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arxiv: 2606.02172 · v1 · pith:R24JS2RFnew · submitted 2026-06-01 · 💻 cs.LG · cs.CV

Closing the Alignment-Maturity Gap in Federated Prototype Learning

Mario Casado-Diez , Alejandro Dopico-Castro , Ver\'onica Bol\'on-Canedo , Bertha Guijarro-Berdi\~nas This is my paper

Pith reviewed 2026-06-28 15:52 UTC · model grok-4.3

classification 💻 cs.LG cs.CV
keywords federated learningprototype learningrepresentation learningnon-IID dataalignment curriculumhypersphere geometryheterogeneous datasemi-supervised extension
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The pith

A curriculum that delays global alignment until local prototypes stabilize, paired with a hypersphere separation loss, improves federated prototype learning on heterogeneous data.

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

The paper identifies an alignment-maturity gap in which early global alignment on noisy prototypes generates large gradients that suppress local discriminative features. It introduces FedSAP to address this through a deterministic schedule that postpones alignment and a geometry-driven loss that separates classes on the unit hypersphere using the existing prototype bank. These changes produce compact, well-separated clusters while leaving the federation's communication protocol unchanged. Experiments on three benchmarks with varying heterogeneity report gains of up to four percentage points, largest under severe non-IID conditions. The same mechanisms extend directly to semi-supervised settings with minimal changes.

Core claim

The paper claims that distance-dependent gradient pressure from immature global prototypes harms local structure formation, and that a deterministic alignment curriculum combined with a proxy separation loss on the unit hypersphere closes this gap, yielding compact well-separated class clusters without additional parameters or communication cost.

What carries the argument

The alignment-maturity gap, addressed by a deterministic curriculum that delays global alignment until local representations stabilize and a geometry-driven proxy separation loss that enforces inter-class distances on the unit hypersphere using the existing prototype bank.

If this is right

  • Class clusters become compact and well-separated in the embedding space under non-IID conditions.
  • Recognition performance rises by as much as four percentage points over standard prototype baselines.
  • No modifications to the existing client-server communication protocol are required.
  • The same scheduled alignment and separation mechanisms transfer to semi-supervised federated settings with only minor adjustments.

Where Pith is reading between the lines

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

  • The curriculum principle of delaying global operations until local stability might extend to other federated representation methods that rely on shared embeddings.
  • Using only existing prototypes for separation could reduce reliance on extra regularization terms in distributed training setups.
  • Applying the same schedule in settings with concept drift might reveal whether repeated realignment remains beneficial after initial stabilization.

Load-bearing premise

That waiting for local representations to stabilize before applying global alignment will reliably stop early noisy prototypes from generating gradients that erase local discriminative structure.

What would settle it

An experiment on a high-heterogeneity benchmark in which the curriculum is applied but local representations remain unstable throughout training, with accuracy gains disappearing or reversing compared to the baseline.

Figures

Figures reproduced from arXiv: 2606.02172 by Alejandro Dopico-Castro, Bertha Guijarro-Berdi\~nas, Mario Casado-Diez, Ver\'onica Bol\'on-Canedo.

Figure 1
Figure 1. Figure 1: FedSAP architecture: a progressive alignment curriculum controls the onset of global prototype alignment, while [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Conceptual illustration of the alignment-maturity [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Accuracy convergence curves across different datasets. Performance evaluated every 5 rounds. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: t-SNE visualisation of the embeddings and prototypes (shown as stars) produced by the selected FL methods across [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: CIFAR-10 3-way test accuracy with classifier infer [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Evolution of the Silhouette score across supervised and semi-supervised phases, comparing FedProto and FedSAP [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of prototype-loss weight schedules on [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sensitivity of prototype-based inference accuracy to [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ablation study on the proxy scale parameter [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Visual trajectory of local client embeddings at Rounds 10, 50, 75, and 100, comparing FedProto (left) and FedSAP [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
read the original abstract

Learning discriminative visual representations from distributed, heterogeneous data is a fundamental challenge in Federated Learning (FL). Prototype-based methods address statistical heterogeneity by sharing class-level representations across clients but create a distance-dependent gradient pressure that is particularly severe during early training rounds: alignment pressure applied to immature global prototypes, aggregated from noisy local representations, generates large gradients that suppress the emergence of local discriminative structure. The result is a poorly organized embedding space and degraded recognition performance, particularly under severe non-IID conditions. We propose FedSAP, a framework that stabilises federated representation learning through two complementary mechanisms: a deterministic alignment curriculum that delays global alignment until local representations become stable and a geometry-driven proxy separation loss that enforces inter-class structure on the unit hypersphere using the existing prototype bank without introducing additional parameters or communication overhead. Together, these mechanisms produce compact, well-separated class clusters without altering the underlying communication protocol between federation's participants. Experiments across three benchmarks and varying degrees of heterogeneity show gains of up to 4 percentage points over the prototype-based baselines evaluated, with improvements most pronounced under high heterogeneity. The representational nature of our framework further enables a straightforward extension to semi-supervised settings, where unlabelled data is incorporated with minimal modification, underscoring the generality of scheduled alignment as a design principle.

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.

Referee Report

2 major / 2 minor

Summary. The paper introduces FedSAP for federated prototype learning to close the alignment-maturity gap, where early global alignment on immature prototypes creates distance-dependent gradients that suppress local discriminative structure. It proposes two mechanisms—a deterministic alignment curriculum delaying global alignment until local stability and a geometry-driven proxy separation loss enforcing inter-class structure on the unit hypersphere—claiming these produce compact clusters without extra parameters or communication changes. Experiments on three benchmarks under varying heterogeneity report gains of up to 4 percentage points over prototype baselines, most pronounced in high heterogeneity, with a straightforward semi-supervised extension.

Significance. If the empirical results hold with proper controls, the work offers a lightweight, communication-preserving stabilization technique for prototype-based FL that directly targets early-training instability. The parameter-free and protocol-unchanged design is a clear strength, as is the noted generality to semi-supervised settings via the scheduled alignment principle. This could inform curriculum-based designs in other heterogeneous representation learning contexts.

major comments (2)
  1. [Abstract / FedSAP mechanisms] Abstract and mechanism description: the central stabilization claim rests on the deterministic alignment curriculum reliably delaying global alignment until local representations stabilize, yet no equation, threshold, or client-specific criterion is given for determining 'stability' (e.g., no loss plateau, gradient norm, or round-based rule). This directly bears on whether the approach prevents suppression of local structure across heterogeneity levels, as a fixed deterministic rule cannot adapt to client-specific rates.
  2. [Experiments] Experiments section: the reported gains of up to 4 percentage points and the claim that improvements are 'most pronounced under high heterogeneity' lack accompanying details on baseline definitions, heterogeneity quantification (e.g., Dirichlet alpha values), number of runs, or error bars. Without these, the cross-heterogeneity comparison cannot be verified as load-bearing evidence for the two-component design.
minor comments (2)
  1. [Method] Notation for the proxy separation loss should be introduced with an explicit equation rather than descriptive text only, to allow reproduction of the geometry-driven term on the unit hypersphere.
  2. [Abstract / Method] The abstract states 'without altering the underlying communication protocol' but does not explicitly confirm in the method section that the curriculum requires zero additional messages or metadata.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our work. We respond point-by-point to the major comments below, indicating revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract / FedSAP mechanisms] Abstract and mechanism description: the central stabilization claim rests on the deterministic alignment curriculum reliably delaying global alignment until local representations stabilize, yet no equation, threshold, or client-specific criterion is given for determining 'stability' (e.g., no loss plateau, gradient norm, or round-based rule). This directly bears on whether the approach prevents suppression of local structure across heterogeneity levels, as a fixed deterministic rule cannot adapt to client-specific rates.

    Authors: We agree that the abstract and mechanism description would benefit from an explicit equation or criterion for the stability threshold. In the revised manuscript we will add the precise deterministic formulation of the alignment curriculum. The fixed, non-adaptive schedule is a deliberate design decision to preserve the original communication protocol and avoid any client-specific information exchange or additional overhead; we will also add a short discussion of this choice and its empirical behavior across heterogeneity levels. revision: yes

  2. Referee: [Experiments] Experiments section: the reported gains of up to 4 percentage points and the claim that improvements are 'most pronounced under high heterogeneity' lack accompanying details on baseline definitions, heterogeneity quantification (e.g., Dirichlet alpha values), number of runs, or error bars. Without these, the cross-heterogeneity comparison cannot be verified as load-bearing evidence for the two-component design.

    Authors: We acknowledge that the experimental details should be stated more explicitly for easy verification. The revised manuscript will expand the experimental setup subsection to list the exact Dirichlet alpha values used for each heterogeneity regime, the precise baseline implementations, the number of independent runs, and confirmation that standard deviations are reported as error bars in all tables and figures. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on experimental evaluation without derivations or self-referential reductions

full rationale

The paper introduces FedSAP via two mechanisms (deterministic alignment curriculum and geometry-driven separation loss) and reports empirical gains of up to 4 points on three benchmarks under varying heterogeneity. No equations, derivations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the provided text. The central claims are justified by experimental outcomes rather than reducing to inputs by construction, satisfying the default expectation of no significant circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the framework reuses the existing prototype bank and standard FL communication.

pith-pipeline@v0.9.1-grok · 5773 in / 1073 out tokens · 20543 ms · 2026-06-28T15:52:53.251694+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

28 extracted references · 6 canonical work pages · 1 internal anchor

  1. [1]

    Pseudo-labeling and confirmation bias in deep semi-supervised learning

    Eric Arazo, Diego Ortego, Paul Albert, Noel E O’Connor, and Kevin McGuinness. Pseudo-labeling and confirmation bias in deep semi-supervised learning. In 2020 International joint conference on neural networks (IJCNN), pages 1–8. IEEE, 2020

    2020

  2. [2]

    Leaf: A benchmark for federated settings,

    Sebastian Caldas, Sai Meher Karthik Duddu, Peter Wu, Tian Li, Jakub Koneˇcn`y, H Brendan McMahan, Virginia Smith, and Ameet Talwalkar. Leaf: A benchmark for fed- erated settings.arXiv preprint arXiv:1812.01097, 2018

    work page arXiv 2018

  3. [3]

    Exploiting shared representations for personalized federated learning

    Liam Collins, Hamed Hassani, Aryan Mokhtari, and Sanjay Shakkottai. Exploiting shared representations for personalized federated learning. InInternational Confer- ence on Machine Learning (ICML). PMLR, 2021

    2021

  4. [4]

    Tackling data heterogeneity in federated learning with class prototypes

    Yutong Dai, Zeyuan Chen, Junnan Li, Shelby Heinecke, Lichao Sun, and Ran Xu. Tackling data heterogeneity in federated learning with class prototypes. InProceed- ings of the AAAI Conference on Artificial Intelligence, volume 37, pages 7314–7322, 2023

    2023

  5. [5]

    Adaptive personalized federated learning

    Yuyang Deng, Mohammad Mahdi Kamani, and Mehrdad Mahdavi. Adaptive personalized federated learning. arXiv preprint arXiv:2003.13461, 2020

    work page arXiv 2003

  6. [6]

    Semifl: Semi- supervised federated learning for unlabeled clients with alternate training

    Enmao Diao, Jie Ding, and Vahid Tarokh. Semifl: Semi- supervised federated learning for unlabeled clients with alternate training. InAdvances in Neural Information 9 Processing Systems, volume 35, pages 17871–17884, 2022

    2022

  7. [7]

    Deep residual learning for image recognition, 2015

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition, 2015

    2015

  8. [8]

    Federated semi-supervised learning with inter-client consistency & disjoint learning.arXiv preprint arXiv:2006.12097, 2020

    Wonyong Jeong, Jaehong Yoon, Eunho Yang, and Sung Ju Hwang. Federated semi-supervised learning with inter-client consistency & disjoint learning.arXiv preprint arXiv:2006.12097, 2020

    work page arXiv 2006

  9. [9]

    Proxy anchor loss for deep metric learning

    Sungyeon Kim, Dongwon Kim, Minsu Cho, and Suha Kwak. Proxy anchor loss for deep metric learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3238–3247, 2020

    2020

  10. [10]

    Protofssl: Federated semi- supervised learning with prototypical networks.arXiv preprint arXiv:2205.13921, 2022

    Woojung Kim, Keondo Park, Kihyuk Sohn, Raphael Shu, and Hyung-Sin Kim. Protofssl: Federated semi- supervised learning with prototypical networks.arXiv preprint arXiv:2205.13921, 2022

    work page arXiv 2022

  11. [11]

    Learning multiple layers of fea- tures from tiny images

    Alex Krizhevsky et al. Learning multiple layers of fea- tures from tiny images. 2009

    2009

  12. [12]

    Model- contrastive federated learning

    Qinbin Li, Bingsheng He, and Dawn Song. Model- contrastive federated learning. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10713–10722, June 2021

    2021

  13. [13]

    Ditto: Fair and robust federated learning through personalization

    Tian Li, Shengyuan Hu, Ahmad Beirami, and Virginia Smith. Ditto: Fair and robust federated learning through personalization. InInternational Conference on Machine Learning (ICML), pages 6357–6368. PMLR, 2021

    2021

  14. [14]

    Federated optimization in heterogeneous networks.Proceedings of Machine learning and systems, 2:429–450, 2020

    Tian Li, Anit Kumar Sahu, Manzil Zaheer, Maziar San- jabi, Ameet Talwalkar, and Virginia Smith. Federated optimization in heterogeneous networks.Proceedings of Machine learning and systems, 2:429–450, 2020

    2020

  15. [15]

    Semifed: Semi-supervised federated learning with consistency and pseudo-labeling.arXiv preprint arXiv:2108.09412, 2021

    Haowen Lin, Jian Lou, Li Xiong, and Cyrus Sha- habi. Semifed: Semi-supervised federated learning with consistency and pseudo-labeling.arXiv preprint arXiv:2108.09412, 2021

    work page arXiv 2021

  16. [16]

    Brendan McMahan, Eider Moore, Daniel Ram- age, Seth Hampson, and Blaise Aguera y Arcas

    H. Brendan McMahan, Eider Moore, Daniel Ram- age, Seth Hampson, and Blaise Aguera y Arcas. Communication-efficient learning of deep networks from decentralized data. InArtificial Intelligence and Statis- tics (AISTATS). PMLR, 2017

    2017

  17. [17]

    No fuss dis- tance metric learning using proxies

    Yair Movshovitz-Attias, Alexander Toshev, Thomas K Leung, Sergey Ioffe, and Saurabh Singh. No fuss dis- tance metric learning using proxies. InProceedings of the IEEE international conference on computer vision, pages 360–368, 2017

    2017

  18. [18]

    Federated prototype-aware pseudo-labeling for semi-supervised medical image clas- sification

    Haiwei Pan, Chunling Chen, Kejia Zhang, Yuchao Zhang, and Jian Guan. Federated prototype-aware pseudo-labeling for semi-supervised medical image clas- sification. InIEEE International Conference on Bioinfor- matics and Biomedicine (BIBM), 2025

    2025

  19. [19]

    The future of digital health with federated learning.NPJ digital medicine, 3(1):119, 2020

    Nicola Rieke, Jonny Hancox, Wenqi Li, Fausto Milletari, Holger R Roth, Shadi Albarqouni, Spyridon Bakas, Mathieu N Galtier, Bennett A Landman, Klaus Maier- Hein, et al. The future of digital health with federated learning.NPJ digital medicine, 3(1):119, 2020

    2020

  20. [20]

    Felix Sattler, Klaus-Robert M ¨uller, and Wojciech Samek. Clustered federated learning: Model-agnostic distributed multitask optimization under privacy constraints.IEEE transactions on neural networks and learning systems, 32(8):3710–3722, 2020

    2020

  21. [21]

    Facenet: A unified embedding for face recog- nition and clustering

    Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recog- nition and clustering. InProceedings of the IEEE confer- ence on computer vision and pattern recognition, pages 815–823, 2015

    2015

  22. [22]

    Fixmatch: Sim- plifying semi-supervised learning with consistency and confidence.Advances in neural information processing systems, 33:596–608, 2020

    Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin A Raffel, Ekin Dogus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Sim- plifying semi-supervised learning with consistency and confidence.Advances in neural information processing systems, 33:596–608, 2020

    2020

  23. [23]

    Fedproto: Federated prototype learning across heterogeneous clients

    Yue Tan, Guodong Long, Lu Liu, Tianyi Zhou, Qinghua Lu, Jing Jiang, and Chengqi Zhang. Fedproto: Federated prototype learning across heterogeneous clients. InAAAI Conference on Artificial Intelligence, volume 36, 2022

    2022

  24. [24]

    Proxynca++: Revisiting and revitalizing proxy neighbor- hood component analysis

    Eu Wern Teh, Terrance DeVries, and Graham W Taylor. Proxynca++: Revisiting and revitalizing proxy neighbor- hood component analysis. InEuropean conference on computer vision, pages 448–464. Springer, 2020

    2020

  25. [25]

    Personalized federated learning with feature alignment and classifier collaboration

    Jian Xu, Xinyi Tong, and Shao-Lun Huang. Personalized federated learning with feature alignment and classifier collaboration. InThe Eleventh International Conference on Learning Representations, 2023

    2023

  26. [26]

    Wenxin Yang, Xingchen Hu, Xiubin Zhu, Rouwan Wu, Witold Pedrycz, Xinwang Liu, and Jincai Huang. Fedmps: Federated learning in a synergy of multi-level prototype-based contrastive learning and soft label gen- eration.IEEE Transactions on Neural Networks and Learning Systems, 2025

    2025

  27. [27]

    Federated Learning with Non-IID Data

    Yue Zhao, Meng Li, Liangzhen Lai, Naveen Suda, Da- mon Civin, and Vikas Chandra. Federated learning with non-iid data.arXiv preprint arXiv:1806.00582, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  28. [28]

    Collaborative unsupervised visual representation learning from decentralized data

    Weiming Zhuang, Xin Gan, Yonggang Wen, Shuai Zhang, and Shuai Yi. Collaborative unsupervised visual representation learning from decentralized data. InPro- ceedings of the IEEE/CVF international conference on computer vision, pages 4912–4921, 2021. 10 A Dataset Configurations DatasetsWe evaluate on three standard federated learning benchmarks.FEMNIST[2] i...

    2021