Related papers: Hierarchical Verification for Adversarial Robustne…

In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when…

We present CLEAR (Cross-Layer Exploration for Architecting Resilience), a first of its kind framework which overcomes a major challenge in the design of digital systems that are resilient to reliability failures: achieve desired resilience…

Recent point cloud completion models, including transformer-based, denoising-based, and other state-of-the-art approaches, generate globally plausible shapes from partial inputs but often leave local geometric inconsistencies. We propose…

Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the…

This paper addresses the problem of localization, which is inherently non-convex and non-smooth in a federated setting where the data is distributed across a multitude of devices. Due to the decentralized nature of federated environments,…

We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage…

High Energy Physics (HEP) distributed computing infrastructures require automatic tools to monitor, analyze and react to potential security incidents. These tools should collect and inspect data such as resource consumption, logs and…

We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…

We investigate to what extent it is possible to solve linear inverse problems with $ReLu$ networks. Due to the scaling invariance arising from the linearity, an optimal reconstruction function $f$ for such a problem is positive homogeneous,…

We consider a problem in which the trajectory of a mobile 3D sensor must be optimized so that certain objects are both found in the overall scene and covered by the point cloud, as fast as possible. This problem is called target search and…

A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…

In the field of high-energy physics, deep learning algorithms continue to gain in relevance and provide performance improvements over traditional methods, for example when identifying rare signals or finding complex patterns. From an…

Recent Progress has shown that exploitation of hidden layer neurons in convolution neural networks incorporating with a carefully designed activation function can yield better classification results in the field of computer vision. The…

Remote sensing scene classification deals with the problem of classifying land use/cover of a region from images. To predict the development and socioeconomic structures of cities, the status of land use in regions is tracked by the…

Over the last decade, the development of deep image classification networks has mostly been driven by the search for the best performance in terms of classification accuracy on standardized benchmarks like ImageNet. More recently, this…

Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real linear system $Ax=b$, where $A$ is an $m \times n$ matrix of…

The implicit bias of gradient-based training algorithms has been considered mostly beneficial as it leads to trained networks that often generalize well. However, Frei et al. (2023) show that such implicit bias can harm adversarial…

Compositional verification algorithms are well-studied in the context of model checking. Properly selecting components for verification is important for efficiency, yet has received comparatively less attention. In this paper, we address…

Recent advances in adversarial attacks uncover the intrinsic vulnerability of modern deep neural networks. Since then, extensive efforts have been devoted to enhancing the robustness of deep networks via specialized learning algorithms and…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…