Modular Federated Learning: A Meta-Framework Perspective

Cl\'audia Soares; Du\v{s}an Jakoveti\'c; Frederico Vicente

REVIEW 4 major objections 5 minor 298 references

Modular Federated Learning: A Meta-Framework Perspective

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This survey claims that federated learning is a modular meta-framework, and that its central operator pair is Aggregation (merging client updates) and Alignment (constraining that merge for fairness, convergence, or robustness)…

desk verdict Useful FL survey with a genuinely organizational meta-framework; the Alignment novelty is overstated and Eq. (2) is not a faithful umbrella. read the letter →

arxiv 2505.08646 v1 pith:SEDH3BYA submitted 2025-05-13 cs.LG

Frederico Vicente , Cláudia Soares , Dušan Jakovetić This is my paper · ORCID

classification cs.LG

keywords FederatedLearningDistributedDecentralisedOptimisationSurveyMeta-FrameworkAlignmentOperatorAggregation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This survey claims that federated learning is best understood not as a family of algorithms but as a modular meta-framework: eight loosely independent components—infrastructure, communication, aggregation, data handling, model-agnostic design, security, privacy, and trustworthiness—that can be designed, improved, and recombined separately. Its core proposal is a new taxonomic division inside the aggregation step: an Aggregation operator, which merges client updates into a global model, and an Alignment operator, which constrains that merge to satisfy objectives such as fairness, convergence, or robustness. The paper formalizes this as a single constrained optimization template, Eq. (2), and argues that consensus FL, robust max-loss FL, personalized penalty methods, and bounded-divergence methods are all special cases. A sympathetic reader would care because a faithful common template would give the field one vocabulary for comparing, composing, and extending methods, and would tie modern FL back to the distributed-optimization literature from which it grew.

What carries the argument

The load-bearing object is Eq. (2), a constrained-optimization template proposed as the general federated-learning objective: minimize $\mathcal{S}(\mathcal{L}_1(\theta_1),\dots,\mathcal{L}_N(\theta_N),\mathcal{L}(\theta))$ subject to $\mathcal{A}(\theta,\{\theta_c\}) \le \epsilon$, with $\theta$ the global model, $\theta_c$ the client-local models, $\mathcal{S}$ the aggregation function, $\mathcal{A}$ the alignment operator, and $\epsilon$ a threshold that makes the constraint an inequality. The template does its work by enumeration: choosing $\mathcal{A}$ to enforce $\theta_i=\theta_j$ recovers consensus FL (Eq. 8); the same constraint with max-aggregation recovers robust FL (Eq. 9); substituting proximity penalties $\|\theta_c-\theta\|^2$ or $\|\theta_c-\theta\|$ recovers the personalized formulations (Eqs. 10-11); keeping consensus as a bounded inequality recovers Eq. (12); and a quadratic-penalty reformulation (Eq. 13) shows hard and soft alignment are interchangeable. The paper's organizational force rests on this template being a faithful umbrella over the methods it surveys.

What would settle it

Take three flagship methods the survey must cover—a token/random-walk protocol with no global model (the model hops between nodes), a vertically partitioned split-learning scheme where no client holds a complete model, and clustered FL with its two-level membership assignment—and attempt to write each as a triple $(\mathcal{S},\mathcal{A},\epsilon)$ in Eq. (2) without changing the published algorithm. If any of them forces a degenerate choice (an empty global parameter space, an identically-zero alignment operator, or a constraint that silently turns the problem into a different optimization), the claim that Eq. (2) is the general FL template fails; the claim stands or falls on how large a fraction of a broad catalog of FL methods admits a natural, non-degenerate representation.

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Extended reading notes

Core claim

The central claim, on the paper's own terms, is that knowledge alignment between clients deserves to be an explicit, first-class operator in federated learning, co-equal with aggregation. Concretely, the paper asserts that essentially any FL procedure can be written as the constrained program $\min_{\theta,\{\theta_c\}} \mathcal{S}(\mathcal{L}_1(\theta_1),\dots,\mathcal{L}_N(\theta_N),\mathcal{L}(\theta))$ subject to $\mathcal{A}(\theta,\{\theta_c\}) \le \epsilon$, where $\mathcal{S}$ is the aggregation function (how local losses combine, e.g., average or max), $\mathcal{A}$ is the alignment operator (a possibly vector-valued measure of how the local models $\theta_c$ and the global model $\theta$ may relate), and $\epsilon$ is a threshold that can be set to zero for exact consensus, to a positive value for bounded divergence, or reversed to force distinct models. In this reading, FedAvg is the special case of weighted-average aggregation under exact consensus; robust model-agnostic FL uses max-aggregation under the same constraint; personalized FL replaces the hard constraint with proximity penalties such as $\|\theta_c-\theta\|^2$; and clustered FL learns several global models with clients partitioned by distance. The contribution is therefore taxonomic and architectural: it names the second operator, collects the field's methods under the pairing $(\mathcal{S},\mathcal{A},\epsilon)$, traces the template's roots in distributed optimization (consensus, ADMM, block coordinate descent), and surveys Python frameworks as partial implementations of the modular blueprint.

Load-bearing premise

The framework assumes that every useful federated-learning method can be faithfully rewritten as one constrained optimization problem of the form Eq. (2), in which an aggregation function $\mathcal{S}$ combines client losses and an alignment constraint $\mathcal{A}(\theta,\{\theta_c\})\le\epsilon$ governs how client models relate to the global model; methods that communicate only predictions or statistics, keep no shared global model, or solve a two-level clustering problem (as in Eqs. 15-16) may not fit the template without distortion.

Editorial extensions

If this is right

Every mainstream FL algorithm becomes a choice of aggregation function $\mathcal{S}$ and alignment operator $\mathcal{A}$ in Eq. (2): FedAvg, robust max-loss FL, personalized proximity-penalty methods, and bounded-divergence methods are all recovered as special cases, so a result proved for one instance can be translated to its siblings.
System builders can treat the eight modules as interchangeable parts—swapping compression, client selection, secure aggregation, or the alignment constraint independently—instead of adopting monolithic algorithms, which is the design pattern the surveyed Python FL frameworks are converging on.
The Alignment/Aggregation distinction gives a common vocabulary across subfields: fairness, robustness, personalization, and client prioritization each become a specific constraint $\mathcal{A}\le\epsilon$, making comparable methods that were previously described in incompatible terms.
The explicit lineage from distributed optimization—consensus, ADMM, block coordinate descent, token methods—means convergence analyses from that older literature can be imported into FL design, and FL formulations can in turn be analyzed with the older theory.
The framework turns open-problem identification into a modular audit: each of the eight modules has a known set of techniques and a known gap, so future work can target missing modules rather than re-invent whole systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

My inference: if the template is accepted, the obvious untaken step is generative design—systematically pairing aggregation strategies (attention-weighted, median-based) with alignment constraints (fairness, bounded divergence) to produce new algorithms the survey itself does not enumerate.
My inference: the paper does not prove a unified convergence theory for Eq. (2); a natural testable extension is whether the convergence analyses of FedProx, SCAFFOLD, and robust FL can be recovered as instances of a single theory parameterized by properties of $\mathcal{A}$, such as its convexity or smoothness constants.
My inference: the bilevel structure of clustered FL (Eqs. 15-16) is the most likely genuine exception to the umbrella; if CFL cannot be flattened into an $(\mathcal{S},\mathcal{A},\epsilon)$ triple, the meta-framework is best read as a partial taxonomy rather than a universal one.
My inference: the penalty reformulation (Eq. 13) shows hard constraints and soft penalties are two encodings of the same alignment intent, so the threshold form $\mathcal{A}\le\epsilon$ is a presentation choice; that suggests the operator itself, not the inequality, is the durable contribution.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read this if you want a broad, readable map of FL, not because of the formal contribution. The survey does a real service: it decomposes FL into eight modules, keeps the historical thread from distributed optimization through FedAvg, and gives a practical comparison of Python frameworks. For a newcomer or someone teaching FL, that is genuinely useful. The taxonomy distinguishes aggregation from alignment in a way that will organize lecture slides and related-work sections. Credit is due for that.

The problem is the packaging. The 'novel Alignment operator' is a constraint function that appears in the personalized and robust FL literature the paper itself cites; Eqs. (5)–(7) are inequalities wearing function-definition clothing. The formal section has a genuine sign error: Eq. (13) defines the penalty as max(−(A−ε),0)^2, which penalizes A below ε; it should be max(A−ε,0)^2. That is minor in the sense that no algorithm or experiment depends on it, but it matters because the paper's only formal apparatus is this constrained-optimization template.

Bigger soft spot: Eq. (2) is presented as the general FL objective. It is not. Clustered FL, which the paper itself formulates as a bilevel problem with K global models and discrete assignments (Eqs. 15–16), cannot be written as one θ, one S, one A, and one ε without losing the mechanism. Heterogeneous-model distillation aligns on public-data logits, not in parameter space; token methods have no persistent global model; vertical FL concatenates disjoint embeddings. The stress-test note is right on this. The paper neither proves a reduction nor explains how acknowledged exceptions embed. So the meta-framework is a partial taxonomy, useful as an organizing device, not a unifying theory.

No empirical claims to check, no fitted parameters, no self-referential derivation; the citation pattern looks appropriate. The authors should fix Eq. (13), stop calling a renamed constraint 'novel,' and either qualify Eq. (2) as covering a large subclass or show explicitly how CFL-type problems fit. With those changes, it is a solid survey. I would send it to referees; it is worth a serious look for the survey section alone, but the central claim needs honest moderation.

Referee Report

4 major / 5 minor

Summary. The paper is a survey of Federated Learning organized around a proposed 'meta-framework' of eight modules (infrastructure, communication, aggregation, data, model, security, privacy, trustworthiness). Its central intellectual claim is that Federated Learning should be understood through two equally fundamental operators: aggregation, which combines client updates, and a newly named 'Alignment' operator, which constrains and guides aggregation toward objectives such as fairness, convergence, or robustness. The survey formalizes this in Section 2.2 as a single constrained optimization template, Eq. (2), and then uses that template to organize a broad literature review covering historical background, aggregation methods, communication strategies, data handling, security, privacy, trustworthiness, Python frameworks, applications, and future directions.

Significance. If the formal template and the Modular Alignment framing were fully faithful, the paper would provide a useful organizing perspective for a fragmented literature. The survey is broad and generally well-referenced, and it does not claim a numerical evaluation, so its value lies in the taxonomy and the historical and practical systematization. The comparison tables for FL frameworks and the coverage of topics such as split learning, token-based aggregation, and trustworthy FL are useful starting points for newcomers. However, the formal core is currently not reliable enough to support the paper's strongest claims: Eq. (2) is presented as a general template for FL optimization, but several FL families discussed in the same paper do not fit it without substantial reinterpretation, and the accompanying formal definitions contain mathematical errors. These are load-bearing issues for the paper's identity as a 'meta-framework' and for the claimed novelty of the Alignment operator, so they need to be repaired or the claims need to be narrowed.

major comments (4)

[§2.2, Eq. (2)] The claim that Eq. (2) is a general template for FL optimization is not supported by the paper's own material. Eq. (2) contains a single global parameter θ, per-client parameters θ_c, an aggregation function S over losses, and one alignment constraint A ≤ ε. However, Clustered FL (Eqs. (15)–(16)) involves K global models and discrete cluster-membership variables; there is no discrete variable and no per-cluster θ_k in Eq. (2). Heterogeneous-model distillation methods (Section 4.2.3, e.g., RHFL) align clients that have no common parameter space, so an alignment operator defined on θ and {θ_c} as in Eqs. (5)–(7) does not describe them. Token-based decentralized aggregation (Section 4.2.4) has no persistent global model, and vertical FL with split networks concatenates client embeddings into a server-side model, which is not an instance of S over client losses. The paper neither proves that every FL method reduces to Eq. (2) nor shows how the acknowledged bilevel CFL objective is embedded. I recommend either restricting the template claim to a well-defined subclass (e.g., server-client FL with a shared parameter space) or explicitly presenting Eq. (2) as one canonical formulation among several, rather than as the unifying umbrella.
[§2.2, Eqs. (5)–(7)] Eqs. (5)–(7) are written as function definitions but contain inequalities. For example, Eq. (5) states 'A(θ,{θ_c}) := ||θ − θ_c|| ≤ ε, c = 1,...,N,' which is a constraint, not a definition of A as a function. The same issue appears in Eq. (7). This matters because Eq. (2) uses A as a function with a componentwise inequality A ≤ ε. The text should define A as a vector-valued function, e.g., A(θ,{θ_c}) = (||θ − θ_1||, ..., ||θ − θ_N||), and then state the constraint separately. The subsequent examples in Eqs. (8)–(12) should be brought into the same notation so that the formal framework is internally consistent.
[§2.2, Eq. (13)] The penalty in Eq. (13) has the wrong sign. The term g(A) := max(−(A − ε),0)^2 penalizes values of A that are below ε, i.e., feasible points of the constraint A ≤ ε, and leaves violating points with A > ε unpenalized. The correct penalty for the constraint A ≤ ε is max(A − ε,0)^2. Since the surrounding paragraph claims a relation between Eq. (13) and Eq. (10), this error directly affects the formal basis of the paper's treatment of alignment as a soft constraint. Please correct the sign and recheck the stated relationship.
[§1 and §4.2.7] The paper repeatedly describes the Alignment operator as 'novel' and as 'as fundamental as aggregation,' but the formal content of A in Eq. (2) is a constraint or regularizer already present in the cited personalization and consensus literature (e.g., references [103, 11, 19] and formulations (8)–(12)). The paper does not provide a criterion distinguishing an 'alignment operator' from an ordinary constraint, nor does it show that the taxonomy yields predictions or design rules that existing surveys do not offer. I would therefore recommend repositioning the contribution: the Alignment perspective is a useful organizing viewpoint, but describing it as a novel operator overstates the formal novelty and should be toned down or supported by a sharper definition with clear scope conditions.

minor comments (5)

[§2.1.1, Eq. (1)] The notation D := ⋃_{c=1}^N D_c with |D| = Σ |D_c| implicitly assumes that the local datasets are disjoint; this assumption should be stated explicitly, since overlapping datasets would change the cardinality identity.
[§2.2.1, Eq. (17)] Eq. (17) bundles the server aggregation rule and the local SGD update into one line; the aggregation update θ ← Σ (|D_c|/|D|) θ_c and the local update θ_c^{s+1} ← θ_c^s − η∇ℓ(θ_c^s) should be numbered or separated to avoid confusion about what is being updated in each step.
[§4.7.3] The text directs the reader to 'Fig. 6' for an overview of Federated Learning algorithms concerning privacy, but Fig. 6 is the Split-NN architecture figure; the cross-reference appears to be incorrect and should be fixed or removed.
[§5, Table 8] The starred quality ratings in Table 8 are not defined; a short rubric explaining what distinguishes (*) from (***) would make the comparison more objective and useful.
[§4.2.4 and §4.3.3] The token in token-based aggregation is described both as 'the global model' and as a local artifact that 'acts as the global model' while hopping between nodes; this ambiguity should be clarified, since it bears directly on whether token-based FL can be represented by Eq. (2) with a single persistent θ.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the Alignment operator is a definitional taxonomy contribution, and no claimed result reduces to its own inputs.

full rationale

This is a survey and meta-framework paper, not a derivation of empirical predictions. Section 2.2 defines Eq. (2) with an aggregation function S and an alignment function A, and Section 4.2.7 recalls Eq. (23) as the same constrained objective and names A the Alignment operator. This is a naming and formalization move, not a claim that A is derived from S or from the survey's own structure. The only author self-citation in the historical section ([119], attributed to Jakovetic et al.) supports a historical remark about distributed Nesterov methods and is not load-bearing for the taxonomy. The paper's Eq. (13) contains a sign error (it penalizes A below epsilon rather than above), but this is a correctness issue, not a circular step. The framework's validity depends on whether Eq. (2) faithfully covers all FL variants, which is a modeling and coverage concern rather than a self-referential derivation; no fitted parameters are renamed as predictions and no load-bearing claim reduces to its own input.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

The paper is a survey, so the ledger contains no fitted parameters. The central conceptual load rests on the assumption that FL reduces to Eq. (2), that eight modules are the right decomposition, and that 'alignment' is a meaningful new primitive. These are domain assumptions, not mathematical axioms. The only invented entity is the alignment operator, which has no external evidence.

assumptions (4)

domain assumption Federated learning can be modeled as one constrained optimisation problem of the form Eq. (2).
Section 2.2 states that a Federated Learning problem can usually be considered an optimisation problem and formalizes all variants through S, A, and epsilon. This is used as the foundation of the meta-framework.
ad hoc to paper The eight modules (infrastructure, communication, aggregation, data, model, security, privacy, trustworthiness) are an adequate and near-exhaustive decomposition of FL.
Section 2.4 introduces the modules without a derivation or a comparison against alternative decompositions. The utility claim rests on reader acceptance.
domain assumption Existing FL methods can be partitioned by the formal alignment operator without loss of meaning.
Section 4.2.7 claims that alignment generalizes works [103, 11, 19], but no mapping or evaluation shows that the taxonomy preserves algorithmic content.
standard math Standard optimization assumptions used in the cited literature, such as convexity, smoothness, the Polyak-Lojasiewicz condition, and bounded gradient noise, are correct where invoked.
Section 2.2.2 surveys convergence results and relies on those published proofs rather than re-deriving them.

invented entities (1)

Alignment operator A
purpose: Conceptual operator that constrains aggregation to enforce fairness, robustness, or personalized similarity in FL.
No falsifiable prediction or algorithmic implementation is attached. Its examples are rearranged constraints from existing FL papers, so it functions as a renaming with no independent empirical handle.

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Cite this review

Pith. "Pith review of Modular Federated Learning: A Meta-Framework Perspective." pith.science (2026). https://pith.science/paper/SEDH3BYA

@misc{pith2026250508646,
  author       = {Pith},
  title        = {Pith review of: Modular Federated Learning: A Meta-Framework Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SEDH3BYA}},
  note         = {Machine review of arXiv:2505.08646}
}

read the original abstract

Federated Learning (FL) enables distributed machine learning training while preserving privacy, representing a paradigm shift for data-sensitive and decentralized environments. Despite its rapid advancements, FL remains a complex and multifaceted field, requiring a structured understanding of its methodologies, challenges, and applications. In this survey, we introduce a meta-framework perspective, conceptualising FL as a composition of modular components that systematically address core aspects such as communication, optimisation, security, and privacy. We provide a historical contextualisation of FL, tracing its evolution from distributed optimisation to modern distributed learning paradigms. Additionally, we propose a novel taxonomy distinguishing Aggregation from Alignment, introducing the concept of alignment as a fundamental operator alongside aggregation. To bridge theory with practice, we explore available FL frameworks in Python, facilitating real-world implementation. Finally, we systematise key challenges across FL sub-fields, providing insights into open research questions throughout the meta-framework modules. By structuring FL within a meta-framework of modular components and emphasising the dual role of Aggregation and Alignment, this survey provides a holistic and adaptable foundation for understanding and advancing FL research and deployment.

Figures

Figures reproduced from arXiv: 2505.08646 by the authors.

**Figure 1.** Standard centralised Federated Learning Setting. Each client 𝑐 learns a local model and shares it with a central server, aggregating the individual model parameters and then sending this new global model back to the clients. This process is repeated for several rounds until a certain criterion is met. Server Cross-Device Cross-Silo Hierarchical FL Server Server Server Server Server ∑ ∑ ∑ [PITH_FULL_IMAGE:figures/fu… view at source ↗

**Figure 2.** Contrasting different infrastructure meta-types of Federated Learning architectures. Cross-Device FL utilises low-resource devices with uncontrollable training availability (e.g. smartphones, microcontrollers). Cross-Silo is based on a reliable infrastructure such as a collection of servers. Hierarchical FL mixes Cross-Device and Cross-Silo FL infrastructure. Client0 Feat 0 Feat 1 Feat n ... Client c Feat 0 Feat 1 F… view at source ↗

**Figure 3.** Abstract overview of the main differences between Horizontal and Vertical Federated Learning. Horizontal Federated Learning (left) expects the same features across clients, while Vertical Federated Learning (right) involves clients with different features. Frederico Vicente et al. Page 64 of 63 [PITH_FULL_IMAGE:figures/full_fig_p064_3.png] view at source ↗

Figures from the paper (20 more)

**Figure 4.** Figure 4: Meta-Framework overview of the Federated Learning paradigm as a fusion of key modules categorised into Infrastructure, Data, Threat Protection, Distributed Optimisation, and Model Design. Client Client Server / Cluster Input Output Heavy Computation [PITH_FULL_IMAGE:f…

**Figure 5.** Figure 5: Abstract depiction of Split Learning, which shares a neural network model computational execution between clients and more computational-powered servers. X1 𝞱1 h1 (𝞱1 ) Xn 𝞱n hn (𝞱n ) A(•) ••• h0 𝞱0 f(𝞱0 ) [PITH_FULL_IMAGE:figures/full_fig_p065_5.png]

**Figure 6.** Figure 6: Split-NN architecture overview. Distributed Learning network where each client trains an intermediate representation and shares it with a server, which then fuses them, applies backpropagation, and defuses the update with the clients. Frederico Vicente et al. Page 65 o…

**Figure 7.** Figure 7: Comparison of distributed network topologies: (Left) Centralised server-client star schema with a single control point. (Middle) Decentralised peer-to-peer system with direct client communication. (Right) Semi-decentralised topology combining peer-to-peer and server co…

**Figure 8.** Figure 8: Impact of stragglers on Synchronous vs Asynchronous Federated Learning. Initially, both approaches behave similarly, but after cohort formation, asynchronous servers/clients progress faster by not waiting for stragglers, leading to quicker convergence in fewer training…

**Figure 9.** Figure 9: Abstract overview over a federated clustering algorithm, which groups together clients in clusters (A: client 1,4; B: client 2,5; C: client 3) according to how similar their data distributions are. The circles represent the class distributions when considering a classi…

**Figure 10.** Figure 10: Popular data preparation techniques involve using Sharding (left), the Dirichlet distribution (middle), and a combination of the Dirichlet distribution and manipulating the number of elements in the datasets (right). The different colors represent distinct features, w…

**Figure 11.** Figure 11: Overview of Horizontal vs. Vertical Reinforcement Federated Learning. (Left) Horizontal FL, where each node explores a different environment. (Right) Vertical FL, with multiple clients observing a shared environment. Adapted from Qi et al. [211]. Average Gradient Well…

**Figure 12.** Figure 12: Byzantine Gradient Attack. Showcasing how a gradient attack can affect the update of the FedSGD algorithm. Server/Client Model Untrusted Client TEE Data ML Algorithms ML Model Training Procedure Inference Procedure [PITH_FULL_IMAGE:figures/full_fig_p067_12.png]

**Figure 13.** Figure 13 [PITH_FULL_IMAGE:figures/full_fig_p067_13.png]

**Figure 14.** Figure 14: Abstract example of how Secure Aggregation mechanism can be applied to Federated Learning. Each client holds one or more masks which are added to the model weights, conditioned that the sum of all masks from the different clients must add up to 0, so they cancel out. …

**Figure 15.** Figure 15: Showcasing the capabilities of the Gradient Inversion technique extracted from gradients obtained from a Federated Learning setting. Adapted from GradInversion [314]. Client Model Parameters Loss Function Input Data Optimiser M(d1 ) M(d2 ) [PITH_FULL_IMAGE:figures/fu…

**Figure 16.** Figure 16: Differential Privacy mechanism and its possible applications (e.g. Model Parameters, Loss Function, Optimiser, Input Data). Frederico Vicente et al. Page 68 of 63 [PITH_FULL_IMAGE:figures/full_fig_p068_16.png]

**Figure 17.** Figure 17: We present a FHE framework applied to a neural network use case. Notice that after a homomorphic operation, noise is additionally added to the encrypted input. Above a certain threshold of noise, FHE execution starts deteriorating the correctness of the decryption pro…

**Figure 18.** Figure 18: We present four different time-evolving types of data distribution shifts occurring in a Federation, also known as Clients Concept Drift. Each colour represents a different concept distribution. Adapted from Jothimurugesan et al. [125]. Global Model (round r - 1) Glob…

**Figure 19.** Figure 19: Clients Models drifting when their intrinsic concept distribution changes. Frederico Vicente et al. Page 69 of 63 [PITH_FULL_IMAGE:figures/full_fig_p069_19.png]

**Figure 20.** Figure 20: Two heterogeneous clients being modelled with Gaussians, depicting how poorly the FedAvg algorithm can be for aligning heterogeneous clients, in comparison with the FL Bayesian framework [164]. Frederico Vicente et al. Page 70 of 63 [PITH_FULL_IMAGE:figures/full_fig_…

**Figure 21.** Figure 21: An architectural overview of the modular options for building an FL framework is presented. The + operator indicates the possibility of stacking modules, while the | operator represents a modular design choice. Although we aimed to cover many modular possibilities in …

**Figure 22.** Figure 22: Standard Machine Learning Application life-cycle. Deployment Machine Learning pipelines, normally, have 3 main phases: 1. Data Management; 2. Model Training; 3. Model Deployment. To make the pipeline robust, the introduction of a cycle comes naturally with the help of…

**Figure 23.** Figure 23: According to Wu et al. [291], Federated Learning can have considerable CO2 emissions (carbon footprint), when compared with standard centralised Large Models training. Frederico Vicente et al. Page 72 of 63 [PITH_FULL_IMAGE:figures/full_fig_p072_23.png]

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