Privacy-Preserving Federated Learning

• Privacy-preserving federated learning is a distributed system that safeguards sensitive data by applying local private mappings and dimensionality reduction, ensuring raw data never leaves client premises.
• It employs a layered architecture where user institutions, intra-group servers, and a central server sequentially process and aggregate privacy‐filtered representations to boost model efficiency.
• The framework achieves a balance between accuracy and privacy using formal guarantees, one-shot communication, and efficient low-rank approximations, making it ideal for bandwidth-constrained environments.

A privacy-preserving federated learning framework is a distributed machine learning system designed to collaboratively train models on data distributed across multiple organizations or devices, while ensuring that sensitive raw data never leaves client premises and that privacy leakage is controlled at every step. Recent research addresses both the accuracy–privacy trade-off and the efficiency bottlenecks of classical federated learning, orchestrating a combination of communication-efficient protocols, formal privacy mappings, and system modularity for diverse trust and application environments.

1. Architectural Principles and System Workflow

Privacy-preserving FL frameworks implement layered architectures that separate raw data handling, intermediate representation computation, secure data exchange, and global model aggregation. In the FedDCL (“Federated Data Collaboration Learning”) example, three main logical layers are defined (Imakura et al., 27 Sep 2024):

• User institutions generate local, dimensionality-reduced intermediate representations $\widetilde X^{(i)}_j$ using private mappings $f^{(i)}_j$, and never transmit raw data or the details of $f^{(i)}_j$.
• Intra-group DC servers (data collaboration servers) locally receive only these representations and labels, compute group-wise low-rank factors, and facilitate the construction of “collaboration representations” $\widehat X^{(i)}_j$ tailored for inter-group federated optimization.
• Central FL server receives only strongly privacy-protected aggregates, performs further low-rank analysis to obtain a global collaboration latent $Z$, coordinates federated optimization (e.g., FedAvg), and propagates updated model parameters.

The workflow dramatically reduces iterative and bandwidth-intensive communication: user institutions conduct “one-shot” uploads and downloads, while iterative steps are confined to intra-group and central federated learning processing. This design is especially suited to environments where persistent connectivity or high-frequency external communication is infeasible.

2. Privacy Mechanisms: Double-Layer Protection and Formal Guarantees

A defining feature of modern frameworks is their multi-layer privacy strategy (Imakura et al., 27 Sep 2024, Hayati et al., 2022, Hayati et al., 25 Sep 2024):

• Local mapping privacy: Each user's mapping $f^{(i)}_j$ used for dimensionality reduction is strictly local and unshared.
• Dimension reduction (DR) privacy: Even in the hypothetical breach of $f^{(i)}_j$, the reduced dimensionality (with $\widetilde m_{ij} \ll m$) ensures $\varepsilon$–DR privacy—a statistical guarantee that the raw data $X^{(i)}_j$ is not reconstructible from the intermediate representations, given sufficient reduction.
• Non-invertibility and honest-but-curious defense: At no step does any aggregation server or collaborating party receive sufficient information to invert the mapping chain or reconstruct private data, assuming no collusion.
• Formal threat model: Protocols generally assume all parties follow the prescribed protocol (honest-but-curious setting) and preclude collusion between aggregation layers or between servers and clients.

Table: Privacy Layers in FedDCL

Privacy Layer	Data Exposed	Attacker Observes	Inversion Feasibility
Layer 1: Mapping	$\widetilde X$, $f$	Not shared	Impossible
Layer 2: DR	$\widetilde X$, $\widetilde A$	Only seen after DR	Feasible only if DR weak
Collab. Repr.	$\widehat X$	Only for FL	Infeasible if DR strong
Final model $w$	Only collaboration domain	Only central FL server	Leakage only for $\widehat X$

This dual-layer approach is augmented in some frameworks with further techniques: secure (secret-sharing or functional-encryption–based) aggregation (Xu et al., 2019, Imakura et al., 27 Sep 2024), local or global differential privacy noise injection (Hayati et al., 2022, Hayati et al., 25 Sep 2024), or dynamic proof-aware protocols for verifiable computation (see also (Yue et al., 25 Sep 2025) for similarity-based, LDP-protected client selection).

3. Data Representation: Dimensionality Reduction, SVD, and Mappings

Local data transformation is foundational for privacy-preserving FL frameworks.

• Private mappings $f^{(i)}_j$: These functions (e.g., PCA, LDA, or user-chosen nonlinear embeddings) compress $X^{(i)}_j \in \mathbb{R}^{n_{ij} \times m}$ to $$\widetilde X^{(i)}_j \in \mathbb{R}^{n_{ij} \times \widetilde m_{ij}}$$, with $\widetilde m_{ij} < m$.
• Anchor representations: Each site applies the same $f^{(i)}_j$ to a public “anchor” matrix $A$ (random or publicly defined), yielding $\widetilde A^{(i)}_j$, serving as a shared reference for cross-party alignment.
• SVD-based low-rank approximation: Intra-group servers stack these anchor representations, compute SVD, and obtain group factors $\widetilde B^{(i)}$, which form the base of subsequent alignment and integration on the central server.
• Final representation alignment: Post-aggregation, each user solves a linear least-squares problem to find $G^{(i)}_j$ such that $\| \widetilde A^{(i)}_j G^{(i)}_j - Z \|_F$ is minimized, aligning their intermediate representations with the global, collaboration-wide latent $Z$.

This design achieves statistical decorrelation between raw and processed data, while preserving enough structure for federated learning.

4. Communication Efficiency and Scalability

Classical federated learning protocols (e.g., FedAvg) require $O(Tp)$ communication per user ($T$ rounds, $p$ model parameters per round). Privacy-preserving frameworks, especially those adopting non-iterative data-collaboration principles, optimize communication as follows (Imakura et al., 27 Sep 2024):

• Single-shot communication: Each user transmits their $\widetilde X^{(i)}_j$ and $\widetilde A^{(i)}_j$ only once per protocol run.
• Parameter size: Transmitted data is $$O(n_{ij} \widetilde m + r \widetilde m + \widetilde m \widehat m + p)$$, only for two messages (upload and download with collaborating transforms/model).
• Comparative efficiency: This yields vast reductions in bandwidth and client-server interaction overhead, crucial for highly distributed or bandwidth-constrained settings.

Such efficiency is achieved without notable accuracy loss (see empirical results section).

5. Empirical Performance and Privacy–Utility Trade-Offs

Privacy-preserving federated learning frameworks are evaluated across diverse datasets (e.g., MNIST, Fashion-MNIST, BatterySmall, CreditRating, eICU) under regression and classification metrics (Imakura et al., 27 Sep 2024):

• Comparative baselines: Centralized, local, FedAvg, data collaboration (DC), FedDCL.
• Performance: FedDCL exceeds local models by a large margin, is on par with both FedAvg and DC, even though its final models use lower-dimensional collaboration representations.
• Convergence properties: Reduced feature dimensionality in collaboration representations often leads to faster per-round convergence compared to conventional FedAvg, due to statistical regularization or noise-reduction effects.
• Communication reduction: User institution communication rounds drop from $T$ (standard FL) to $1$–$2$; this is especially critical where connectivity is sporadic.
• Trade-offs:
  • Accuracy vs. Compression: Reducing $\widehat m \ll m$ can result in minor fidelity loss, but practical metrics remain competitive.
  • Privacy vs. Utility: DR projections are selected to support both privacy masking and retention of prediction-critical information.
  • One-shot vs. Iterative transfer: FedDCL trades up-front intermediate data transmission for the elimination of repeated gradient/model exchanges.

Performance summary:

Method	User comm. rounds	Test accuracy/convergence	Privacy risk (raw $X$)
FedAvg	$T$	Baseline	High (model inversion)
DC	1	Comparable	Lower, but not full FL
FedDCL	1–2	Comparable/slightly better	Provably low

6. Algorithmic Pipeline and Implementation

Formalizing the FedDCL procedure (Algorithm 1 in (Imakura et al., 27 Sep 2024)):

1. Initialization (user): Each institution computes $f^{(i)}_j$, $\widetilde X^{(i)}_j$, and $\widetilde A^{(i)}_j$.
2. Data transfer: $$\widetilde X^{(i)}_j, \widetilde A^{(i)}_j, Y^{(i)}_j$$ are transmitted to intra-group DC server.
3. Group processing: DC server stacks $\widetilde A^{(i)}_j$, computes group-level SVD, constructs $\widetilde B^{(i)}$.
4. Global coordination: Central FL server computes overall SVD, obtains $Z$, broadcasts $Z$.
5. Per-user collaboration representation: Each group server determines $G^{(i)}_j$ to minimize $\| \widetilde A^{(i)}_j G^{(i)}_j - Z \|_F$, computes $$\widehat X^{(i)}_j = \widetilde X^{(i)}_j G^{(i)}_j$$.
6. Federated optimization: Central FL server (possibly with arbitrary FL optimizer) operates solely on collaboration representations $\{\widehat X^{(i)}, Y^{(i)}\}$.
7. Model distribution: The final model, along with transformation matrices, is returned to clients, who use their private $f^{(i)}_j$ to project new data for inference.

No iterative user–server cycling is required once initial data representations are exchanged; all iterative FL protocol coordination is limited to higher-level servers handling only privacy-filtered data.

7. Broader Context and Significance

The recent evolution in privacy-preserving FL frameworks, exemplified by FedDCL and related hybrid protocols, reflects recognition that conventional approaches—pure federated averaging, secure aggregation, differential privacy—alone are insufficient to resolve the efficiency-privacy-utility triad. The interplay between intermediate-representation privacy, communication minimization, and robust model performance characterizes current leading designs.

Key advantages of this paradigm (Imakura et al., 27 Sep 2024):

• Enables FL in highly regulated domains or in settings with intermittent connectivity.
• Provides formal, compositional privacy analysis under realistic attacker models.
• Achieves end-to-end learning accuracy comparable with iterative, high-bandwidth approaches.
• Generalizes to settings with highly heterogeneous data, modular communication, and customizable privacy mappings.

A plausible implication is that integration of such hybrid, multi-layer privacy-preserving structures will become foundational in the next generation of FL infrastructure, particularly where trust, efficiency, and privacy compliance are mandatory.