相关论文: Dual Graphs of Polyhedral Decompositions for the D…

Researchers typically investigate neural network representations by examining activation outputs for one or more layers of a network. Here, we investigate the potential for ReLU activation patterns (encoded as bit vectors) to aid in…

A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph. We show that while this dual graph is a coarse quantization of input space, it is sufficiently robust that it can be…

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the…

Training neural networks which are robust to adversarial attacks remains an important problem in deep learning, especially as heavily overparameterized models are adopted in safety-critical settings. Drawing from recent work which…

We develop a novel theoretical framework for analyzing ReLU neural networks through the lens of a combinatorial object we term the ReLU Transition Graph (RTG). In this graph, each node corresponds to a linear region induced by the network's…

A neural network consisting of piecewise affine building blocks, such as fully-connected layers and ReLU activations, is itself a piecewise affine function supported on a polyhedral complex. This complex has been previously studied to…

In the past, research on a single low dimensional activation function in networks has led to internal covariate shift and gradient deviation problems. A relatively small research area is how to use function combinations to provide property…

Classification of biological images is an important task with crucial application in many fields, such as cell phenotypes recognition, detection of cell organelles and histopathological classification, and it might help in early medical…

The existence of adversarial attacks on convolutional neural networks (CNN) questions the fitness of such models for serious applications. The attacks manipulate an input image such that misclassification is evoked while still looking…

We study the realization map of deep ReLU networks, focusing on when a function determines its parameters up to scaling and permutation. To analyze hidden redundancies beyond these standard symmetries, we introduce a framework based on…

Deep neural networks (DNNs) are playing key roles in various artificial intelligence applications such as image classification and object recognition. However, a growing number of studies have shown that there exist adversarial examples in…

We extend the ReLU Transition Graph (RTG) framework into a comprehensive graph-theoretic model for understanding deep ReLU networks. In this model, each node represents a linear activation region, and edges connect regions that differ by a…

Adversarial attacks expose a fundamental vulnerability in modern deep vision models by exploiting their dependence on dense, pixel-level representations that are highly sensitive to imperceptible perturbations. Traditional defense…

Recently, researchers have started decomposing deep neural network models according to their semantics or functions. Recent work has shown the effectiveness of decomposed functional blocks for defending adversarial attacks, which add small…

We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out- put distribution, we compare the differences in graphs…

In recent years, neural networks have become the default choice for image classification and many other learning tasks, even though they are vulnerable to so-called adversarial attacks. To increase their robustness against these attacks,…

Adversarial examples raise questions about whether neural network models are sensitive to the same visual features as humans. In this paper, we first detect adversarial examples or otherwise corrupted images based on a class-conditional…

Graph deep learning models, such as graph convolutional networks (GCN) achieve remarkable performance for tasks on graph data. Similar to other types of deep models, graph deep learning models often suffer from adversarial attacks. However,…

A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these…

Despite the success of convolutional neural networks (CNNs) in many computer vision and image analysis tasks, they remain vulnerable against so-called adversarial attacks: Small, crafted perturbations in the input images can lead to false…