arxiv_ml 98% Match Research Paper Machine learning researchers,AI security experts,Deep learning engineers,Theoretical computer scientists 20 hours ago

Feature compression is the root cause of adversarial fragility in neural network classifiers

ai-safety › robustness

📄 Abstract

Abstract: In this paper, we uniquely study the adversarial robustness of deep neural networks (NN) for classification tasks against that of optimal classifiers. We look at the smallest magnitude of possible additive perturbations that can change a classifier's output. We provide a matrix-theoretic explanation of the adversarial fragility of deep neural networks for classification. In particular, our theoretical results show that a neural network's adversarial robustness can degrade as the input dimension $d$ increases. Analytically, we show that neural networks' adversarial robustness can be only $1/\sqrt{d}$ of the best possible adversarial robustness of optimal classifiers. Our theories match remarkably well with numerical experiments of practically trained NN, including NN for ImageNet images. The matrix-theoretic explanation is consistent with an earlier information-theoretic feature-compression-based explanation for the adversarial fragility of neural networks.

Key Contributions

This paper provides a novel matrix-theoretic explanation for the adversarial fragility of deep neural networks, showing that their robustness can degrade as input dimension increases, potentially being only $1/\sqrt{d}$ of optimal classifiers. This theoretical insight aligns with and strengthens previous feature-compression-based explanations, offering a deeper understanding of why neural networks are susceptible to adversarial perturbations.

Business Value

Improving the robustness of AI systems against adversarial attacks is critical for deploying them in security-sensitive applications like autonomous driving, medical diagnosis, and financial fraud detection, thereby increasing trust and reliability.

Paper Metadata

Innovation Type

Theoretical

Deployment Feasibility

The findings are theoretical and explanatory, guiding future research and development towards more robust architectures rather than providing a direct deployment solution.

Limitations Addressed

Adversarial fragility of neural networks,Lack of theoretical understanding of robustness degradation,Gap in robustness between NNs and optimal classifiers

Technical Tags

adversarial robustnessneural networksclassificationperturbationsmatrix theoryfeature compressioninput dimensionoptimal classifiers

Research Topics

Adversarial Machine LearningRobustness of Neural NetworksTheoretical Machine LearningDeep Learning AnalysisClassification Theory

Methods & Architectures

Matrix-theoretic analysisTheoretical derivationNumerical experiments Neural Networks (general)

Applications & Tasks

Computer Vision Natural Language Processing Any domain using neural network classifiers Adversarial fragilityDegradation of robustness with input dimensionComparison to optimal classifiers Understanding adversarial robustnessExplaining adversarial fragilityImproving robustness of neural networks

Datasets & Benchmarks

Datasets

ImageNet

Related Fields

Machine LearningDeep LearningComputer VisionCybersecurityOptimization

Keywords

Adversarial RobustnessNeural NetworksDeep LearningClassificationAdversarial AttacksPerturbationsFeature CompressionInput DimensionMatrix TheoryOptimal ClassifierMachine Learning TheoryCybersecurity

Academic Context

#Adversarial Machine Learning#Robustness of Neural Networks#Theoretical Machine Learning#Deep Learning Analysis#Classification Theory

Commercial Potential

Potential Products

More robust AI models for critical applicationsAdversarial defense libraries

Target Industries

CybersecurityAutomotiveHealthcareFinanceTechnology

Use Case Examples

Developing self-driving car perception systems resistant to adversarial visual noiseCreating medical image analysis tools that are not fooled by subtle adversarial manipulations

Competitive Edge

Provides a fundamental theoretical explanation for adversarial fragility, complementing empirical findings and guiding the development of more robust architectures compared to current ad-hoc defense mechanisms.

Market Opportunity

Significant market interest in AI security and robustness.

Revenue Models

Consultingdevelopment of robust AI solutions

Resource Requirements

Compute Needs

Low (theoretical analysis), High (for numerical experiments)

Data Requirements

Standard image datasets (e.g., ImageNet) for numerical validation

Deployment Constraints

Theoretical insights need to be translated into practical architectural changes or training methods.

Scalability

The theoretical findings apply to networks of varying sizes and dimensions.

Regulatory Considerations

Ensuring AI safety and reliability in regulated industries.

Production Readiness

Maturity Level

Theoretical Foundation

Time to Market

Ongoing research and development

Patent Potential

Low (theoretical explanation)

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