arxiv: 2605.04827 · v2 · submitted 2026-05-06 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

Trustworthy Federated Label Distribution Learning under Annotation Quality Disparity

Junxiang Wu , Zhiqiang Kou , Hongwei Zeng , Wenke Huang , Biao Liu , Hanlin Gu , Yuheng Jia , Di Jiang

show 3 more authors

Yang Liu Xin Geng Qiang Yang

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:18 UTC · model grok-4.3

classification 💻 cs.LG

keywords Federated Label Distribution LearningAnnotation Quality DisparityClient CalibrationReliability-aware AggregationHeterogeneous SupervisionTrustworthy Federated Learning

0 comments

The pith

In federated label distribution learning with varying annotation quality, client-specific calibration is strictly better than any uniform calibration.

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

The paper shows that when clients in a federated system have different levels of annotation quality for label distributions, adapting training to each client's quality level leads to better overall models than using one calibration rule for all. This addresses the issue that standard aggregation methods like FedAvg break down when some clients provide less reliable updates due to noisier labels. By introducing a global semantic anchor for calibration and reweighting contributions based on reliable information, the approach maintains privacy while handling quality disparities. It includes new benchmarks to evaluate such settings and a theoretical proof of the superiority of tailored calibration.

Core claim

We propose FedQual, a quality-aware Fed-LDL framework with quality-adaptive client training guided by a global semantic anchor and reliability-aware server aggregation. We provide a theoretical guarantee showing that under heterogeneous supervision quality, client-specific calibration is strictly better than any uniform calibration. We construct four new Fed-LDL benchmarks with controlled annotation quality disparity.

What carries the argument

Quality-adaptive client training guided by a global semantic anchor that calibrates low-quality clients while preserving high-quality autonomy, paired with reliability-aware server aggregation that reweights by effective reliable information instead of sample size.

If this is right

Local model updates from low-quality clients become more reliable through targeted calibration without affecting high-quality clients.
Server aggregation prioritizes clients with more effective reliable information, improving global model quality.
Standard sample-size-based methods like FedAvg are outperformed in heterogeneous quality scenarios.
The theoretical result implies that uniform approaches cannot achieve optimal performance when quality varies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This suggests that in real deployments, identifying a shared semantic structure could help bootstrap quality improvement across clients.
Applications in domains with varying expert annotation qualities could retain more data without forcing uniform standards.
Dynamic quality estimation that updates as the model trains might reduce reliance on fixed anchors.

Load-bearing premise

A usable global semantic anchor exists that can calibrate low-quality clients while preserving high-quality autonomy, and that effective reliable information per client can be quantified without circular dependence on the final model performance.

What would settle it

Observing on one of the new benchmarks that a uniform calibration strategy matches or exceeds the performance of client-specific calibration would contradict the theoretical guarantee.

Figures

Figures reproduced from arXiv: 2605.04827 by Biao Liu, Di Jiang, Hanlin Gu, Hongwei Zeng, Junxiang Wu, Qiang Yang, Wenke Huang, Xin Geng, Yang Liu, Yuheng Jia, Zhiqiang Kou.

**Figure 1.** Figure 1: Illustration of the Federated Label Distribution Learning (Fed-LDL) framework and its inherent challenges. (a) The Fed-LDL Workflow: Clients with varying levels of reliability (e.g., top-tier hospitals vs. community clinics) locally optimize LDL models based on their private datasets, which exhibit diverse label distributions. (b) Core Challenges. Challenge I (Quality-Agnostic Aggregation): The server aggr… view at source ↗

**Figure 2.** Figure 2: Overview of our Fed-LDL benchmarks. (a) 10-expert ensemble annotation and label-distribution construction, yielding the latent ground-truth distribution dGT . (b) Dataset statistics, including dataset scale and aggregated label-distribution profiles for FER-LDL, FI-LDL, KADID-LDL, and PIPAL-LDL. (c) A qualitative emotion-recognition example with an 8-class distribution, illustrating cognitive ambiguity. (d… view at source ↗

**Figure 3.** Figure 3: Robustness analysis against Annotation Quality Heterogeneity. (a) Sensitivity to Noise Intensity: The impact of varying the quality indicator qm ∈ {5, 6, 7, 8} on the four benchmarks. The flat curves indicate that FedQual maintains high performance regardless of the local noise variance. (b) Impact of Noisy Client Ratio: Performance comparison under different ratios of lowquality clients (ρnoise ∈ {0.25,… view at source ↗

**Figure 4.** Figure 4: Sensitivity analysis of the label distribution skew parameter γ on the FER-LDL benchmark. We evaluate the performance across varying skew levels γ ∈ {0.25, 0.5, 0.75, 1.0}. The results across six metrics demonstrate that our proposed FedQual framework remains robust to different degrees of label distribution skew. performance across all six evaluation metrics, regardless of the label density. These resul… view at source ↗

**Figure 5.** Figure 5: Impact of partition label multiplicity (Top-K) on FERLDL. We vary the Top-K parameter (K ∈ {1, 2, 3, 4}) used to discretize dGT for simulating Non-IID feature skew. The flat trends across all six metrics demonstrate that FedQual maintains robust performance regardless of the label density used for client partitioning. is robust to variations in label multiplicity and effectively adapts to diverse label co… view at source ↗

read the original abstract

Label Distribution Learning (LDL) models supervision as an instance-wise probability distribution, enabling fine-grained learning under inherent ambiguity, but its success relies on high-fidelity label distributions that are costly to obtain and thus often noisy. Motivated by privacy-sensitive applications, we study Federated Label Distribution Learning (Fed-LDL), where data isolation further induces heterogeneous annotation quality across clients, making local updates unevenly reliable and breaking sample-size-based aggregation (e.g., FedAvg). To address this trust dilemma, we propose FedQual, a quality-aware Fed-LDL framework with two coupled mechanisms: (i) quality-adaptive client training guided by a global semantic anchor that calibrates low-quality clients while preserving high-quality autonomy, and (ii) reliability-aware server aggregation that reweights client contributions by effective reliable information rather than raw sample size. To enable rigorous evaluation, we construct four new Fed-LDL benchmarks (FER-LDL, FI-LDL, PIPAL-LDL, and KADID-LDL) with controlled annotation quality disparity. We further provide a theoretical guarantee showing that under heterogeneous supervision quality, client-specific calibration is strictly better than any uniform calibration. Extensive experiments on the proposed benchmarks demonstrate the effectiveness of FedQual.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

FedQual brings a global semantic anchor plus reliability reweighting to federated LDL with quality disparity, plus four new controlled benchmarks and a calibration theorem, but the proof's independence from model-dependent weights needs verification.

read the letter

The core of this paper is FedQual, which adds two linked pieces to federated label distribution learning: a global semantic anchor that steers low-quality clients during local training while leaving high-quality ones alone, and a server-side aggregation step that weights clients by their effective reliable information instead of sample count. They back this with four new benchmarks (FER-LDL, FI-LDL, PIPAL-LDL, KADID-LDL) built to have explicit quality gaps, and they claim a theorem that client-specific calibration strictly outperforms uniform calibration when supervision quality varies across clients.

Referee Report

1 major / 2 minor

Summary. The paper introduces FedQual, a quality-aware framework for Federated Label Distribution Learning (Fed-LDL) under heterogeneous annotation quality. It couples a global semantic anchor for client-specific calibration (preserving high-quality client autonomy) with reliability-aware server aggregation that reweights contributions by effective reliable information rather than sample size. Four new benchmarks (FER-LDL, FI-LDL, PIPAL-LDL, KADID-LDL) with controlled quality disparity are constructed, a theoretical guarantee is provided that client-specific calibration is strictly superior to any uniform calibration under heterogeneous supervision, and experiments demonstrate effectiveness.

Significance. If the central theoretical claim holds without circular dependence, the work meaningfully advances trustworthy federated learning for label-distribution tasks by replacing sample-size aggregation with quality-aware mechanisms and supplying both a strict superiority result and new evaluation benchmarks. These elements would be useful for privacy-sensitive applications where annotation quality varies.

major comments (1)

[Theoretical Analysis] The theoretical guarantee (abstract and theoretical analysis section) asserts strict superiority of client-specific calibration over uniform calibration under heterogeneous quality, relying on the global semantic anchor providing an independent high-fidelity reference. However, the anchor is constructed from aggregated client updates whose reliability weights are defined in terms of effective reliable information (itself model-dependent). This introduces a potential circularity that could violate the independence assumption required for the strict inequality; the proof should explicitly derive or assume non-circularity of the anchor construction.

minor comments (2)

[Benchmark Construction] The description of how controlled annotation quality disparity is injected into the four new benchmarks would benefit from additional implementation details to support reproducibility.
[Preliminaries and Method] Notation for 'effective reliable information' and the precise definition of the global semantic anchor should be introduced earlier and used consistently to improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and insightful feedback on our manuscript. We address the major comment regarding the theoretical analysis below. We agree that greater clarity is needed on the independence assumptions and will revise accordingly.

read point-by-point responses

Referee: [Theoretical Analysis] The theoretical guarantee (abstract and theoretical analysis section) asserts strict superiority of client-specific calibration over uniform calibration under heterogeneous quality, relying on the global semantic anchor providing an independent high-fidelity reference. However, the anchor is constructed from aggregated client updates whose reliability weights are defined in terms of effective reliable information (itself model-dependent). This introduces a potential circularity that could violate the independence assumption required for the strict inequality; the proof should explicitly derive or assume non-circularity of the anchor construction.

Authors: We thank the referee for identifying this important point on potential circularity. The theoretical result shows that, under heterogeneous supervision, client-specific calibration (guided by the anchor) is strictly superior to any uniform calibration because it preserves autonomy for high-quality clients while correcting low-quality ones. The proof treats the global semantic anchor as an independent high-fidelity reference whose construction is separate from the per-client calibration step being analyzed. In the algorithm the anchor is formed via reliability-weighted aggregation, where weights reflect effective reliable information derived from divergence to the current anchor; however, the superiority inequality is derived conditionally on the anchor already being fixed and of higher average fidelity than the heterogeneous client distributions. This conditional framing avoids direct circular dependence in the mathematical argument. That said, we acknowledge the referee's concern that the iterative nature of anchor construction could be stated more explicitly to rule out any implicit dependence. In the revised manuscript we will (i) add an explicit assumption statement in the theoretical analysis section that the anchor is independent of the calibrated client models for the purpose of the inequality, (ii) provide a short derivation showing that the reliability weights are computed from the pre-calibration models and therefore do not create a feedback loop within the proof, and (iii) include a brief remark on how the iterative procedure converges to a stable anchor without violating the strict inequality. These changes will strengthen the rigor of the theoretical contribution without altering its core claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; theoretical guarantee presented as independent

full rationale

The abstract and description outline a theoretical guarantee that client-specific calibration is strictly better than uniform calibration under heterogeneous supervision quality. No equations, self-citations, or derivations are visible that reduce this claim by construction to fitted parameters, self-definitions, or load-bearing self-citations. Reliability-aware aggregation and the global semantic anchor are described as mechanisms to address the problem, but without exhibited reduction to inputs (e.g., no shown equivalence like reliability weight = model performance by definition), the derivation chain remains self-contained against external benchmarks. This is the expected honest non-finding for papers without load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on the existence of a usable global semantic anchor and a quantifiable measure of reliable information per client; these are introduced by the paper rather than derived from prior results.

axioms (2)

domain assumption A global semantic anchor can be maintained that calibrates low-quality clients while preserving high-quality autonomy
Invoked in the quality-adaptive client training mechanism described in the abstract.
domain assumption Effective reliable information contributed by each client can be measured independently of final model performance
Basis for the reliability-aware server aggregation.

invented entities (1)

FedQual framework no independent evidence
purpose: Quality-aware federated LDL under annotation disparity
Newly proposed method combining the two mechanisms.

pith-pipeline@v0.9.0 · 5540 in / 1473 out tokens · 53068 ms · 2026-05-12T02:18:43.652670+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 3.1 ... Jadapt < Juni ... lambda^*_m = sigma_m^2 / (sigma_m^2 + delta_m^2)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Global Semantic Anchor A(x) ≜ z(x; w^t_g) ... alpha_m = sigma(beta (lambda(q_m) - lambda_0))

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages

[1]

URL https: //doi.org/10.1109/JBHI.2021.3095128

doi: 10.1109/JBHI.2021.3095128. URL https: //doi.org/10.1109/JBHI.2021.3095128. Chen, H. and Chao, W. Fedbe: Making bayesian model ensemble applicable to federated learning. In9th Inter- national Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenRe- view.net, 2021. URL https://openreview.net/ forum?id=dgtpE6gKjH...

work page doi:10.1109/jbhi.2021.3095128 2021
[2]

URL https: //doi.org/10.1109/TPAMI.2007.70733

doi: 10.1109/TPAMI.2007.70733. URL https: //doi.org/10.1109/TPAMI.2007.70733. Goodfellow, I. J., Erhan, D., Carrier, P. L., Courville, A. C., Mirza, M., Hamner, B., Cukierski, W., Tang, Y ., Thaler, D., Lee, D., Zhou, Y ., Ramaiah, C., Feng, F., Li, R., Wang, X., Athanasakis, D., Shawe-Taylor, J., Milakov, M., Park, J., Ionescu, R. T., Popescu, M., Grozea...

work page doi:10.1109/tpami.2007.70733 2007
[4]

URL https: //doi.org/10.1609/aaai.v38i4.28095

doi: 10.1609/AAAI.V38I4.28095. URL https: //doi.org/10.1609/aaai.v38i4.28095. Li, Q., He, B., and Song, D. Model-contrastive federated learning. InIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, virtual, June 19-25, 2021, pp. 10713–10722. Computer Vision Foundation / IEEE, 2021. doi: 10.1109/CVPR46437.2021.01057. URL https: //openac...

work page doi:10.1609/aaai.v38i4.28095 2021
[5]

org/paper_files/paper/2020/hash/ 1f5fe83998a09396ebe6477d9475ba0c-Abstract

URL https://proceedings.mlsys. org/paper_files/paper/2020/hash/ 1f5fe83998a09396ebe6477d9475ba0c-Abstract. html. 10 Trustworthy Federated Label Distribution Learning under Annotation Quality Disparity Li, X., Liang, X., Luo, G., Wang, W., Wang, K., and Li, S. ULTRA: uncertainty-aware label distribution learn- ing for breast tumor cellularity assessment. I...

work page doi:10.1007/978-3-031-16437-8_29 2020
[6]

Ren, T., Jia, X., Li, W., and Zhao, S

URL http://proceedings.mlr.press/ v54/mcmahan17a.html. Ren, T., Jia, X., Li, W., and Zhao, S. Label distribu- tion learning with label correlations via low-rank ap- proximation. In Kraus, S. (ed.),Proceedings of the Twenty-Eighth International Joint Conference on Ar- tificial Intelligence, IJCAI 2019, Macao, China, Au- gust 10-16, 2019, pp. 3325–3331. ijc...

work page doi:10.24963/ijcai.2019/461 2019
[7]

2022/168

URL https://doi.org/10.24963/ijcai. 2017/443. Xu, N., Liu, Y ., and Geng, X. Label enhancement for label distribution learning.IEEE Trans. Knowl. Data Eng., 33(4):1632–1643, 2021. doi: 10.1109/ TKDE.2019.2947040. URL https://doi.org/10. 1109/TKDE.2019.2947040. Xu, S., Shang, L., Shen, F., Yang, X., and Pedrycz, W. Incomplete label distribution learning vi...

work page doi:10.24963/ijcai 2017
[8]

However, these approaches generally target discrete categorical noise

introduces an end-to-end framework for noisy label correction, while FedES (Zeng et al., 2024) utilizes federated early-stopping to prevent models from memorizing noisy patterns. However, these approaches generally target discrete categorical noise. They typically treat noise as binary errors, making them ill-equipped for tasks requiring dense, continuous...

work page 2024
[9]

employ low-rank approximation to model these dependencies, while others (Xu & Zhou, 2017; Xu et al., 2025) utilize correlation decomposition mechanisms to effectively complete missing label information in sparse distribution settings. Despite their effectiveness, these remediation strategies predominantly rely on a centralized data access assumption, wher...

work page 2017
[10]

The original annotations define eight emotion categories based on Mikels’ psychological model: Amusement, Anger, Awe, Contentment, Disgust, Excitement, Fear, and Sadness

FIThis dataset is a large-scale benchmark for affective computing which consists of over 23,000 real-world images collected from social media platforms (Flickr and Instagram) (You et al., 2016). The original annotations define eight emotion categories based on Mikels’ psychological model: Amusement, Anger, Awe, Contentment, Disgust, Excitement, Fear, and ...

work page 2016
[11]

All images are standardized to a resolution of 512×384 pixels

KADID-10kThe Konstanz Artificially Distorted Image quality Database (KADID-10k) contains 10,125 distorted images derived from 81 pristine reference images collected from Pixabay (Lin et al., 2019). All images are standardized to a resolution of 512×384 pixels. The dataset covers 25 distortion types (including blur, color shifts, and compression) across 5 ...

work page 2019
[12]

texture-like

PIPALThe Perceptual Image Processing ALgorithms (PIPAL) dataset is a large-scale IQA benchmark explicitly designed to evaluate Image Restoration (IR) algorithms (Gu et al., 2020). It contains 29,000 distorted images generated from 250 high-quality reference patches (288×288 pixels) selected from the DIV2K and Flickr2K datasets. A distinguishing feature of...

work page 2020