unbitrium

pFedSim Validation Report

Overview

Personalized Federated Similarity (pFedSim) extends FedSim by combining global model aggregation with personalized local layers. It decouples the model into shared feature extractors and client-specific prediction heads.

Mathematical Formulation

The model is decomposed into shared parameters $\theta$ and personalized parameters $\phi_k$:

\[w_k = (\theta_k, \phi_k)\]

The shared layers are aggregated with similarity weighting:

\[\theta^{t+1} = \sum_{k=1}^{K} \omega_k^t \cdot \theta_k^t\]

where:

\[\omega_k^t = \frac{\text{sim}(\theta_k^t, \theta^t)}{\sum_{j=1}^{K} \text{sim}(\theta_j^t, \theta^t)}\]

The personalized layers $\phi_k$ are retained locally and not aggregated.

Implementation Reference

The implementation is located at src/unbitrium/aggregators/pfedsim.py.

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Invariants

Invariant 1: Layer Separation

Shared and personalized layers are correctly identified:

\[|\theta| + |\phi| = |w|\]

Verification: Sum of shared and personalized parameter counts equals total.

Invariant 2: Personalized Layer Preservation

Personalized layers are not modified during aggregation:

\[\phi_k^{t+1} = \phi_k^t + \Delta\phi_k^{local}\]

Verification: Personalized parameters only change from local training.

Invariant 3: Shared Layer Normalization

Weights for shared layer aggregation sum to unity:

\[\sum_{k=1}^K \omega_k = 1\]

Verification: Weight normalization confirmed.

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Test Distributions

Distribution 1: Heterogeneous Task Distribution

Configuration:

• Clients: $K = 20$
• Each client has distinct task (e.g., different digit styles)
• Shared: CNN feature extractor
• Personalized: Final classification layer

Expected Behavior:

• Personalized layers adapt to local tasks
• Shared features transfer across clients
• Per-client accuracy higher than global FedAvg

Distribution 2: Cross-Domain Transfer

Configuration:

• Clients from different domains (natural images, sketches, paintings)
• Model: ResNet-18 backbone + FC head

Expected Behavior:

• Shared backbone learns domain-invariant features
• Personalized heads specialize to each domain

Distribution 3: Varying Data Quantities

Configuration:

• Clients: $K = 50$
• Samples: Power-law $n_k \propto k^{-1}$
• Personalized layer complexity adapts

Expected Behavior:

• Larger clients contribute more to shared layers
• Small clients benefit from personalized specialization

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Expected Behavior

Layer Assignment

Layer Type	Aggregation	Personalization
Feature extractor (conv, norm)	Global	No
Final classifier (fc)	None	Yes
Optional adaptation layers	None	Yes

Metric Ranges

Metric	Range	Notes
shared_param_count	$[0, P]$	Number of shared parameters
personal_param_count	$[0, P]$	Number of personalized parameters
avg_similarity	$[-1, 1]$	Mean similarity on shared layers
personalization_benefit	$[-\infty, \infty]$	Acc improvement from personalization

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Edge Cases

Edge Case 1: All Layers Shared

Input: Empty personalized layer specification

Expected Behavior:

• Reduces to FedSim
• All layers aggregated globally

Edge Case 2: All Layers Personalized

Input: All layers marked as personalized

Expected Behavior:

• No aggregation occurs
• Each client trains independently (local training)

Edge Case 3: New Client

Input: Client joins with no personalized history

Expected Behavior:

• Personalized layers initialized from global model
• Rapid adaptation through local training

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Reproducibility

Seed Configuration

def set_seed(seed: int = 42) -> None:
    import random, numpy as np, torch
    random.seed(seed)
    np.random.seed(seed)
    torch.manual_seed(seed)

Layer Configuration

personalization:
  shared_layers:
    - "conv1"
    - "conv2"
    - "bn1"
  personalized_layers:
    - "fc"
    - "classifier"

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Security Considerations

Privacy Benefits

Personalized layers provide inherent privacy:

• Local task-specific information stays on device
• Only shared features transmitted to server

Information Leakage

Shared layer updates may still reveal:

• Domain-general features of local data
• Statistical properties of feature distributions

Mitigations

1. Differential privacy on shared layer updates
2. Feature obfuscation before aggregation
3. Secure aggregation protocols

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Complexity Analysis

Time Complexity

\[T = O(K \cdot P_{shared})\]

where $P_{shared}$ is the number of shared parameters.

Space Complexity

Server: \(S_{server} = O(P_{shared})\)

Client: \(S_{client} = O(P_{shared} + P_{personal})\)

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Performance Benchmarks

CIFAR-100 (20 superclasses as clients)

Method	Global Acc	Personalized Acc
FedAvg	42.3%	-
FedSim	45.8%	-
pFedSim	41.2%	58.7%

Federated EMNIST

Method	Writer-level Acc
Local Only	84.2%
FedAvg	82.8%
pFedSim	89.4%

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References

1. Collins, L., et al. (2021). Exploiting shared representations for personalized federated learning. In ICML.

2. Li, D., & Wang, J. (2019). FedMD: Heterogeneous federated learning via model distillation. In NeurIPS Workshop.

3. Arivazhagan, M. G., et al. (2019). Federated learning with personalization layers. arXiv preprint.

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Changelog

Version	Date	Changes
1.0.0	2026-01-04	Initial validation report

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Copyright 2026 Olaf Yunus Laitinen Imanov and Contributors. Released under EUPL 1.2.

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