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REVIEW 5 major objections 5 minor 35 references

Multimodal Online Federated Learning with Modality Missing in Internet of Things

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

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Pith's one-line read This paper shows that missing modalities in multimodal online federated learning enlarge the regret bound from $O(\sqrt{T})$ to $O(\sqrt{T}+T(1-\beta))$, and that prototype substitution can offset the loss in practice.

desk verdict New problem setting and a plausible prototype-based fix, but Theorem 3's off-by-one definition of the missing-modality ratio breaks the claimed no-missing limit, and the experiments are too thin to support the 'beats FM' claim. read the letter →

arxiv 2505.16138 v1 pith:6AJRKBVQ submitted 2025-05-22 cs.LG cs.DC

Heqiang Wang , Xiang Liu , Xiaoxiong Zhong , Lixing Chen , Fangming Liu , Weizhe Zhang This is my paper · ORCID
classification cs.LGcs.DC MSC 68T05
keywords multimodalfederatedlearningonlinemodalitymissingprototyperegretboundinternetofthingsedgeintelligence
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 paper introduces Multimodal Online Federated Learning (MMO-FL), a setup where edge devices in the Internet of Things learn on streaming multimodal data while some sensors fail and leave modalities missing. The authors' central claim is that modality missing degrades the cumulative regret bound from $O(\sqrt{T})$ to $O(\sqrt{T}+T(1-\beta))$, where $\beta$ is the minimum fraction of available modalities. To counter that degradation, they propose Prototypical Modality Mitigation (PMM), which builds persistent class-level prototypes for each modality and substitutes them for absent encoder outputs. On two multimodal datasets, PMM consistently beats the partial-modality and zero-filling baselines and, in the reported runs, surpasses the full-modality upper bound.

What carries the argument

The load-bearing object is the persistent global prototype collection: per-class, per-modality feature averages maintained across rounds. Online Prototypes Construction computes local prototypes from each client's encoder outputs and updates global prototypes via a running average; Online Prototypes Substitution replaces missing encoder outputs with the cached prototypes matched by class. The theory is carried by the availability proportion $\beta^k_t = |\mathcal{M}^k_t|/(M+1)$ and the assumption that $\beta^k_t \ge \beta$, which inserts the $(1-\beta)$ term into the regret.

What would settle it

Measure cumulative regret, not accuracy, on a convex surrogate of UCI-HAR and MVSA-Single with a fixed missing ratio $\beta<1$; if the empirical regret deviates from $O(\sqrt{T}+T(1-\beta))$ under the paper's Lipschitz and smoothness assumptions, Theorem 3's bound would be disproved.

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Extended reading notes

Core claim

The paper establishes a theoretical regret analysis for a federated online learning algorithm with multiple modality encoders and a head encoder. Under convex, Lipschitz per-round losses, the missing-modality bound contains a term $2(1-\beta)(M+1)T D K \sigma L / E$, which makes the regret $O(\sqrt{T}+T(1-\beta))$; this term vanishes only when no modality is ever missing. The proposed PMM algorithm addresses the missing-modality gap by computing local prototypes, averaging them into temporal global prototypes, forming persistent global prototypes through a running average, and replacing missing modality features with the prototype of the predicted class. The experiments show PMM compensating for missing modalities on UCI-HAR and MVSA-Single, with accuracy that improves over rounds and ultimately exceeds the full-modality setting.

Load-bearing premise

The regret bounds assume the per-round loss is convex and differentiable, while the experiments train non-convex deep CNN and LSTM encoders; if convexity is essential, the stated $O(\sqrt{T}+T(1-\beta))$ guarantee does not cover the models actually tested.

Editorial extensions

If this is right

  • If Theorem 3 is correct, any online multimodal federated algorithm that ignores missing modalities pays a term linear in $T$ unless the availability fraction $\beta$ equals 1.
  • The bound gives a concrete target for mitigation: an algorithm improves on the missing-modality baseline exactly when it effectively pushes $\beta$ toward 1.
  • With $\beta=1$, PMM's running-average prototypes reduce to the standard full-modality regret rate $O(\sqrt{T})$, so the framework subsumes ordinary MMO-FL.
  • The experiments imply that prototypes refined over rounds can carry class information across time, making them usable beyond compensation, for example as regularizers or as priors for later rounds.

Reading between the lines

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

  • A direct test the paper does not run: apply PMM to the convex losses used in Theorem 3; if the $O(\sqrt{T}+T(1-\beta))$ rate holds there, the gap between theory and the nonconvex experiments becomes the main unresolved issue.
  • If prototypes substituted for absent encoder outputs can beat full-modality training, the same mechanism may act as a regularizer; a testable extension is to use persistent prototypes as auxiliary targets in full-modality rounds and check whether head-encoder overfitting drops.
  • PMM's persistent prototypes suggest a cheap test-time fallback: for a newly deployed client with a permanently failed sensor, the server can serve class prototypes without local retraining, a deployment mode the paper does not evaluate.
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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

5 major / 5 minor

Summary. The paper introduces MMO-FL, an online federated learning framework for multimodal IoT data that explicitly handles dynamically missing modalities. It presents regret bounds for three settings: E=1 without missing modalities (Theorem 1), E>1 without missing modalities (Theorem 2), and E>1 with missing modalities (Theorem 3), where the last is claimed to be O(sqrt(T) + T(1-beta)) with beta a lower bound on the available-modality proportion. The paper then proposes PMM, which builds persistent class prototypes per modality on the server and substitutes missing modality features with these prototypes. Experiments on UCI-HAR and MVSA-Single compare PMM against full-modality, partial-modality, and zero-filling baselines, and ablate the missing rate, non-IID level, prototype quantization, and delayed prototype updates. The paper claims that PMM significantly outperforms the baselines and even exceeds the full-modality setting.

Significance. If the theoretical and experimental issues are corrected, the paper addresses a real and underexplored gap: online federated learning for streaming multimodal data with per-client, time-varying missing modalities. The regret analysis is in the standard OGD framework and the missing-modality penalty term is a useful qualitative insight. The PMM mechanism is easy to understand, and the ablations of quantized upload and delayed update address practical IoT constraints. However, the current form has several load-bearing problems: an off-by-one definition of the missing-modality ratio, a label-dependent prototype substitution rule that appears to leak label information, and an evaluation protocol that does not match the theoretical setting and lacks state-of-the-art baselines. These issues must be resolved before the central claims can be accepted.

major comments (5)
  1. [Section V-C, Eq. (14)] The definition beta_t^k = |M_t^k|/(M+1) cannot reach 1 because M_t^k contains at most the M modality encoders and excludes the head encoder. In the no-missing case beta = M/(M+1), so the term 2(1-beta)(M+1)T D K sigma L/E in Eq. (14) equals 2T D K sigma L/E and does not vanish. Therefore the statement after Theorem 3 that beta=1 corresponds to 'no modality is missing' and yields O(sqrt(T)) is not supported by the paper's own definition. Please redefine beta, for example by including the always-available head encoder in the available-set count, and re-derive the bound and the claimed rate accordingly.
  2. [Section V, Assumption 1 and Section VII-C] The regret analysis assumes that the per-round loss F_t is convex and differentiable, while the experiments use non-convex deep models: a CNN encoder and an LSTM encoder for UCI-HAR, and a four-layer CNN and a two-layer LSTM for MVSA-Single. The manuscript never states that the regret guarantees apply only to the convex case or that the experiments are not intended to verify the regret bounds. Since the abstract and conclusion claim that rigorous theoretical analysis supports the proposed approach, this mismatch should be explicitly acknowledged and the theoretical claims should be scoped to the assumptions under which they are proved.
  3. [Section VI-B, Eq. (19) and Algorithm 1, line 10] The online prototype substitution selects the prototype for the true class label c(k,n) of each sample. At inference time labels are unavailable, and using them during training leaks label information into the reconstructed features. Please clarify how OPS is applied to unlabeled test data, for example by using pseudo-labels predicted from the available modalities, and describe exactly how the reported test accuracy is computed. Without this clarification, the claim in Fig. 4 that PMM outperforms all benchmarks, including full modality, is not a valid evaluation of the algorithm's predictive performance.
  4. [Section VII-B and Section VI-A, Eq. (16)] The missing-modality simulation assumes that all clients lose the same modality in the same global rounds. In such rounds the set S_t of clients with complete modality availability is empty, so the temporal global prototype p_t,m_c in Eq. (16) is undefined because it divides by |S_t|. The paper should either define S_t per modality or explain how prototypes are updated when no client has full modality availability. It should also evaluate the per-client, time-varying missing scenario that the theoretical model actually describes.
  5. [Section VII-D and Section VII-E] The experimental comparison uses only FM, PM, and ZF baselines. The paper itself cites existing missing-modality multimodal federated learning methods ([25], [26], [34]) but does not compare against any of them, and the figures report no error bars or confidence intervals despite stating that results are averaged over 10 random runs. Please add at least one representative state-of-the-art baseline or justify why it is not applicable, and include variance information in all accuracy plots.
minor comments (5)
  1. [Section IV] The text defines T = {0,1,...,T-1}, but the rest of the paper uses t = 1,...,T; please make the round indexing consistent.
  2. [Eq. (10)] The notation E_t[.] is used in the regret definition without being defined; if it denotes an expectation over the streaming data distribution, define it at first use.
  3. [Section III] The sample notation D_t^k is introduced with size |D_t^k|, but then it is assumed that each client collects exactly N samples per round; align the notation so that the cardinality is consistently N.
  4. [Section IV, step 1] The heading 'Client - New Data Collect' is grammatically incomplete; rename it to 'Client - Data Collection'.
  5. [Section VII-B] Please state explicitly how the train/test split is performed for both datasets and report the number of test samples, since the figures only show test accuracy but no test-set description is provided.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the regret bounds are derived by standard online-gradient-descent analysis, and the PMM algorithm is validated experimentally against external benchmarks rather than fitted to its own conclusions.

full rationale

The paper's main theoretical result (Theorem 3) is a regret bound for a distributed OGD procedure with zeroed gradients on missing modalities. The bound O(sqrt(T)+T(1-beta)) follows algebraically from the gradient-update equations (13), the Lipschitz/smoothness assumptions (Assumptions 1-4), and Assumption 5, which only parameterizes the missing ratio beta_t^k=|M_t^k|/(M+1); it is not fitted to data and does not presuppose the desired regret rate. Theorems 1 and 2 are standard OGD regret bounds with an extra local-iteration term. The PMM algorithm is not part of the theorem; its effectiveness is supported by experiments comparing against Full Modality, Partial Modality, and Zero-Filling benchmarks, i.e., it is benchmarked externally rather than derived from the claim it is supposed to prove. The paper cites several prior works by its own authors ([2], [4], [17]) only as related work on streaming federated learning and online vertical FL; none of these citations is used to justify the regret bound, the convexity assumptions, or the prototype-substitution design, so they are not load-bearing self-citations. The apparent inconsistency that beta=1 is unreachable under the definition beta_t^k=|M_t^k|/(M+1) is a technical correctness issue in the interpretation of Theorem 3, not a circularity: the derivation does not assume its conclusion, it merely makes a boundary claim that does not follow from the stated definition. Overall, the derivation chain is self-contained and no circular step is present.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted to data; beta, lambda, and alpha are simulation constants. The theoretical result rests on standard OCO assumptions. No new physical or architectural entities are introduced.

assumptions (6)
  • domain assumption Assumption 1: The per-round loss function Ft is convex and differentiable.
    Standard in online convex optimization, but violated by the deep neural networks used in the experiments.
  • standard math Assumption 2: The loss function is L-Lipschitz continuous with bounded partial gradients.
    Standard regularity condition for online gradient descent regret analysis.
  • standard math Assumptions 3 and 4: Gradients are smooth with respect to model changes, and model coordinates are bounded.
    These assumptions support the E>1 regret bound, following standard OCO practice.
  • domain assumption Assumption 5: For every client and round, the available modality proportion beta_t_k is at least beta in [0,1].
    Guarantees at least one modality is present so training can continue; controls the missing-modality term in the regret bound.
  • domain assumption Each client collects exactly N samples per round, and ground-truth labels are available for prototype substitution.
    Equations 15 and 19 require labels to compute class prototypes and to select prototypes for each sample.
  • ad hoc to paper The missing-modality simulation assumes all clients lose the same modality in the same global rounds.
    Section VII-B imposes this for experimental simplicity, removing client-level heterogeneity that the framework otherwise motivates.

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Pith. "Pith review of Multimodal Online Federated Learning with Modality Missing in Internet of Things." pith.science (2026). https://pith.science/paper/6AJRKBVQ

@misc{pith2026250516138,
  author       = {Pith},
  title        = {Pith review of: Multimodal Online Federated Learning with Modality Missing in Internet of Things},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6AJRKBVQ}},
  note         = {Machine review of arXiv:2505.16138}
}
read the original abstract

The Internet of Things (IoT) ecosystem generates vast amounts of multimodal data from heterogeneous sources such as sensors, cameras, and microphones. As edge intelligence continues to evolve, IoT devices have progressed from simple data collection units to nodes capable of executing complex computational tasks. This evolution necessitates the adoption of distributed learning strategies to effectively handle multimodal data in an IoT environment. Furthermore, the real-time nature of data collection and limited local storage on edge devices in IoT call for an online learning paradigm. To address these challenges, we introduce the concept of Multimodal Online Federated Learning (MMO-FL), a novel framework designed for dynamic and decentralized multimodal learning in IoT environments. Building on this framework, we further account for the inherent instability of edge devices, which frequently results in missing modalities during the learning process. We conduct a comprehensive theoretical analysis under both complete and missing modality scenarios, providing insights into the performance degradation caused by missing modalities. To mitigate the impact of modality missing, we propose the Prototypical Modality Mitigation (PMM) algorithm, which leverages prototype learning to effectively compensate for missing modalities. Experimental results on two multimodal datasets further demonstrate the superior performance of PMM compared to benchmarks.

Figures

Figures reproduced from arXiv: 2505.16138 by the authors.

Figure 1
Figure 1. IoT-Based MMO-FL with Modality Missing While traditional MFL has primarily focused on offline settings with fixed datasets, real-world IoT applications are inherently dynamic. IoT devices operate continuously, gener￾ating streaming data in real time, which makes online learning a more realistic paradigm. Furthermore, due to the instability arXiv:2505.16138v1 [cs.LG] 22 May 2025 [PITH_FULL_IMAGE:figures/full_fig_p00… view at source ↗
Figure 2
Figure 2. The time diagram of MMO-FL in one global round [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Illustration of PMM: Online Prototypes Construction (OPC) involves generating prototypes from continuously evolving [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Performance comparison of proposed algorithm and [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Performance comparison of proposed algorithm with [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Performance comparison of proposed algorithm with [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 8
Figure 8. Figure 8: Performance comparison of proposed algorithm with [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

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