FedMGP: Federated Multi-Group Paradigm

• FedMGP is a federated learning paradigm that splits model state into shareable global structure and private local components for enhanced personalization.
• It employs selective communication strategies, including similarity-guided probabilistic sampling and selective prompt fusion, to balance global commonality with client-specific nuances.
• Variants span vision-language prompt learning, federated continual learning, and multi-output Gaussian processes, demonstrating robustness in non-IID settings.

Searching arXiv for papers explicitly using the term “FedMGP” and closely related variants to ground the article. FedMGP denotes a small but heterogeneous cluster of federated-learning methods centered on selective knowledge sharing under client heterogeneity. In current arXiv usage, the term is used most explicitly for prompt-based personalization in vision-language and continual-learning settings, while a broader probabilistic usage connects it to federated multi-output Gaussian-process modeling (Bo et al., 1 Nov 2025, Yu et al., 2024, Gao et al., 2024). This suggests that FedMGP is best understood as a family label organized around a common design principle: preserve local specificity, communicate only compact shared structure, and avoid raw-data centralization.

1. Terminological scope

In the arXiv record, “FedMGP” does not name a single universally standardized algorithm. Instead, it appears in at least three distinct but related contexts.

Usage	Paper	Defining idea
Personalized federated prompt learning	"FedMGP: Personalized Federated Learning with Multi-Group Text-Visual Prompts" (Bo et al., 1 Nov 2025)	Multiple groups of paired textual and visual prompts
Personalized federated continual learning	"Personalized Federated Continual Learning via Multi-granularity Prompt" (Yu et al., 2024)	Coarse-grained global prompt and fine-grained local prompt
Federated multi-output Gaussian processes	"Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes" (Gao et al., 2024)	Federated LMC with spike-and-slab latent selection

The first usage is the most literal: FedMGP is introduced as “a new paradigm for personalized federated prompt learning in vision-LLMs,” in which each client maintains “multiple groups of paired textual and visual prompts” and uses “a dynamic prompt aggregation strategy based on similarity-guided probabilistic sampling” (Bo et al., 1 Nov 2025). The second usage is structurally related but targets Personalized Federated Continual Learning rather than vision-language prompt learning; there the core notion is a “multi-granularity prompt,” with explicit separation between shared and personalized knowledge (Yu et al., 2024). The third usage is more semantic than titular: the Gaussian-process paper frames the topic as a federated multi-output Gaussian process framework, but the concrete proposed model is named FedLMC-SS rather than FedMGP (Gao et al., 2024).

A common misconception is that every paper near this acronym refers to the same method. The literature does not support that reading. The term is overloaded, and careful disambiguation is necessary.

2. FedMGP as multi-group text-visual prompt learning

In its most direct arXiv usage, FedMGP is a personalized federated prompt-learning method for vision-LLMs. The method equips “each client with multiple groups of paired textual and visual prompts,” with the stated aim of capturing “diverse, fine-grained semantic and instance-level cues” (Bo et al., 1 Nov 2025). Rather than using a single prompt block, the method redistributes a fixed prompt budget across several groups.

The organizing mechanism is a diversity constraint over prompt groups. A “diversity loss” is introduced so that “each prompt group” specializes in “distinct and complementary semantic aspects,” and the groups “collectively cover a broader range of local characteristics” (Bo et al., 1 Nov 2025). This makes the prompt decomposition explicitly semantic rather than merely architectural.

Communication is governed by a selective aggregation rule. FedMGP uses “a dynamic prompt aggregation strategy based on similarity-guided probabilistic sampling”: each client computes “the cosine similarity between its prompt groups and the global prompts from the previous round,” then “samples $s$ groups via a softmax-weighted distribution” (Bo et al., 1 Nov 2025). The intended effect is to “preferentially aggregate semantically aligned knowledge while still enabling exploration of underrepresented patterns,” thereby balancing “the preservation of common knowledge with client-specific features” (Bo et al., 1 Nov 2025).

The paper also emphasizes communication efficiency. FedMGP “maintains parameter efficiency by redistributing a fixed prompt capacity across multiple groups,” and reports “state-of-the-art performance with the lowest communication parameters among all federated prompt learning methods” (Bo et al., 1 Nov 2025). Its theoretical claim is that the dynamic aggregation strategy “promotes robust global representation learning by reinforcing shared semantics while suppressing client-specific noise,” while the empirical claim is consistent gains in “both personalization and domain generalization across diverse federated vision-language benchmarks” (Bo et al., 1 Nov 2025).

Within the broader prompt-learning literature, this positions FedMGP as a personalization-oriented alternative to single-prompt or uniformly averaged prompt-sharing schemes. A plausible implication is that it treats prompt groups as a structured communication primitive, not merely as trainable adapters.

3. FedMGP as multi-granularity prompt in personalized federated continual learning

A second established usage of the name is the PFCL method introduced in "Personalized Federated Continual Learning via Multi-granularity Prompt" (Yu et al., 2024). Here FedMGP stands for Federated Multi-Granularity Prompt and is motivated by what the paper calls Spatial-Temporal Catastrophic Forgetting (STCF). The central design is a two-level prompt space built on a pre-trained frozen ViT backbone: a coarse-grained global prompt for shared knowledge and a fine-grained local prompt for client-, task-, and class-specific knowledge (Yu et al., 2024).

The PFCL setting is formalized over clients

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$

with per-client task streams

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$

The paper distinguishes server-side generalized knowledge fusion from client-side continual adaptation and personalization. To measure forgetting, it defines temporal knowledge retention

$$KR_t=\frac{1}{a}\sum_{i=1}^a\frac{Acc(\theta^r_i;T^0_i)}{Acc(\theta^0_i;T^0_i)},$$

and spatial knowledge retention

$$KR_s=\frac{1}{a}\sum_{i=1}^a\frac{Acc(\theta^r_g;T^r_i)}{Acc(\theta^r_i;T^r_i)}.$$

These metrics are intended to separate temporal forgetting on each client from degradation caused by federated aggregation (Yu et al., 2024).

The coarse-grained global prompt pool is written as

$\mathcal{P}_g=\{P_g^1, P_g^2, \ldots, P_g^M\},$

with prompt-augmented embedding

$$E' = \left[ P_g^{s_1}, \ldots, P_g^{s_k} ; E\right], \quad 1 \leq N \leq M.$$

Prompt selection is driven by key-query matching:

$K_g^{in} = \mathcal{V}(E),$

$\mathcal{K}^s_g = \underset{\mathcal{K}_g}{\operatorname{argmin} \sum_{i=1}^{N} \text{dis}(K_g^{in}, K_g^{i}).$

The corresponding optimization objective is

$\underset{H^i_g,\mathcal{P}_g,\mathcal{K}_g}{\operatorname{min} \mathcal{L}(\mathcal{V}^i_g(E'),y)+ \lambda_1 \sum_{\mathcal{K}^{s}_g} \operatorname{dis}(K_g^{in},K_g^{s_i}).$

This part is explicitly designed to capture “temporal-spatial invariant knowledge” and to support server aggregation without transmitting the full model (Yu et al., 2024).

The fine-grained local prompt is class-wise,

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$0

and is injected into the multi-head self-attention layers through Prefix Tuning. The paper writes

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$1

with

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$2

and the modified attention as

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$3

The paper notes that this notation is slightly inconsistent as written, but the intended role is clear: local prompts alter attention computation to encode finer-grained local knowledge (Yu et al., 2024).

Aggregation does not use ordinary FedAvg over full parameters. Instead, the method introduces Selective Prompt Fusion with a server proxy dataset $\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$4. For two prompt pools $\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$5 and $\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$6, the fusion loss is written as

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$7

Only coarse-grained global prompts are fused; local prompts remain private (Yu et al., 2024).

Experimentally, the method is evaluated on CIFAR-100 with 5 clients and 5 tasks per client. Under the asynchronous setting, average accuracies include FedViT: 82.46, FedL2P: 90.11, and FedMGP: 90.56; under the synchronous setting, FedL2P: 81.89 and FedMGP: 83.46 are reported (Yu et al., 2024). The ablations indicate that removing local prompts causes temporal retention to drop dramatically, while removing global prompts reduces spatial transfer and personalization. This supports the paper’s core division of labor: coarse prompts for shareable knowledge, fine prompts for continual personalized adaptation.

4. FedMGP in federated multi-output Gaussian processes

In a broader probabilistic usage, FedMGP refers to federated multi-output Gaussian-process modeling rather than prompt learning. The most relevant arXiv paper is "Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes" (Gao et al., 2024). There, the concrete model is FedLMC-SS, described as “a federated linear model of coregionalization (LMC) with spike-and-slab priors over latent-process coefficients” (Gao et al., 2024).

The underlying multi-output GP is written in LMC form as

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$8

where each latent process satisfies

$\mathcal{A}=\{A_1, A_2, \ldots, A_a\}$9

Cross-output covariance is induced through shared latent functions:

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$0

with

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$1

This is a transfer-learning construction in which units share latent structure but retain unit-specific loadings (Gao et al., 2024).

Automatic latent-process selection is introduced through spike-and-slab priors:

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$2

The model is reparameterized as

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$3

with Bernoulli selectors $\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$4. This enables the model to “automatically select only needed latent processes by shrinking the coefficients of unnecessary ones to zero” (Gao et al., 2024).

Inference is variational. The ELBO is

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$5

with client-decomposable objective

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$6

That decomposition makes federated optimization possible: clients optimize local terms using only local data, then the server aggregates shared parameters in FedAvg-style form,

$\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$7

The paper also gives a local adaptation mechanism for a new unit by fixing the shared latent structure and optimizing only the new unit’s local objective (Gao et al., 2024).

Empirically, the paper reports simulation and case studies on Li-ion battery degradation and air temperature data. In a simulation with six true latent eigenfunctions and ten candidate latent functions, average MSEs include LMC-SS: $\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$8 and FedLMC-SS: $\mathcal{T}_i=\{T_i^1, T_i^2, \ldots, T_i^{n_i}\}.$9, while FedLMC-SS selects on average about 6.7 latent functions (Gao et al., 2024). This usage of FedMGP is therefore probabilistic, uncertainty-aware, and regression-oriented, in contrast to the prompt-based personalization methods.

5. Adjacent acronyms and frequent confusions

The literature around FedMGP is unusually prone to acronym collision. Several nearby methods are distinct and should not be conflated with FedMGP.

Most directly, Fed-PMG in "Federated Pseudo Modality Generation for Incomplete Multi-Modal MRI Reconstruction" is not FedMGP; it addresses missing-modality MRI reconstruction through pseudo modality generation in frequency space and reports that clustering reduces extra information-sharing cost by about 97.5% relative to direct amplitude-spectrum sharing (Yan et al., 2023). FedGradMP in "Federated Gradient Matching Pursuit" is a sparse optimization algorithm for federated learning, not a prompt method or Gaussian-process model (Jeong et al., 2023). FedMGS in "Towards Modality-imbalanced Federated Graph Learning: A Data Synthesis-based Approach" handles modality imbalance in multimodal federated graph learning through latent semantic synthesis, not prompt personalization (Wu et al., 18 Jun 2026). FedMGDA+ in "Federated Learning Meets Multi-objective Optimization" is a Pareto-oriented multi-objective federated optimization method rather than a FedMGP variant (Hu et al., 2020).

Other confusions are conceptual rather than nominal. "Federated Multi-Agent Deep Reinforcement Learning Approach via Physics-Informed Reward for Multi-Microgrid Energy Management" proposes F-MADRL, a federated PPO-based controller for decentralized multi-microgrid energy management, which is relevant only if “FedMGP” is being used loosely to mean federated optimization for microgrids (Li et al., 2022). "Federated Martingale Posterior Samping" proposes FMP, a one-shot federated approximation to martingale-posterior inference, not FedMGP (Zhang et al., 18 May 2026). "Federated Gaussian Mixture Models" proposes FedGenGMM, again outside the prompt-learning and Gaussian-process usages of FedMGP (Pettersson et al., 2 Jun 2025).

The practical implication is straightforward: the acronym alone is insufficient for bibliographic precision. Title-level disambiguation is often necessary.

6. Recurring design principles and research significance

Despite the diversity of usages, the FedMGP family exhibits a stable set of architectural ideas. First, all variants split model state into shareable global structure and private local structure. In the multi-group text-visual prompt formulation, this appears as prompt groups selectively sampled for communication (Bo et al., 1 Nov 2025). In PFCL, it appears as coarse-grained global prompts versus fine-grained local prompts (Yu et al., 2024). In the Gaussian-process setting, it appears as global latent processes and local loading coefficients (Gao et al., 2024).

Second, communication is deliberately structure-aware rather than uniform. FedMGP for vision-LLMs uses similarity-guided probabilistic sampling over prompt groups (Bo et al., 1 Nov 2025). The PFCL variant communicates only coarse prompts and keys, with reported transmitted size 84,480 parameters, while total trainable parameters per client are 4,700,160 (Yu et al., 2024). The Gaussian-process formulation aggregates only global variational parameters while retaining personalized parameters on-device (Gao et al., 2024). This suggests that FedMGP methods generally reject indiscriminate full-parameter averaging in favor of semantically or statistically filtered communication.

Third, FedMGP methods are designed for non-IID personalization rather than purely global optimization. The multi-group text-visual prompt version targets both “personalization and domain generalization” (Bo et al., 1 Nov 2025). The PFCL version explicitly addresses federated heterogeneity and sequential task arrival under STCF (Yu et al., 2024). The Gaussian-process version supports “a new unit within our proposed federated framework” by reusing previously learned shared latent structure (Gao et al., 2024). Across domains, the shared objective is not only privacy-preserving collaboration, but also client-specific adaptation without forfeiting cross-client transfer.

A plausible synthesis is that FedMGP names a methodological direction rather than a single closed-form recipe. Its characteristic move is to federate only the representation components most likely to encode common structure—prompt groups, coarse prompts, latent processes—while leaving task- or client-specific detail local. That principle links the otherwise disparate prompt-learning, continual-learning, and Gaussian-process branches of the literature.