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REVIEW 6 major objections 5 minor 1 cited by

Ten Challenging Problems in Federated Foundation Models

T0 review · 6 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A single weighted-loss equation unifies the ten hard problems of federated foundation models, the paper argues.

desk verdict Useful FedFM taxonomy undermined by a unified equation that misrepresents its own per-problem formulations. read the letter →

arxiv 2502.12176 v1 pith:IPTAIWPG submitted 2025-02-14 cs.LG cs.AI

Tao Fan , Hanlin Gu , Xuemei Cao , Chee Seng Chan , Qian Chen , Yiqiang Chen , Yihui Feng , Yang Gu
show 25 more authors
Jiaxiang Geng Bing Luo Shuoling Liu Win Kent Ong Chao Ren Jiaqi Shao Chuan Sun Xiaoli Tang Hong Xi Tae Yongxin Tong Shuyue Wei Fan Wu Wei Xi Mingcong Xu He Yang Xin Yang Jiangpeng Yan Hao Yu Han Yu Teng Zhang Yifei Zhang Xiaojin Zhang Zhenzhe Zheng Lixin Fan Qiang Yang
This is my paper · ORCID
classification cs.LGcs.AI
keywords federatedfoundationmodelslearningmulti-objectiveoptimizationprivacy-utilitytrade-offmachineunlearningmodelwatermarkingcontributionevaluation
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 identifies ten open problems that block practical Federated Foundation Models (FedFMs), systems in which a large server-side foundation model and many small client-side domain models train together without sharing raw data. For each problem it states an optimization objective, reviews existing methods, and lists open challenges. The paper's central claim is that all ten problems can be written as one weighted objective over five losses — utility, efficiency, watermark, contribution, and privacy — subject to a no-free-lunch constraint. If that unification holds, algorithm design for FedFMs becomes a single multi-objective optimization problem, and progress on one problem can be compared against the others in common terms. The paper also asserts that this is the first mathematical treatment of the FedFM problem set.

What carries the argument

The unifying object is Eq. (17), a five-term weighted objective with a no-free-lunch constraint. Each term is a loss evaluated on the server model, client models, client actions, aggregation mechanism, contribution evaluation mechanism, the sequence of tasks, and graph data; the five weights are nonnegative and sum to 1. The machinery works by coefficient selection: setting one weight to 1 collapses the general objective into the specific formulation of one of the ten problems, so the same equation serves both as a common framework and as a generator of individual problem statements.

What would settle it

Train two FedFM systems to identical final model weights using different numbers of communication rounds or different aggregation randomness, then measure membership-inference or gradient-inversion leakage on the same target client. If leakage differs while the model weights and local data are the same, privacy loss is not a function of weights and data alone, and the unified objective cannot faithfully represent the privacy constraints it claims to encode.

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Extended reading notes

Core claim

The paper's central claim is Eq. (17): minimize, over the server model, client models, client actions, aggregation mechanism, and contribution evaluation mechanism, a weighted sum of five loss terms — utility loss, efficiency loss, watermark loss, contribution loss, and privacy loss — subject to the constraint that the sum of utility, privacy, and efficiency losses is strictly positive. By setting one weight to 1 and the others to 0, the equation is claimed to recover the individual problems: utility-only covers private data utilization, continual learning, Non-IID and graph data, bidirectional knowledge transfer, and game mechanisms; efficiency-only covers Problem 10; watermark-only covers Problem 9; contribution-only covers Problem 7; privacy-only covers unlearning; and the constraint encodes the foundational-theory trade-off of Problem 1. The paper presents this as the first unified mathematical formulation of the key problems of FedFMs.

Load-bearing premise

The unified objective treats privacy loss as a fixed function of the model weights and the local dataset, but in real federated systems privacy leakage also depends on the training algorithm, the number of communication rounds, the adversary's prior knowledge, and randomness — none of which appear as variables in Eq. (17).

Editorial extensions

If this is right

  • If Eq. (17) is accepted, FedFM research can be organized as a single multi-objective optimization, with each of the ten problems a special case obtained by choosing weights.
  • The no-free-lunch constraint makes explicit that utility, privacy, and efficiency cannot all be minimized simultaneously, so every FedFM design must state which trade-off it accepts.
  • Problems 2, 3, 5, 6, and 8 are claimed to share the utility-loss term, meaning methods for private-data utilization, continual learning, Non-IID and graph learning, bidirectional transfer, and game mechanisms can be evaluated within one utility objective.
  • The framework folds incentive design (contribution loss) and security (watermark and privacy losses) into the training objective itself, making fairness and protection part of optimization rather than post-hoc add-ons.
  • The per-problem formulations in Eqs. (1) through (16) give concrete objective functions that future FedFM algorithms can instantiate, compare, and test against.

Reading between the lines

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

  • If the unification is taken literally, an immediate test is whether real FedFM systems admit a single set of weights that reproduces observed trade-offs; the paper does not propose how to choose those weights, so weight selection becomes a key open design problem.
  • A consequence the authors leave implicit is that the same equation could serve as a benchmark generator: each problem's objective can be turned into a synthetic task suite where methods are scored by how much they reduce the corresponding term without inflating the others.
  • Because the privacy term is written as a function of weights and local data alone, the framework will likely need an extended version that conditions privacy loss on communication rounds, randomness, and adversary knowledge — a natural next step beyond the paper.
  • The five-loss structure connects naturally to multi-objective federated learning formalizations, and the no-free-lunch constraint could be sharpened into concrete information-theoretic bounds if privacy loss were replaced by a mutual-information or differential-privacy based quantity.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

6 major / 5 minor

Summary. This manuscript is a survey/position paper on federated foundation models (FedFMs). It identifies ten problems—foundational theory, private data utilization, continual learning, unlearning, Non-IID/graph data, bidirectional knowledge transfer, incentive and contribution evaluation, game mechanisms, model watermarking, and efficiency—and organizes them under five themes. For each problem it gives a short optimization formulation (Eqs. (1)–(16)), reviews representative methods, and lists challenges and potential solutions. Section XII then proposes Eq. (17) as a single weighted objective over utility, efficiency, watermark, contribution, and privacy losses, and claims that this is the first mathematical perspective unifying all ten problems. The per-problem formulations and the survey material are the paper's main content.

Significance. The survey is timely and useful as a map of a rapidly growing area: it assembles a large reference set, compares against existing reviews in Table II, and attempts to give each of the ten challenges a crisp mathematical statement. If Eq. (17) were a faithful unification, it would provide a valuable common formalism for reasoning about trade-offs across privacy, utility, efficiency, watermarking, and contribution. However, the central unification claim is not supported by the equations as written: several per-problem formulations are informal or inconsistent, and Eq. (17) drops the privacy thresholds and mislabels Problem 4. The value of the manuscript lies mainly in its taxonomy and literature coverage; the mathematical contributions need substantial revision before they can serve as a foundation.

major comments (6)
  1. [Section XII, Eq. (17)] The unified equation does not subsume the privacy-constrained problems it claims to cover. In Eqs. (4), (9), and (16), privacy appears as a hard constraint ℓ_{p,k}(w) < δ_k, while Eq. (17) contains no δ_k and places ℓ_{p,k} only in the weighted objective. A weighted objective term cannot enforce a hard constraint without an explicit constraint set, so the reductions α1=1 and α5=1 do not reproduce Problems 2, 5, or 10. The additional claim that α5=1 'optimizes the privacy loss (i.e., problem 4)' is also incorrect: Problem 4 is defined in Eq. (7) as minimizing dist(w_un, w_re), with no ℓ_p term in the objective. The mapping from Eq. (17) to Problem 8 is likewise unexplained, since Eq. (12) is a utility maximization rather than a utility-loss minimization. Until these reductions are actually carried out, the 'first mathematical perspective' claim in Section XII is unsupported.
  2. [Section XII, Eq. (17)] Eq. (17) is not a well-defined optimization program. The minimization is over wg, {a_k}, F, and C, where F is an aggregation mechanism and C a contribution evaluation mechanism; these are function-valued objects, and no function space, feasible set, or regularity condition is given for them. The notation F_{k∈[K],t∈[T]} appearing before the objective is undefined, and the loss terms are written with arguments (ws, wk, ak, C, {D_t^k}, G) even though C is simultaneously an optimization variable and an argument of the losses. A reader cannot evaluate, solve, or instantiate Eq. (17) for any of the ten problems.
  3. [Section II-A, Eq. (1)] The 'no free lunch' constraint ℓu(w)+ℓp(w)+ℓe(w)>0 is trivial for any nonnegative loss functions and therefore does not express the privacy-utility-efficiency trade-off the text describes. A trade-off requires either a lower bound relating the three losses, as in Eq. (2), or a Pareto-front characterization. The same trivial inequality is reused as the constraint in Eq. (17), so the foundational-theory Problem 1 is not captured by the unified equation.
  4. [Section VIII-A, Eq. (11)] The contribution-evaluation objective depends on an Oracle that knows the true contribution C*_k for each client. Such ground-truth contributions are unobservable in any real federated system, and the manuscript does not define C*_k or explain how existing schemes (Shapley value, leave-one-out, least core) relate to it. As written, Eq. (11) turns contribution evaluation into supervised regression against an unknown target, which cannot be computed or verified. The formulation needs either an operational definition of C*_k or a restatement in terms of the fairness properties that contribution evaluation is meant to satisfy.
  5. [Section IX-A, Eqs. (12)–(14)] The game-mechanism formulation is internally inconsistent. The text writes that attackers minimize their utility Uatt, but in a defense game an attacker should be maximizing its own utility subject to costs; the equilibrium condition in Eq. (13) is the standard Nash condition U_k(a*_k,a*_-k) ≥ U_k(a_k,a*_-k), which presupposes maximization. The subsequently 'unified' objective in Eq. (14), max Σ_k U_k & min Σ_k Cost_k, also leaves the trade-off between utility and cost unspecified, and it does not follow from the two preceding displayed objectives. Problem 8 therefore lacks a coherent mathematical statement, and Eq. (17) cannot inherit one from it.
  6. [Throughout, Eqs. (1), (4), (9), (16), (17)] Privacy loss is treated throughout as a deterministic function ℓ_{p,k}(w, D_k) of the model and local data. In real federated systems, privacy leakage depends on the training algorithm, the number of communication rounds, the adversary's prior knowledge, and the randomness of the mechanism. Because Eq. (17) and the per-problem formulations do not include these variables, the unified framework cannot faithfully represent privacy guarantees such as differential privacy or membership-inference risk. A formal treatment should either define ℓ_{p,k} through a specific privacy mechanism or state explicitly that the formulation abstracts away from mechanism-dependent leakage.
minor comments (5)
  1. [Section X-A, Eq. (15)] The notation min_w F_{k=0,1,...,K} αℓu,k(ws)+... is ambiguous: F appears both as an aggregation mechanism and as part of the minimization expression, and the relationship between the outer weight α and the stated constraint α+β+γ=1 is unclear. Please rewrite with explicit aggregation and separate index notation.
  2. [Section VIII-A, Eq. (11)] In Eq. (11), k is used both for the client on the left-hand side and as the summation index on the right-hand side; the sum should run over a different index (e.g., Σ_{j=1}^K ||C(ws,D_j)-C*_j||²). The current notation also defines ℓc,k as a global sum rather than a per-client loss, which conflicts with the surrounding text.
  3. [Section IV-A, Eq. (5)] In Eq. (5), the old-task arguments are written as {D^t_k}_{t=1}^T inside ℓu,k(wg, {D^t_k}_{t=1}^T), but the aggregation F then takes a comma-separated list of old-task and new-task losses. The syntax suggests two different function types and should be made uniform.
  4. [Section VII-A, Settings 2 and 3] The server-side loss is written as ℓu,s(ws|wk,Dp) in one line and as ℓu,k(ws|wk,Dp) in the adjacent displays; the subscripts should be standardized to avoid confusion between the server and client indices.
  5. [Throughout] There are numerous typos and inconsistent terms: 'mechanishm' in Eqs. (6), (8), and (9), 'receptively' in Eq. (15), 'Tand' in Section IV-A, 'How to to improve' in the Problem 10 heading, and 'foundation theory' versus 'foundational theory' are used interchangeably. A careful copy-edit is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Section XII's Eq. (17) is a stated synthesis of the paper's own per-problem formulations, not an independent derivation, and the internal inconsistencies flagged by the skeptic are correctness concerns rather than circular reductions.

full rationale

This is a survey/position paper rather than a derivation of new empirical predictions. Each of the ten problems is formulated independently in Sections II-XI and grounded in the cited literature (e.g., FedAvg [112], the no-free-lunch trade-off [108], FedIPR [92], FedMKT [64]). Section XII then writes Eq. (17) as a weighted sum of the same loss symbols (ell_u, ell_e, ell_m, ell_c, ell_p) and asserts that setting one alpha_i to 1 reduces the equation to one of the earlier problems. That assertion is a synthesis claim, not a fitted parameter or a theorem derived from external constraints. The skeptical objection that Eq. (17) drops the delta_k privacy constraints and mislabels Problem 4 (unlearning, Eq. (7)) as "privacy loss" is an internal-consistency/correctness problem with the claimed unification; it does not make the unification circular, because Eq. (17) is not being used to predict or derive the per-problem results. The self-citations to [108], [64], [92], [111], etc. are used as literature grounding, not as a load-bearing uniqueness argument, and the no-free-lunch constraint in Eqs. (1) and (17) is attributed to an external peer-reviewed theorem rather than assumed into existence by this paper. Accordingly, no step satisfies the standard of "Eq. X = Eq. Y by construction" or "fitted parameter renamed as prediction." The strongest claim of being the "first" mathematical perspective is a novelty assertion that may be contestable on scope or correctness, but it is not circular.

Assumptions & free parameters 2 free parameters · 3 assumptions · 1 invented entities

The paper's central contribution is a set of formal optimization objectives. The free parameters are the weights and thresholds that tune the objectives. The axioms are the background assumptions needed for the unified equation to be meaningful, including the no-free-lunch constraint and the reduction of all ten problems to loss functions. The Oracle is the only invented entity, and it lacks an operational grounding.

free parameters (2)
  • weights α, β, γ and α1..α5
    Hand-chosen coefficients in Eqs. (1), (15), (16), and (17) that balance privacy, utility, efficiency, watermark, and contribution losses. They are not derived from data.
  • privacy thresholds δ_k
    User-specified bounds on privacy loss in Eqs. (4), (9), (15), and (16). No method to set them is provided.
assumptions (3)
  • standard math The 'no free lunch' trade-off: ℓu + ℓp + ℓe > 0, borrowed from Zhang et al. [108].
    Invoked as the constraint in Eq. (1) and Eq. (17) to justify that privacy, utility, and efficiency cannot all be minimized. It is cited, not proven in this paper.
  • ad hoc to paper All ten challenges are representable as minimization of additive loss terms over model weights through an aggregation mechanism F.
    The whole framework assumes that problems such as unlearning and game mechanisms can be captured by loss functions ℓ_u, ℓ_p, ℓ_e, ℓ_c, ℓ_m, as done in Eq. (17). This is the paper's own modeling choice.
  • domain assumption Privacy loss ℓ_{p,k}(w, Dk) is a deterministic function of the model and data.
    Equations (1), (4), (9), (16), (17) treat privacy leakage as a function of w and Dk, ignoring the dependence on the training algorithm, the number of rounds, and the adversary's prior knowledge.
invented entities (1)
  • Oracle true contribution C*_k
    purpose: A hypothetical ground-truth value for each client's data contribution in Eq. (11), used to define the objective of contribution evaluation.
    The Oracle is not measurable in practice; the paper provides no way to obtain C*_k, so the optimization target in Eq. (11) is not directly operational.

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Cite this review

Pith. "Pith review of Ten Challenging Problems in Federated Foundation Models." pith.science (2026). https://pith.science/paper/IPTAIWPG

@misc{pith2026250212176,
  author       = {Pith},
  title        = {Pith review of: Ten Challenging Problems in Federated Foundation Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IPTAIWPG}},
  note         = {Machine review of arXiv:2502.12176}
}
read the original abstract

Federated Foundation Models (FedFMs) represent a distributed learning paradigm that fuses general competences of foundation models as well as privacy-preserving capabilities of federated learning. This combination allows the large foundation models and the small local domain models at the remote clients to learn from each other in a teacher-student learning setting. This paper provides a comprehensive summary of the ten challenging problems inherent in FedFMs, encompassing foundational theory, utilization of private data, continual learning, unlearning, Non-IID and graph data, bidirectional knowledge transfer, incentive mechanism design, game mechanism design, model watermarking, and efficiency. The ten challenging problems manifest in five pivotal aspects: ``Foundational Theory," which aims to establish a coherent and unifying theoretical framework for FedFMs. ``Data," addressing the difficulties in leveraging domain-specific knowledge from private data while maintaining privacy; ``Heterogeneity," examining variations in data, model, and computational resources across clients; ``Security and Privacy," focusing on defenses against malicious attacks and model theft; and ``Efficiency," highlighting the need for improvements in training, communication, and parameter efficiency. For each problem, we offer a clear mathematical definition on the objective function, analyze existing methods, and discuss the key challenges and potential solutions. This in-depth exploration aims to advance the theoretical foundations of FedFMs, guide practical implementations, and inspire future research to overcome these obstacles, thereby enabling the robust, efficient, and privacy-preserving FedFMs in various real-world applications.

Figures

Figures reproduced from arXiv: 2502.12176 by the authors.

Figure 1
Figure 1. An illustration of Federated Foundation Models [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. This surface effectively identifies solutions that achieve [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FedFMs utilize locally stored private data from orga [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: An illustration of Continual Learning with FedFMs. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Machine Unlearning in FedFMs. B. Existing Methods We summarize the four key aspects of the FU process: un￾learning targets, unlearning executors, unlearning verification, and unlearning principles. 1) Unlearning Targets Unlearning requests are typically classified into…
Figure 6
Figure 6. Figure 6: FedFMs with Graphs and Graphs of FedFMs. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Illustration of the three settings for bidirectional [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Contribution Evaluation across Medical Institutions. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Illustration of FedFMs Game Mechanism Design. [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Illustration of watermarking methods in FedFMs. [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Summary of Efficiency in FedFMs condensing lengthy prompts or learning compact representa￾tions of prompts [206]. 2) Model-oriented Methods Model-oriented methods focus on reducing the sizes and the number of arithmetic operations of FMs, i.e., model compression. Quan…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.