Narimani et al., 12 Sep 2025). Each client then computes

$O(n)$8

and sends only this projected quantity to the server.

The paper explicitly invokes the Johnson–Lindenstrauss lemma: for any two vectors $O(n)$9 and $O(m)$0, with high probability,

$O(m)$1

provided

$O(m)$2

Accordingly, the projection is used to preserve pairwise geometry approximately while shrinking the transmitted representation from dimension $O(m)$3 to dimension $O(m)$4.

A common misunderstanding is to treat the projection step as only a compression device. In FedRP, the projection is also the source of the privacy argument: the server only ever sees the $O(m)$5-dimensional $O(m)$6 instead of the full $O(m)$7-dimensional model parameters, and the randomness of $O(m)$8 is central to the stated privacy guarantee. The paper therefore positions random projection as simultaneously a dimensionality-reduction mechanism, a communication-control mechanism, and a privacy mechanism.

3. Consensus ADMM in projected space

FedRP rewrites the local objective in the projected domain as

$O(m)$9

The protocol is iterative. On the server side, round $n$0 consists of broadcasting the current $n$1, receiving projected updates $n$2, and aggregating them as

$n$3

On the client side, the update sequence is (Narimani et al., 12 Sep 2025):

1. primal update,

$n$4

2. dual update,

$n$5

1. generation of a new random matrix $n$6;
2. computation and transmission of

$n$7

This procedure differs structurally from FedAvg. FedAvg averages model parameters or updates directly in the ambient space, whereas FedRP aggregates the projected variables under an ADMM consensus constraint. A plausible implication is that FedRP’s convergence and privacy behavior are inseparable from the projected optimization geometry; replacing the projected ADMM step with ordinary parameter averaging would alter the method materially.

4. Differential privacy guarantee

FedRP states an $n$8-differential privacy definition in the usual neighboring-dataset sense:

$n$9

for all neighboring datasets $m \ll n$0 and all measurable $m \ll n$1 (Narimani et al., 12 Sep 2025).

The privacy analysis assumes neighboring models $m \ll n$2 satisfy $m \ll n$3 and that each $m \ll n$4. Under that setup, the paper states that the mechanism outputs $m \ll n$5 whose distribution is

$m \ll n$6

Its Theorem 1 gives the privacy bound

$m \ll n$7

The summary further states that no additional noise is needed, because the randomness of $m \ll n$8 itself suffices, and that over $m \ll n$9 rounds, by basic composition, total $K$0.

The privacy claim is therefore analytically tied to the projection mechanism rather than to Gaussian perturbation added after optimization. This is the central conceptual distinction between FedRP and conventional differentially private FL schemes that rely on explicit noise injection. The paper also reports resilience to data reconstruction attacks and states that there is no analytic inversion of $K$1, which it presents as part of the security rationale.

5. Communication complexity and empirical evaluation

FedRP’s communication claim is straightforward: baseline FedAvg transmits $K$2 parameters each round, or approximately $K$3 bytes, whereas FedRP transmits only $K$4 parameters, giving per-client per-round complexity $K$5 rather than $K$6 and a reduction factor of $K$7 (Narimani et al., 12 Sep 2025). The paper’s Table 2 gives a concrete example for LeNet-5: $K$8 versus $K$9, described as a $i$0 factor.

The reported experiments use MNIST, CIFAR-10, and CIFAR-100, with LeNet-5, ResNet-18, and pre-trained VGG16. The client counts are:

• LeNet-5: 10, 50, 100, 200 clients,
• ResNet-18: 10, 50, 100 clients,
• VGG16: 5 clients.

The random projection dimensions are listed as

$i$1

with local epochs per round equal to 30 and batch size 64.

The main empirical findings reported in the summary are concise. FedRP matches FedAvg in accuracy within approximately $i$2–$i$3, outperforms FedAvg+DP, reduces communication by orders of magnitude, and remains robust even for pre-trained VGG16, where it is described as avoiding the accuracy collapse caused by added noise (Narimani et al., 12 Sep 2025). Table 3 is summarized as showing that FedRP with $i$4 yields lower $i$5 and comparable or better accuracy than FedAvg+DP. The comparison set includes FedAvg, FedAvg+DP, FedADMM, and FWC, and Figure 1 reports accuracy versus rounds.

These results position FedRP as a method whose communication savings are not incidental but extreme in the low-$i$6 regime. At the same time, the reported accuracy behavior suggests that the projection dimension can be aggressively reduced without immediate collapse in predictive performance, at least for the models and datasets studied.

6. Relation to adjacent methods and nomenclature

The name “FedRP” can be confused with nearby acronyms in the federated learning literature. It should be distinguished from "FedRPCA: Enhancing Federated LoRA Aggregation Using Robust PCA" (Jhunjhunwala et al., 1 Jun 2025), which addresses heterogeneity in LoRA-based federated fine-tuning by decomposing client LoRA updates into low-rank and sparse components via Robust PCA, and from "FedREP: A Byzantine-Robust, Communication-Efficient and Privacy-Preserving Framework for Federated Learning" (Yang et al., 2023), which is built around consensus sparsification, secure aggregation, and Byzantine-robust aggregation.

This distinction matters because the three methods solve different problems with different primitives. FedRP uses random Gaussian projection and ADMM consensus in projected space. FedRPCA uses Robust PCA to separate common and client-specific LoRA signals before aggregation. FedREP uses ConSpar, SecAgg, and a robust aggregator under Byzantine assumptions. The overlap is therefore mainly nominal and thematic: all are federated learning methods concerned with efficiency or robustness, but their mechanisms, guarantees, and target settings differ.

A second interpretive point concerns where FedRP sits relative to standard DP-FL. The paper’s framing suggests that FedRP belongs to a class of methods in which privacy is obtained from the stochastic transmission map itself rather than from explicit additive noise. A plausible implication is that the quality of the privacy-utility tradeoff depends directly on the projection dimension $i$7, the lower norm bound $i$8, and the round count $i$9, because these quantities appear explicitly in the privacy expression and in the composition statement. In that sense, communication, privacy, and optimization are tightly coupled rather than modularly separable in FedRP.