10,472 research outputs found
Robustness Verification of Support Vector Machines
We study the problem of formally verifying the robustness to adversarial
examples of support vector machines (SVMs), a major machine learning model for
classification and regression tasks. Following a recent stream of works on
formal robustness verification of (deep) neural networks, our approach relies
on a sound abstract version of a given SVM classifier to be used for checking
its robustness. This methodology is parametric on a given numerical abstraction
of real values and, analogously to the case of neural networks, needs neither
abstract least upper bounds nor widening operators on this abstraction. The
standard interval domain provides a simple instantiation of our abstraction
technique, which is enhanced with the domain of reduced affine forms, which is
an efficient abstraction of the zonotope abstract domain. This robustness
verification technique has been fully implemented and experimentally evaluated
on SVMs based on linear and nonlinear (polynomial and radial basis function)
kernels, which have been trained on the popular MNIST dataset of images and on
the recent and more challenging Fashion-MNIST dataset. The experimental results
of our prototype SVM robustness verifier appear to be encouraging: this
automated verification is fast, scalable and shows significantly high
percentages of provable robustness on the test set of MNIST, in particular
compared to the analogous provable robustness of neural networks
End-to-End Kernel Learning with Supervised Convolutional Kernel Networks
In this paper, we introduce a new image representation based on a multilayer
kernel machine. Unlike traditional kernel methods where data representation is
decoupled from the prediction task, we learn how to shape the kernel with
supervision. We proceed by first proposing improvements of the
recently-introduced convolutional kernel networks (CKNs) in the context of
unsupervised learning; then, we derive backpropagation rules to take advantage
of labeled training data. The resulting model is a new type of convolutional
neural network, where optimizing the filters at each layer is equivalent to
learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We
show that our method achieves reasonably competitive performance for image
classification on some standard "deep learning" datasets such as CIFAR-10 and
SVHN, and also for image super-resolution, demonstrating the applicability of
our approach to a large variety of image-related tasks.Comment: to appear in Advances in Neural Information Processing Systems (NIPS
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