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FreqX: Analyze the Attribution Methods in Another Domain

Zechen Liu, Feiyang Zhang, Wei Song, Xiang Li, Wei Wei

TL;DR

This work tackles interpretability in Personalized Federated Learning under non-IID data and fairness constraints by introducing FreqX, a frequency-domain interpretability framework that leverages signal processing and information theory to disclose both attribution and concept information with low computational cost. The method maps neuron operations to the frequency domain, defines energy-based quantities and an SNR criterion to separate feature signals from noise, and demonstrates the ability to generate global explanations suitable for federated settings. Across functionality, faithfulness, concept extraction, and global aggregation experiments, FreqX shows faster explanations and competitive, or superior, fidelity relative to baselines, while enabling client-contribution assessment with reduced overhead. The results suggest a practical path toward scalable, privacy-preserving interpretability in PFL that can integrate with existing aggregation and contribution-estimation pipelines.

Abstract

Personalized Federal learning(PFL) allows clients to cooperatively train a personalized model without disclosing their private dataset. However, PFL suffers from Non-IID, heterogeneous devices, lack of fairness, and unclear contribution which urgently need the interpretability of deep learning model to overcome these challenges. These challenges proposed new demands for interpretability. Low cost, privacy, and detailed information. There is no current interpretability method satisfying them. In this paper, we propose a novel interpretability method \emph{FreqX} by introducing Signal Processing and Information Theory. Our experiments show that the explanation results of FreqX contain both attribution information and concept information. FreqX runs at least 10 times faster than the baselines which contain concept information.

FreqX: Analyze the Attribution Methods in Another Domain

TL;DR

This work tackles interpretability in Personalized Federated Learning under non-IID data and fairness constraints by introducing FreqX, a frequency-domain interpretability framework that leverages signal processing and information theory to disclose both attribution and concept information with low computational cost. The method maps neuron operations to the frequency domain, defines energy-based quantities and an SNR criterion to separate feature signals from noise, and demonstrates the ability to generate global explanations suitable for federated settings. Across functionality, faithfulness, concept extraction, and global aggregation experiments, FreqX shows faster explanations and competitive, or superior, fidelity relative to baselines, while enabling client-contribution assessment with reduced overhead. The results suggest a practical path toward scalable, privacy-preserving interpretability in PFL that can integrate with existing aggregation and contribution-estimation pipelines.

Abstract

Personalized Federal learning(PFL) allows clients to cooperatively train a personalized model without disclosing their private dataset. However, PFL suffers from Non-IID, heterogeneous devices, lack of fairness, and unclear contribution which urgently need the interpretability of deep learning model to overcome these challenges. These challenges proposed new demands for interpretability. Low cost, privacy, and detailed information. There is no current interpretability method satisfying them. In this paper, we propose a novel interpretability method \emph{FreqX} by introducing Signal Processing and Information Theory. Our experiments show that the explanation results of FreqX contain both attribution information and concept information. FreqX runs at least 10 times faster than the baselines which contain concept information.

Paper Structure

This paper contains 13 sections, 1 theorem, 14 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Personalized Federated Learning
  4. Interpretability of Deep Neural Network
  5. Method
  6. Neuron In Frequency Domain
  7. SNR and Neuron
  8. Experiments
  9. Functionality and Cost Comparison
  10. Faithfulness Analysis
  11. Concept and Parameter Analysis
  12. Effectiveness
  13. Conclusion

Key Result

Theorem 3.1

In an unbiased neuron, or a neuron with a negative bias or the bias is regarded as a feature with value $1$, if the neuron is activated, the $SNR$ after the compounding of signals is larger than the original ones.

Figures (8)

  • Figure 1: \ref{['fig:intro mlp']}: The cluster operations of a 3-layer MLP towards a simulated binary classification dataset with only two features( $\varepsilon$ denotes the augmentation coefficient). \ref{['fig:intro res']}: We visualize the spatial transformation operations of Resnet-50.
  • Figure 2: The deletion operation in the time/space domain is not real Deletion. It introduced new signals.
  • Figure 3: The FreqDIG.
  • Figure 4: \ref{['fig:methodres']}: The transformations of ResNet-50 towards a single sample of the imgNet dataset. \ref{['fig:methodfashion']}: The classification procedure of a 3-layer MLP from the input layer to the output layer(left to right). The red points emphasize the similar transformations between the samples with the same label. Blue lines indicate that there are two kinds of sandals in FashionMNIST.
  • Figure 5: The results of the deletion and insertion game. The results of FullGrad and GradCAM are block-like because they smoothed their values. They perform well in most cases like the first example. However, when there are several important individuals such as the third example, they go wrong. But our method is more stable as displayed in this figure and the Figure.\ref{['fig:fide']}.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Theorem 3.1
  • Proof 3.2