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Disparate Impact on Group Accuracy of Linearization for Private Inference

Saswat Das, Marco Romanelli, Ferdinando Fioretto

TL;DR

This work investigates whether privacy-focused inference via ReLU linearization inadvertently hurts fairness. It establishes a bound linking group-specific loss increases to gradient norms and Hessian eigenvalues, and empirically shows minority groups suffer larger accuracy drops as more activations are linearized across UTKFace, SVHN, and CIFAR-10 with ResNet architectures. A mitigation strategy based on fairness-aware finetuning using a Lagrangian regularizer is proposed and shown to improve minority accuracy with minimal cost to overall performance. The results reveal a substantive privacy-computationTradeoff, underscoring the need for fairness-aware design in private inference systems.

Abstract

Ensuring privacy-preserving inference on cryptographically secure data is a well-known computational challenge. To alleviate the bottleneck of costly cryptographic computations in non-linear activations, recent methods have suggested linearizing a targeted portion of these activations in neural networks. This technique results in significantly reduced runtimes with often negligible impacts on accuracy. In this paper, we demonstrate that such computational benefits may lead to increased fairness costs. Specifically, we find that reducing the number of ReLU activations disproportionately decreases the accuracy for minority groups compared to majority groups. To explain these observations, we provide a mathematical interpretation under restricted assumptions about the nature of the decision boundary, while also showing the prevalence of this problem across widely used datasets and architectures. Finally, we show how a simple procedure altering the fine-tuning step for linearized models can serve as an effective mitigation strategy.

Disparate Impact on Group Accuracy of Linearization for Private Inference

TL;DR

This work investigates whether privacy-focused inference via ReLU linearization inadvertently hurts fairness. It establishes a bound linking group-specific loss increases to gradient norms and Hessian eigenvalues, and empirically shows minority groups suffer larger accuracy drops as more activations are linearized across UTKFace, SVHN, and CIFAR-10 with ResNet architectures. A mitigation strategy based on fairness-aware finetuning using a Lagrangian regularizer is proposed and shown to improve minority accuracy with minimal cost to overall performance. The results reveal a substantive privacy-computationTradeoff, underscoring the need for fairness-aware design in private inference systems.

Abstract

Ensuring privacy-preserving inference on cryptographically secure data is a well-known computational challenge. To alleviate the bottleneck of costly cryptographic computations in non-linear activations, recent methods have suggested linearizing a targeted portion of these activations in neural networks. This technique results in significantly reduced runtimes with often negligible impacts on accuracy. In this paper, we demonstrate that such computational benefits may lead to increased fairness costs. Specifically, we find that reducing the number of ReLU activations disproportionately decreases the accuracy for minority groups compared to majority groups. To explain these observations, we provide a mathematical interpretation under restricted assumptions about the nature of the decision boundary, while also showing the prevalence of this problem across widely used datasets and architectures. Finally, we show how a simple procedure altering the fine-tuning step for linearized models can serve as an effective mitigation strategy.
Paper Structure (24 sections, 5 theorems, 18 equations, 15 figures, 1 algorithm)

This paper contains 24 sections, 5 theorems, 18 equations, 15 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Settings
  4. Why Network Linearization May Increase Unfairness?
  5. Decision Boundary Approximation and Fairness
  6. Empirical Results on the Fairness Analysis
  7. Impact on Accuracy
  8. Gradient Norms and Fairness
  9. Distance to the Decision Boundary and Fairness
  10. Mitigation and Impact on Fairness
  11. Discussion
  12. Conclusion
  13. Additional Theoretical Results
  14. Underrepresented groups have larger gradients.
  15. An upper-bound for the residual loss.
  16. ...and 9 more sections

Key Result

Proposition 4.1

Consider a function $f\in \mathcal{F}$ and let $f_{n}^{\star}$ be its optimal approximation through a piecewise linear function with $n$ segments. Then, the approximation error $\Delta( f_{n}^{\star})$ is bounded by the number of its segments, and it decreases at a rate of $O(\frac{1}{n^{2}})$.

Figures (15)

  • Figure 1: *r18 accuracy on *utk across various ReLU linearization budgets using *snl ChoJRGH2022ICML. 100% ReLUs corresponds to the original model. Subgroup sample sizes are shown above the corresponding bars. The accuracy for the majority group remains almost unchanged while other groups, in particular the minority one, are diversely impacted.
  • Figure 2: Decision boundary estimated by a relu model (left) and a linearized model (right). The ground truth decision boundary (black dotted line) separates majority (blue) from minority (red) samples. The linearized model shows an inferior approximation of the decision boundary, and therefore a lower prediction accuracy. Moreover, its decision boundary is deeper into to the minority class resulting in accuracy disparities.
  • Figure 3: Grad Norms for classification on UTKFace with race labels using ResNet18 and SNL-based ChoJRGH2022ICML relu linearization across various relu budgets. Subgroup sizes are reported on top of each bar group.
  • Figure 4: ResNet-18: Highest eigenvalues of Hessians for UTKFace with race labels obtained from the base model.
  • Figure 5: Global test accuracy on UTKFace with age labels using ResNet18 for snl and dr. The red horizontal line represents the original (no relu linearization) global test accuracy.
  • ...and 10 more figures

Theorems & Definitions (7)

  • Proposition 4.1
  • Proposition 4.2
  • Proposition 4.3
  • Theorem 4.4
  • Proposition 4.5
  • proof
  • proof