Draft:Adversarial geometry
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Adversarial geometry is a field of study that explores the intersection of geometry and adversarial strategies, often in the context of machine learning and artificial intelligence (AI). It focuses on understanding how geometric structures can be manipulated or exploited to create adversarial examples—inputs designed to deceive AI models into making incorrect predictions or classifications.[1] The study of adversarial geometry involves analyzing the vulnerabilities in the geometric representations of data and designing methods to either enhance the robustness of models against adversarial attacks or create sophisticated adversarial strategies.[2] It has applications in various domains such as computer vision, natural language processing, and autonomous systems, where the spatial properties of data can be leveraged for both attack and defense.[3]
Background
[edit]The study of adversarial geometry emerged from the field of adversarial machine learning, which investigates how inputs can be intentionally crafted to fool neural networks and other machine learning models.[4] The first prominent research on adversarial examples was conducted by Ian Goodfellow, who demonstrated that small perturbations to input data could cause a machine learning model to make incorrect predictions.[1] These perturbations, though imperceptible to humans, exploit the high-dimensional space in which neural networks operate, revealing geometric vulnerabilities.
The concept of adversarial geometry arises from this understanding, focusing specifically on the geometric structure of decision boundaries in neural networks. The decision boundary is the surface in high-dimensional space that separates different classes predicted by a model.[5] Adversarial geometry examines how these boundaries can be altered by slight changes in the input data, leading to misclassification. This understanding has led to the development of new techniques for creating adversarial examples and improving model robustness through adversarial training and regularization methods.[2]
Formal Definition
[edit]Adversarial geometry is concerned with the geometric properties of the decision boundaries in machine learning models, particularly neural networks. In formal terms, a machine learning classifier can be considered as a function , where represents the input space, and denotes the number of classes.[6]
References
[edit]- ^ a b Goodfellow, I. J.; Shlens, J.; Szegedy, C. (2015). "Explaining and harnessing adversarial examples". arXiv:1412.6572 [stat.ML].
- ^ a b Madry, A.; Makelov, A.; Schmidt, L.; Tsipras, D.; Vladu, A. (2018). "Towards deep learning models resistant to adversarial attacks". arXiv:1706.06083 [stat.ML].
- ^ Papernot, N.; McDaniel, P.; Goodfellow, I. (2016). "Practical black-box attacks against machine learning". arXiv:1602.02697 [cs.CR].
- ^ Szegedy, C.; Zaremba, W.; Sutskever, I.; Bruna, J.; Erhan, D.; Goodfellow, I.; Fergus, R. (2014). "Intriguing properties of neural networks". arXiv:1312.6199 [cs.CV].
- ^ Fawzi, A.; Moosavi-Dezfooli, S. M.; Frossard, P. (2016). "Robustness of classifiers: from adversarial to random noise". arXiv:1608.08967 [cs.LG].
- ^ Szegedy, C.; Zaremba, W.; Sutskever, I. (2014). "Intriguing properties of neural networks". arXiv:1312.6199 [cs.CV].