Finding the exact robust test error is a good way to compare the robustness of neural networks, but it is a difficult task even on small networks and datasets like MNIST. However, finding reasonable lower and upper bounds is possible and can be done using either complete methods or attacks. On the one hand, complete methods such as Mixed Integer Program (MIP) give exact robust test accuracy but are time-consuming. On the other hand, attacks are usually fast but tend to perform badly against robust networks and underestimate the lower bound on the robust test error. The purpose of this paper is to present a novel attack method that is both fast and gives better lower bounds than previous attacks. This method exploits the algebraic properties of networks with piecewise linear activation functions to partition the input space in such a way that for each subset of that partition, finding the local optimal adversarial example is done by solving a linear program. Moving from one subset to another is done using classical gradient-based attack tools. To evaluate the quality of the produced adversarial examples, we compare our lower bound on the robust test error to the one previously found. The results found are satisfying in the sense that it does better than previous lower bounds on several models and finds adversarial examples that the MIP failed to expose before reaching its time limit.

This paper presents a theoretical foundation for an SVM solver in Kreĭn spaces. Up to now, all methods are based either on the matrix correction, or on non-convex minimization, or on feature-space embedding. Here we justify and evaluate a solution that uses the original (indefinite) similarity measure, in the original Kreĭn space. This solution is the result of a stabilization procedure. We establish the correspondence between the stabilization problem (which has to be solved) and a classical SVM based on minimization (which is easy to solve). We provide simple equations to go from one to the other (in both directions). This link between stabilization and minimization problems is the key to obtain a solution in the original Kreĭn space. Using KSVM, one can solve SVM with usually troublesome kernels (large negative eigenvalues or large numbers of negative eigenvalues). We show experiments showing that our algorithm KSVM outperforms all previously proposed approaches to deal with indefinite matrices in SVM-like kernel methods.

The recent technological progress contribute to a huge increase of 3D models available in digital forms. Numerous applications were developed to deal with this amount of information, especially for 3D shape retrieval. One of the main issues is to break the semantic gap between shapes wanted by users and shapes returned by retrieval methods. In this paper, we propose an algorithm to address this question. 3D shapes that match a semantic query are retrieved in three main steps. First, the semantic query is described by a sample of 3D shapes designed under uncertainty. Second, we learn the concept behind this sample. Then, we use a state-of-the-art retrieval method to return real-world 3D shapes that match this semantic query. We present results from an experiment. Three semantic concepts are learned and 3D shapes from SHREC’07 database that match each concept are retrieved using our algorithm. The result are good and promising.

Recent face detectors used in human robot interaction are boosted cascades. These cascades can detect upright faces but are very sensible to occlusions. We propose a generic framework to handle occlusions at prediction time in a boosted cascade. The contribution is a probabilistic formulation of the cascade structure that considers the uncertainty introduced by missing weak classifiers. This new formulation involves two problems: (1) the approximation of posterior probabilities on each level and (2) the computation of thresholds on these probabilities to make a decision. Both problems are studied and solutions are proposed and evaluated. The method is then applied on the problem of occluded faces detection. Experimental results are provided on classic databases to evaluate the proposed solution related to the basic one.

In a recently published paper in JMLR, Tsang et al. (2005) present an algorithm for SVM called Core Vector Machines (CVM) and illustrate its performances through comparisons with other SVM solvers. After reading the CVM paper we were surprised by some of the reported results. In order to clarify the matter, we decided to reproduce some of the experiments. It turns out that to some extent, our results contradict those reported. Reasons of these different behaviors are given through the analysis of the stopping criterion.