We introduce a nonlinear model, Masked Sparse Bottleneck Centroid-Encoder (MSBCE), for determining the features that discriminate between two or more classes. The algorithm aims to extract discriminatory features in groups while reconstructing the class centroids in the ambient space and simultaneously use additional penalty terms in the bottleneck layer to decrease within-class scatter and increase the separation of different class centroids. The model has a sparsity-promoting layer (SPL) with a one-to-one connection to the input layer. Along with the primary objective, we minimize the $l_{2,1}$-norm of the sparse layer, which filters out unnecessary features from input data. During training, we update class centroids by taking the Hadamard product of the centroids and weights of the sparse layer, thus masking the irrelevant features from the target. Therefore the proposed method learns to reconstruct the critical features of the class centroids. The algorithm is applied to various real-world data sets, including high-dimensional biological, image, speech, and accelerometer sensor data. We compared our method to different state-of-the-art feature selection techniques, including supervised Concrete Autoencoders (SCAE), Feature Selection Networks (FsNet), Stochastic Gates (STG), and LassoNet. We empirically showed that MSBCE features often produced better classification accuracy than other methods on the sequester test sets, setting new state-of-the-art results. Apart from achieving state-of-the-art results, this is the first time feature selection is done on two high-energy particle physics data sets, SUSY and HIGGS, with 4.5 million and 10 million samples, respectively. The selected features, which are only 25-30% of the total number of variables, attained almost similar prediction rates compared to all features.

Previous work has shown that a neural network with the rectified linear unit (ReLU) activation function leads to a convex polyhedral decomposition of the input space. These decompositions can be represented by a dual graph with vertices corresponding to polyhedra and edges corresponding to polyhedra sharing a facet, which is a subgraph of a Hamming graph. This paper illustrates how one can utilize the dual graph to detect and analyze adversarial attacks in the context of digital images. When an image passes through a network containing ReLU nodes, the firing or non-firing at a node can be encoded as a bit (1 for ReLU activation, 0 for ReLU non-activation). The sequence of all bit activations identifies the image with a bit vector, which identifies it with a polyhedron in the decomposition and, in turn, identifies it with a vertex in the dual graph. We identify ReLU bits that are discriminators between non-adversarial and adversarial images and examine how well collections of these discriminators can ensemble vote to build an adversarial image detector. Specifically, we examine the similarities and differences of ReLU bit vectors for adversarial images, and their non-adversarial counterparts, using a pre-trained ResNet-50 architecture. While this paper focuses on adversarial digital images, ResNet-50 architecture, and the ReLU activation function, our methods extend to other network architectures, activation functions, and types of datasets.

Dimensionality-reduction methods are a fundamental tool in the analysis of large datasets. These algorithms work on the assumption that the "intrinsic dimension" of the data is generally much smaller than the ambient dimension in which it is collected. Alongside their usual purpose of mapping data into a smaller-dimensional space with minimal information loss, dimensionality-reduction techniques implicitly or explicitly provide information about the dimension of the dataset.In this paper, we propose a new statistic that we call the kappa-profile for analysis of large datasets. The kappa-profile arises from a dimensionality-reduction optimization problem: namely that of finding a projection that optimally preserves the secants between points in the dataset. From this optimal projection we extract kappa, the norm of the shortest projected secant from among the set of all normalized secants. This kappa can be computed for any dimension k; thus the tuple of kappa values (indexed by dimension) becomes a kappa-profile. Algorithms such as the Secant-Avoidance Projection algorithm and the Hierarchical Secant-Avoidance Projection algorithm provide a computationally feasible means of estimating the kappa-profile for large datasets, and thus a method of understanding and monitoring their behavior. As we demonstrate in this paper, the kappa-profile serves as a useful statistic in several representative settings: weather data, soundscape data, and dynamical systems data.