1,404 research outputs found
Classification and Geometry of General Perceptual Manifolds
Perceptual manifolds arise when a neural population responds to an ensemble
of sensory signals associated with different physical features (e.g.,
orientation, pose, scale, location, and intensity) of the same perceptual
object. Object recognition and discrimination requires classifying the
manifolds in a manner that is insensitive to variability within a manifold. How
neuronal systems give rise to invariant object classification and recognition
is a fundamental problem in brain theory as well as in machine learning. Here
we study the ability of a readout network to classify objects from their
perceptual manifold representations. We develop a statistical mechanical theory
for the linear classification of manifolds with arbitrary geometry revealing a
remarkable relation to the mathematics of conic decomposition. Novel
geometrical measures of manifold radius and manifold dimension are introduced
which can explain the classification capacity for manifolds of various
geometries. The general theory is demonstrated on a number of representative
manifolds, including L2 ellipsoids prototypical of strictly convex manifolds,
L1 balls representing polytopes consisting of finite sample points, and
orientation manifolds which arise from neurons tuned to respond to a continuous
angle variable, such as object orientation. The effects of label sparsity on
the classification capacity of manifolds are elucidated, revealing a scaling
relation between label sparsity and manifold radius. Theoretical predictions
are corroborated by numerical simulations using recently developed algorithms
to compute maximum margin solutions for manifold dichotomies. Our theory and
its extensions provide a powerful and rich framework for applying statistical
mechanics of linear classification to data arising from neuronal responses to
object stimuli, as well as to artificial deep networks trained for object
recognition tasks.Comment: 24 pages, 12 figures, Supplementary Material
Not all adversarial examples require a complex defense : identifying over-optimized adversarial examples with IQR-based logit thresholding
Detecting adversarial examples currently stands as one of the biggest challenges in the field of deep learning. Adversarial attacks, which produce adversarial examples, increase the prediction likelihood of a target class for a particular data point. During this process, the adversarial example can be further optimized, even when it has already been wrongly classified with 100% confidence, thus making the adversarial example even more difficult to detect. For this kind of adversarial examples, which we refer to as over-optimized adversarial examples, we discovered that the logits of the model provide solid clues on whether the data point at hand is adversarial or genuine. In this context, we first discuss the masking effect of the softmax function for the prediction made and explain why the logits of the model are more useful in detecting over-optimized adversarial examples. To identify this type of adversarial examples in practice, we propose a non-parametric and computationally efficient method which relies on interquartile range, with this method becoming more effective as the image resolution increases. We support our observations throughout the paper with detailed experiments for different datasets (MNIST, CIFAR-10, and ImageNet) and several architectures
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