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Publication# Measuring Robustness of Classifiers to Geometric Transformations

Abstract

For many classification tasks, the ideal classifier should be invariant to geometric transformations such as changing the view angle. However, this cannot be said decisively for the state-of-the-art image classifiers, such as convolutional neural networks. Mainly, this is because there is a lack of methods for measuring the transformation invariance in them, especially for transformations with higher dimensions. In this project, we are proposing two algorithms to do such measurement. The first one, Manifool, uses the structure of the image appearance manifold for finding small enough transformation examples and uses these to compute the invariance of the classifier. Second one, the iterative projection algorithm, uses adversarial perturbation methods in neural networks to find the fooling examples in the given transformation set. We compare these methods to similar algorithms in the areas of speed and validity, and use them to show that transformation invariance increases with the depth of the neural networks, even in reasonably deep networks. Overall, we believe that these two algorithms can be used for analysis of different architectures and can help to build more robust classifiers.

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Transformation matrix

In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.

Transformation (function)

In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations.

Types of artificial neural networks

There are many types of artificial neural networks (ANN). Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research.

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