ProxyFL: A Proxy-Guided Framework for Federated Semi-Supervised Learning

AI summary

Overview

Research area: Federated learning (FL) and semi-supervised learning (SSL), specifically the intersection known as Federated Semi-Supervised Learning (FSSL).

Technical level: Advanced. The paper assumes familiarity with federated aggregation (FedAvg, FedProx), pseudo-labeling and consistency regularization (FixMatch), Dirichlet-based non-IID data simulation, and contrastive learning objectives.

Scope: The paper proposes ProxyFL, a framework that uses the learnable weights of a model's classifier as a shared "proxy" to simultaneously address data heterogeneity across clients and the mismatch between labeled and unlabeled data within each client.

Note: the provided content is truncated; the conclusion ends mid-sentence, and Appendices A–D (heterogeneity definitions, pseudo-code, theoretical proofs, and further setup details) are referenced but not included.

What This Paper Is About

Federated semi-supervised learning lets many clients collaboratively train one global model using a small amount of labeled data plus a large amount of unlabeled data, without sharing raw data. Two problems make this hard: clients have different data distributions from each other (external heterogeneity), and within a single client the labeled and unlabeled data do not match (internal heterogeneity). ProxyFL's goal is to handle both problems at once by treating the classifier's weight vectors as a "proxy" for category distribution, rather than averaging client parameters directly or throwing away low-confidence unlabeled samples.

Key Contributions

1. A unified proxy concept for FSSL. The paper states it is the first to propose a single unified proxy to mitigate both internal and external heterogeneity in FSSL, using the classifier's learnable weights. The paper argues the proxy introduces no privacy concern and negligible extra communication cost because the proxy is already part of the model parameters transmitted in FL.

2. Global Proxy Tuning (GPT). A server-side mechanism that initializes global proxies by weighted averaging of client proxies and then explicitly optimizes them so each global category proxy is pulled toward local proxies of the same category and pushed away from local proxies of other categories, reducing bias from outlier clients.

3. Indecisive-Categories Proxy Learning (ICPL). A local mechanism that re-includes low-confidence unlabeled samples instead of discarding them, by assigning each such sample a set of possible categories rather than a single pseudo-label, and by building a positive-negative proxy pool relating all samples in a batch.

4. Empirical and theoretical validation. State-of-the-art results reported on four datasets across three heterogeneity levels, plus ablation studies, convergence-rate measurements, overhead analysis, and theoretical proofs referenced in Appendix C.

Main Findings

• Averaging classifier weights is skew-prone. Observation 1: simply averaging classifier weights tends to skew toward outliers and fails to capture the global category distribution across clients. A t-SNE visualization of sliced client classifier weights shows some clients as clear outliers, placing the averaged "centroid" outside most points of a category cluster.

• Discarding low-confidence samples is not universally better. Observation 2: as data heterogeneity increases, more unlabeled samples are excluded from local training, and those excluded samples have the potential to boost performance. The paper reports that w/ low-confidence samples beats w/o low-confidence samples at high heterogeneity (α = 0.1), while the reverse holds at lower heterogeneity (α = 1 or 10), so neither policy dominates.

• State-of-the-art accuracy at 10% label. ProxyFL reaches 88.56 / 90.00 / 89.96 on CIFAR-10, 57.50 / 58.75 / 58.24 on CIFAR-100, 95.09 / 95.18 / 95.26 on SVHN, and 77.98 / 78.96 / 79.59 on CINIC-10, for α = 0.1 / 0.5 / 1 respectively. Reported improvements over the second-best method are ↑1.51, ↑1.95, ↑0.88 (CIFAR-10); ↑3.32, ↑2.93, ↑2.18 (CIFAR-100); ↑1.24, ↑0.91, ↑0.61 (SVHN); ↑3.39, ↑3.22, ↑2.91 (CINIC-10) — in every case the second-best method is SAGE.

• Comparison against the fully-supervised upper bound. FedAvg-SL, trained on fully labeled data, is designated the ideal upper bound, reaching 90.46 / 91.24 / 91.32 (CIFAR-10), 67.98 / 68.83 / 69.10 (CIFAR-100), 94.11 / 94.41 / 94.40 (SVHN), and 77.82 / 80.42 / 81.29 (CINIC-10). The paper notes ProxyFL reaches comparable performance to FedAvg-SL on SVHN and CINIC-10 at α = 0.1 (95.09 vs. 94.11 and 77.98 vs. 77.82).

• Both modules contribute, and combine best. Against a FedAvg+FixMatch-GPL baseline of 84.56 / 86.05 / 86.66 (CIFAR-10), 48.96 / 51.80 / 52.19 (CIFAR-100), 90.50 / 91.94 / 92.31 (SVHN), 71.67 / 73.26 / 74.80 (CINIC-10), adding GPT alone gives 87.59 / 89.23 / 89.71, 54.86 / 56.58 / 57.09, 94.29 / 94.49 / 94.53, 77.15 / 79.03 / 79.31; adding ICPL alone gives 87.81 / 89.58 / 89.66, 57.21 / 57.98 / 57.74, 94.82 / 94.69 / 95.15, 77.80 / 78.04 / 78.57; using both gives the best results.

• Faster convergence. On CIFAR-100 with α = 0.1, ProxyFL reaches 30% / 40% / 50% accuracy in 45 / 89 / 177 rounds, corresponding to speedups of 2.64× / 2.72× / 3.18× over the LPL baseline (119 / 242 / 562 rounds). SAGE required 60 / 124 / 267 rounds (1.98× / 1.95× / 2.10×).

• Category-set supervision beats single pseudo-labels for ambiguous samples. Against designs that simply assign pseudo-labels to all low-confidence samples (GPL-ALL, LPL-ALL) or select the top-1/top-5 categories, the proposed prior-based set design achieves the best accuracy on all four datasets: ICPL-P′_G(Y) at 87.81 / 57.21 / 94.82 / 77.80 versus ICPL-Top1 at 87.13 / 55.66 / 94.56 / 77.01 and ICPL-Top5 at 87.77 / 56.58 / 94.71 / 77.65. A plot of "correct category in ξ" versus "correct pseudo-label" ratios shows the set-based recall stays considerably high and substantially outperforms pseudo-label accuracy, though the specific ratio values are not reported in the provided text.

• Proxies outperform prototypes. Compared with a FedProto+FSSL variant, the paper's approach wins on CIFAR-10 (87.81 vs. 85.89 for PROTO, 86.56 for PROTO-ALL, 86.55 for PROTO-Labeled), CIFAR-100 (57.21 vs. 49.56 / 54.69 / 48.83), SVHN (94.82 vs. 93.48 / 19.59 / 93.60) and CINIC-10 (77.80 vs. 72.53 / 73.16 / 72.57). The PROTO-ALL SVHN figure of 19.59 is an example of the failure mode the authors attribute to high-dimensional feature prototypes risking reverse reconstruction.

• Low server-side overhead. Tuning complexity is stated as O_GPT = O(Q × M × C² × d), where Q is tuning epochs, M is clients, C is categories, and d is proxy dimension. For CIFAR-100, O_GPT ≈ 0.4 GFLOPs, which the authors compare to the 0.5 ∼ 1 GFLOPs required to infer just one image through ResNet.

Methodology in Plain English

The framework splits the work between the server and the clients.

On the server (Global Proxy Tuning). Each client's classifier ends in one weight vector per category. The server first computes the usual weighted average of these vectors to initialize a set of global proxies. Rather than stopping there, it then explicitly optimizes the global proxies with a loss that, for each category, pulls the global proxy toward every client's proxy for that same category and pushes it away from client proxies of other categories. Distances are converted into probabilities with an exponential form and optimized with a negative log-likelihood objective. The tuned global proxies are then sent back to clients alongside the other aggregated parameters to initialize the next local round.

On the clients (Indecisive-Categories Proxy Learning). Each unlabeled sample is passed through weak augmentation and evaluated by both the local model (local logits) and the global model (global logits). Samples are sorted into three groups. Labeled samples use their ground-truth label as a single-element category set. Unlabeled samples whose maximum global logit exceeds a threshold τ = 0.95 are treated as high-confidence and get a pseudo-label as a single-element set. Unlabeled samples at or below the threshold are treated as low-confidence, and instead of a single pseudo-label they receive an indecisive-categories set: all categories whose logits exceed a per-category global prior. That prior is a running average, across clients, of the proportion of predictions falling into each category — computed without needing real per-class counts, and acting as a higher threshold for majority classes and a lower one for minority classes.

Every sample in a batch then contributes to a positive-negative proxy pool. The positive proxy for a high-confidence sample is the classifier proxy of its pseudo-label; for a low-confidence sample it is a weighted sum of the proxies of all categories in its indecisive set. Any other sample in the batch whose category set does not overlap with the current sample's set is treated as a negative. A contrastive objective then trains all samples, so no sample is discarded and wrong single pseudo-labels are not imposed on ambiguous data.

Total objective. Locally the loss combines a supervised cross-entropy term on labeled data, a KL divergence term on high-confidence unlabeled data against their pseudo-labels, and the ICPL term, with α and β both empirically set to 1. The GPT loss is added as the global term.

Experimental setup. The evaluation follows SAGE's FSSL setting. Datasets are CIFAR-10, CIFAR-100, SVHN, and CINIC-10, with label proportions of 10% and 20% per category. Internal and external heterogeneity are simulated by sampling labeled and unlabeled data from Dirichlet distributions with α ∈ {0.1, 0.5, 1}, where smaller α means greater heterogeneity. There are 20 clients per setting, with 8 randomly sampled per round; the local backbone is ResNet-8, local epochs are 5, local learning rate is 0.1, the pseudo-labeling confidence threshold τ is 0.95, the global proxy tuning learning rate is 0.005, and tuning epochs are 10 for CIFAR-100 and 100 for the other datasets.

Why This Matters

Impact on research. Most FSSL work attacks external and internal heterogeneity with separate mechanisms: weighted aggregation on the server and confidence filtering on the client. ProxyFL argues for a single object — the classifier's own weights — that can serve both roles at no privacy or communication cost, since it is already part of the transmitted model. If the results hold, this reframes "how should we aggregate?" as "how should we fit a category distribution?", and it pushes back on the common practice of discarding low-confidence unlabeled data, showing empirically that discarded samples carry usable signal and that representing ambiguity as a set is better than forcing a single label.

Real-world applications (the paper does not enumerate deployments; these follow from the settings and motivations it describes — edge devices, IoT, and expensive or laborious annotation):

• On-device keyboard, speech, or vision models where user data cannot leave the device and only a fraction of it is labeled.
• IoT and sensor networks spread across sites whose local class distributions differ from one another.
• Clinical or industrial deployments where expert labeling is scarce and each site sees a different patient or product mix.
• Any cross-organization federation where privacy rules forbid sharing raw data or high-dimensional feature prototypes that could be reverse-reconstructed.

Industry relevance. The practical claims are the ones a deployment team would care about: the server-side tuning adds roughly 0.4 GFLOPs on CIFAR-100, described as comparable to a single ResNet image inference; the proxy is not an extra artifact to protect because it is already a model parameter; and faster convergence (2.64×–3.18× fewer rounds on the reported CIFAR-100 setting) directly translates to less communication and less training cost under non-IID conditions.

Future Directions

• Verify the theoretical claims. The paper states that theoretical proofs of ProxyFL appear in Appendix C, but those proofs are not included in the provided content; their scope and assumptions remain to be examined.
• Test beyond the reported configuration. All experiments use 20 clients, 8 sampled per round, ResNet-8, and Dirichlet α ∈ {0.1, 0.5, 1}. Behavior under much larger client counts, other backbones, or other heterogeneity patterns is not reported.
• Probe the prior and threshold design. The global category prior P′_G(Y) is central to constructing the indecisive-categories set, and τ = 0.95 is fixed. Sensitivity to τ, to the prior update rule, and to situations where the prior itself drifts under extreme non-IID conditions is not reported.
• Extend to other FSSL label scenarios. The work covers the Label-at-All-Client setting only; the paper describes two other scenarios (Labels-at-Server and Labels-at-Partial-Cli

Authors’ abstract

Federated Semi-Supervised Learning (FSSL) aims to collaboratively train a global model across clients by leveraging partially-annotated local data in a privacy-preserving manner. In FSSL, data heterogeneity is a challenging issue, which exists both across clients and within clients. External heterogeneity refers to the data distribution discrepancy across different clients, while internal heterogeneity represents the mismatch between labeled and unlabeled data within clients. Most FSSL methods typically design fixed or dynamic parameter aggregation strategies to collect client knowledge on the server (external) and / or filter out low-confidence unlabeled samples to reduce mistakes in local client (internal). But, the former is hard to precisely fit the ideal global distribution via direct weights, and the latter results in fewer data participation into FL training. To this end, we propose a proxy-guided framework called ProxyFL that focuses on simultaneously mitigating external and internal heterogeneity via a unified proxy. I.e., we consider the learnable weights of classifier as proxy to simulate the category distribution both locally and globally. For external, we explicitly optimize global proxy against outliers instead of direct weights; for internal, we re-include the discarded samples into training by a positive-negative proxy pool to mitigate the impact of potentially-incorrect pseudo-labels. Insight experiments & theoretical analysis show our significant performance and convergence in FSSL.