Federated Category Discovery

• Federated Category Discovery is a framework that integrates open-world discovery with federated learning to enable clients to identify novel classes while retaining base-class knowledge.
• It employs secure aggregation and prototype-based clustering methods to align heterogeneous local discoveries into a coherent global catalogue without sharing raw data.
• The approach addresses challenges like data heterogeneity, non-IID label spaces, limited communication, and privacy, offering actionable insights for decentralized learning.

Searching arXiv for the cited federated category discovery and federated clustering papers to ground the article in current literature. Federated Category Discovery (FCD) denotes the combination of open-world category discovery with the constraints of federated learning: multiple privacy-constrained clients each hold private labelled data from base classes and private unlabelled data that may contain both known and novel classes, and the objective is to train a shared global model that retains base-class knowledge, clusters unlabelled samples into novel categories, aligns those clusters across clients, and does so without any raw-data exchange (He et al., 26 Sep 2025). In the more task-specific formulation of Federated Generalized Category Discovery (Fed-GCD), the training data are distributively stored in local clients and cannot be shared among clients, so the learned model must simultaneously recognize labeled classes and discover unknown classes across heterogeneous local label spaces (Pu et al., 2023). A related but distinct fully unsupervised formulation, termed Federated Clustering, removes labelled base classes entirely and aims to identify the complete set of categories across clients under label-free, non-uniform data distributions (Nardi et al., 2024).

1. Formal setting and scope

In the survey formulation of FCD, client $n$ holds a private labelled set $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$ with $y_i\in\mathcal{Y}_n^L$, and a private unlabelled set $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$ whose hidden labels lie in $\mathcal{Y}_n^U$. The local label space is $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$, and across clients the label spaces need not align exactly: $\mathcal{Y}_m\cap\mathcal{Y}_n$ may be non-empty for $m\ne n$, while novel classes may appear on some clients but not others (He et al., 26 Sep 2025). The central objective is to learn a shared model $f_\theta$ that preserves knowledge of base classes, discovers categories in unlabelled data, and aligns local discoveries into a global catalogue of unseen classes.

A prototypical FedAvg-style training round is described as follows. The server broadcasts the current global model $\theta^{(t)}$; each participating client performs local training for $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$0 epochs on both its labelled and unlabelled data; clients return encrypted or noise-perturbed updates; and the server aggregates them by sample-count weighting: $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$1 The local optimization target combines supervised classification and an unsupervised discovery term: $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$2 Here $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$3 may be a contrastive loss such as InfoNCE, a clustering objective such as normalized cut or mutual-information maximization, or a prototype-based assignment loss (He et al., 26 Sep 2025).

Fed-GCD instantiates this setting with $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$4 clients and one server. Each client $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$5 has a small labeled set $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$6 containing only known classes and an unlabeled set $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$7 that may contain both known and unknown classes. The high-level federated objective is

$\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$8

subject to $\mathcal{D}_n^L=\{(x_i,y_i)\}_{i=1}^{N_n^L}$9 each round and the condition that raw data never leave the client (Pu et al., 2023).

A related neighboring problem is Federated Clustering, where client $y_i\in\mathcal{Y}_n^L$0 holds an unlabeled local dataset $y_i\in\mathcal{Y}_n^L$1, each $y_i\in\mathcal{Y}_n^L$2 contains samples from an unknown subset of global categories $y_i\in\mathcal{Y}_n^L$3, and the goal is to discover all global categories in a fully unsupervised, federated manner and learn a model for each (Nardi et al., 2024). This suggests a spectrum of decentralized discovery problems ranging from generalized category discovery with labelled anchors to completely label-free global category induction.

2. Structural difficulties in decentralized discovery

FCD inherits the main challenges of open-world clustering and compounds them with federated constraints. The survey identifies five recurrent difficulties: data heterogeneity, non-IID label spaces, limited communication, privacy, and client resource heterogeneity (He et al., 26 Sep 2025). Data heterogeneity arises because clients differ not only in the distribution of base classes but also in which novel classes they observe; some unseen classes appear only on a handful of clients. Non-IID label spaces mean there is no single unified partition available at the server side. Limited communication makes it impractical to transmit full embeddings or dense cluster summaries every round. Privacy constraints matter even when raw data are never shared, because prototypes or similarity matrices can leak information about individual samples. Resource heterogeneity further complicates aggregation because some clients may support only a few local epochs or low-precision models.

Fed-GCD isolates two concrete failure modes. First, representation degradation occurs when each client model is trained with fewer data than in centralized GCD. Second, label-space heterogeneity is acute because different clients may have partially overlapping or disjoint $y_i\in\mathcal{Y}_n^L$4 (Pu et al., 2023). These two issues explain why a naive reduction of FCD to local category discovery plus standard weight averaging is inadequate.

The fully unsupervised Federated Clustering setting exhibits an additional difficulty: the global number of categories $y_i\in\mathcal{Y}_n^L$5 is unknown, and each client only estimates a local cluster count $y_i\in\mathcal{Y}_n^L$6 with $y_i\in\mathcal{Y}_n^L$7. Since each local clustering may be “dirty,” downstream grouping and refinement must tolerate incorrect initial partitions while still recovering the full set of global data distributions (Nardi et al., 2024). A plausible implication is that class-number estimation and cross-client semantic alignment are not peripheral subproblems in decentralized discovery; they are central to whether the federation recovers a coherent global semantic structure at all.

3. Method families and design patterns

The survey states that, to date, only three FCD methods have been proposed in the literature: FedoSSL, Fed-GCD, and GAL (He et al., 26 Sep 2025). Their organization follows three technical axes: representation learning, label assignment and clustering, and class-number estimation.

Method	Main mechanism	Class-number handling
FedoSSL	Federated contrastive learning plus federated self-supervision	Assumes the total number of classes $y_i\in\mathcal{Y}_n^L$8 is known a priori
Fed-GCD	Prototype aggregation with GMMs; semi-supervised FINCH; global alignment	Uses splitting–merging mechanics of a global GMM
GAL	Continual FCD with prototype communication and prototype merge	Merges when a new center lies within a touch-threshold of an old prototype; otherwise creates a new class

For representation learning, both FedoSSL and Fed-GCD adopt contrastive losses at each client. The survey gives the local InfoNCE form

$y_i\in\mathcal{Y}_n^L$9

where positives are drawn from augmentations or pseudo-labels (He et al., 26 Sep 2025). FedoSSL further augments labelled and unlabelled sets with rotation or jigsaw pretext tasks, and the resulting gradients are aggregated server-side under secure protocols.

For label assignment and clustering, Fed-GCD exemplifies prototype aggregation. Each client fits a Gaussian-Mixture Model on local features to propose cluster centers $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$0; the server averages these centers across clients,

$\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$1

and broadcasts the resulting global centers so that clients align to the same global clusters (He et al., 26 Sep 2025). The same survey notes that Fed-GCD also shows a semi-supervised variant of FINCH can be run at each client, while only first-neighbor graph messages are sent to the server to construct a global cluster dendrogram.

Class-number estimation remains a defining difficulty. The survey contrasts three positions. FedoSSL assumes the total class count is known a priori. Fed-GCD lets clients suggest split operations when a component’s variance exceeds a threshold and merge operations when two component means become too close; the server only needs to aggregate these split-merge proposals. GAL uses a prototype-merge algorithm in a continual setting, creating a new class only when a newly discovered center does not fall within a touch-threshold of any old prototype (He et al., 26 Sep 2025). This division indicates that FCD methods differ less in whether they cluster, and more in how they externalize semantic evidence from private clients into a globally actionable representation.

4. Federated generalized category discovery and AGCL

Fed-GCD introduces Associated Gaussian Contrastive Learning (AGCL), a framework organized around three modules: per-client learnable GMMs, Client Semantics Association (CSA) on the server, and Global–Local GMM Contrastive Learning (GCL) on each client (Pu et al., 2023). The framework is designed to address both representation degradation and label-space heterogeneity.

On each client $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$2, features $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$3 are used to initialize a Gaussian mixture

$\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$4

via a parameter-free clustering method, semi-FINCH. The GMM parameters are then learned with a posterior-style GMM loss plus a regularizer to avoid trivial large-covariance solutions. The local GCL-only objective is given as

$\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$5

CSA performs cross-client semantic alignment without exchanging raw data. The server samples $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$6 virtual features from each local Gaussian component, collects them into a set $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$7, runs parameter-free FINCH on $\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$8, and then forms a global GMM by taking the mean and diagonal covariance of each resulting cluster. In closed form,

$\mathcal{D}_n^U=\{x_j\}_{j=1}^{N_n^U}$9

The paper states that this global GMM encodes both shared and client-specific categories (Pu et al., 2023).

After receiving the global GMM $\mathcal{Y}_n^U$0, each client minimizes a combined objective consisting of an instance-level contrastive loss, a local GMM contrastive loss, and a global GMM contrastive loss: $\mathcal{Y}_n^U$1 Positive pairs are defined by the assigned GMM component of a sample, and negatives are all other components in the same GMM (Pu et al., 2023).

The federated protocol departs from plain FedAvg in a targeted way. Only the feature extractor $\mathcal{Y}_n^U$2 is averaged on the server, whereas GCL heads and local GMMs remain local, except for the server-constructed global GMM. At round $\mathcal{Y}_n^U$3, the server aggregates feature-extractor weights

$\mathcal{Y}_n^U$4

broadcasts $\mathcal{Y}_n^U$5, each client updates its local GMM via semi-FINCH, sends the GMM to the server for CSA, receives $\mathcal{Y}_n^U$6, minimizes the AGCL loss, and returns updated feature-extractor weights (Pu et al., 2023). The privacy boundary is explicit: raw images and labels never leave clients; only model weights and GMM parameters are exchanged.

A common simplification is to treat FCD as ordinary FedAvg applied to a local GCD objective. The reported ablations argue against that simplification. In the Fed-GCD benchmark, FedAvg + GCD is a baseline, while AGCL consistently improves over it on generic and fine-grained datasets, indicating that client-semantics association and global-local GMM supervision are not cosmetic additions but part of the core solution (Pu et al., 2023).

5. Label-free federated discovery: Federated Cluster-Wise Refinement

Federated Clustering, introduced as a fully unsupervised federated learning methodology for identifying the complete set of categories across multiple clients within label-free, non-uniform data distributions, provides a useful adjacent formulation (Nardi et al., 2024). The method, Federated Cluster-Wise Refinement (FedCRef), replaces the seen-versus-unseen structure of FCD with a purely unlabeled setting in which each client begins from local clusters and the system must infer the global catalogue of data distributions.

FedCRef proceeds in four recurring phases. First, each client splits its local dataset $\mathcal{Y}_n^U$7 into local clusters $\mathcal{Y}_n^U$8, typically via DEC or a simulated “dirty” clustering, and trains one autoencoder $\mathcal{Y}_n^U$9 per cluster by minimizing reconstruction error. In the reported experiments, each autoencoder uses a flat MLP with encoder layers $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$0 and a mirrored decoder (Nardi et al., 2024).

Second, clients exchange local autoencoder parameters and test received models on their own clusters. For a pair of clusters $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$1 and $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$2, the method compares reconstruction-error vectors in both directions, computes normalized element-wise absolute differences, and declares the clusters associated when

$\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$3

Third, all bidirectional associations are assembled into an undirected graph $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$4, connected components $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$5 are extracted, and each component with at least two clusters is used to run a standard FL instance such as FedAvg over 15 rounds to train a group-specific autoencoder $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$6 (Nardi et al., 2024).

Fourth, each client refines its local clustering by reassigning points according to whichever local or federated model reconstructs them best. Stability is measured by the unsupervised clustering accuracy between consecutive local labelings,

$\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$7

and a client is deemed stable when $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$8, with $\mathcal{Y}_n=\mathcal{Y}_n^L\cup\mathcal{Y}_n^U$9 typically used. Global stopping monitors the number of active clients, the number of communities, and the number of isolated clusters; the process halts if over three consecutive rounds none of these change by more than 10% (Nardi et al., 2024).

FedCRef is not formulated as FCD because it has no labelled base classes, no supervised retention objective, and no seen/unseen partition. A plausible implication is that it represents an unlabeled limiting case of decentralized discovery, useful for understanding how category alignment can emerge from model exchange and reconstruction-based association alone.

6. Empirical landscape, privacy mechanisms, and unresolved issues

The empirical record for FCD remains narrow. The survey states that FCD methods have been evaluated only on synthetic federated splits of CIFAR-100 and ImageNet-100, typically by partitioning 100 classes into 5 clients with 20 classes per client, of which 10 are labelled and 10 unlabelled, and using global clustering accuracy ACC under a task-agnostic protocol with Hungarian matching over all 100 labels (He et al., 26 Sep 2025). Within that protocol, FedoSSL achieves 78.5% ACC on CIFAR-100 with 50 federation rounds, Fed-GCD reaches 82.1% ACC in only 20 rounds, and GAL attains 61.8% continual ACC on a 4-stage TinyImageNet split versus 55.3% for the best prior CCD baseline. The same survey reports that removing the global GMM merger in Fed-GCD drops ACC by 5–7%, highlighting the importance of server-side prototype aggregation (He et al., 26 Sep 2025).

Fed-GCD itself builds a broader benchmark based on six visual datasets: CIFAR-10, CIFAR-100, ImageNet-100, CUB-200, Stanford Cars, and Oxford-IIIT Pet (Pu et al., 2023). The split procedure randomly selects half the classes as old, allocates 50% of images from each known class to a labeled pool and the remainder to unlabeled data, and distributes all training images across $\mathcal{Y}_m\cap\mathcal{Y}_n$0 clients with a Dirichlet($\mathcal{Y}_m\cap\mathcal{Y}_n$1) distribution, using $\mathcal{Y}_m\cap\mathcal{Y}_n$2 for normally heterogeneous and $\mathcal{Y}_m\cap\mathcal{Y}_n$3 for extremely heterogeneous settings. The model uses a ViT-B/16 backbone pretrained by DINO, fine-tuning only the last transformer block and projection head. On generic datasets under the normally heterogeneous setting, FedAvg + AGCL reports 84.7 on CIFAR-10, 56.1 on CIFAR-100, and 74.8 on ImageNet-100 for overall accuracy, compared with 80.7, 49.6, and 69.8 for the FedAvg + GCD baseline. On fine-grained datasets, FedAvg + AGCL reports 55.2 on CUB-200, 38.2 on Cars, and 82.7 on Pets, exceeding both the baseline and purely local GCL (Pu et al., 2023).

The adjacent Federated Clustering literature reports evaluation on EMNIST Digits, KMNIST, and KMNIST49, with 25–50 clients, $\mathcal{Y}_m\cap\mathcal{Y}_n$4, 500 samples per cluster, and overlap levels $\mathcal{Y}_m\cap\mathcal{Y}_n$5 (Nardi et al., 2024). On EMNIST, FedCRef is reported to find $\mathcal{Y}_m\cap\mathcal{Y}_n$6 with $\mathcal{Y}_m\cap\mathcal{Y}_n$7 wrong links, reduce $\mathcal{Y}_m\cap\mathcal{Y}_n$8 from $\mathcal{Y}_m\cap\mathcal{Y}_n$9 to $m\ne n$0, and raise ACC from 0.78 to 0.89, whereas centralized DEC achieves ACC $m\ne n$1. The same report states that performance holds for dirtiness up to 0.5, across varying overlap levels, and up to 50 clients (Nardi et al., 2024).

Privacy and communication are treated as first-class design dimensions rather than implementation details. The survey states that all three FCD methods layer in standard secure aggregation so that the server only ever sees sums of encrypted vectors (He et al., 26 Sep 2025). For differential privacy, a client may send

$m\ne n$2

and FedoSSL reports $m\ne n$3-DP bounds by adding calibrated Gaussian noise to each local prototype before encryption. The same source gives the standard calibration rule

$m\ne n$4

when prototype updates have bounded sensitivity $m\ne n$5. Fed-GCD is further described as using 8-bit quantization of prototypes and 1-bit sign-SGD for gradient updates, reducing communication by 80% at a small cost of 1–2% ACC in the reported experiments (He et al., 26 Sep 2025). At the same time, the survey explicitly notes that prototypes or similarity matrices can leak information about individual samples, so the absence of raw-data exchange is not itself a complete privacy guarantee.

Current limitations are stated plainly in the literature. The survey characterizes FCD research as nascent and identifies fixed class-count assumptions, loss of fine-grained structure under prototype-only aggregation, degradation from DP noise by 5–10 points, and the reliance of all existing benchmarks on IID clients and synthetic splits (He et al., 26 Sep 2025). FedCRef adds that no formal global convergence proof is given, although the method relies on local reconstruction minimization, graph-based grouping that converges as clusters purify, and stability-based stopping to guarantee termination (Nardi et al., 2024). Proposed directions include personalized FCD, hierarchical FCD, communication-adaptive protocols, realistic federated benchmarks in domains such as herbarium images or medical scans, and better DP/utility trade-offs via mechanisms such as Rényi DP or functional-mechanism DP (He et al., 26 Sep 2025). Taken together, these points indicate that the central unresolved problem is not simply discovering novel categories under privacy constraints, but doing so when class spaces are genuinely heterogeneous, counts are unknown, clients are dynamically non-IID, and the communication and privacy layers materially alter the semantics available for alignment.