相关论文: Mathematical Analysis of Adversarial Attacks

Deep neural networks have been shown to be fooled rather easily using adversarial attack algorithms. Practical methods such as adversarial patches have been shown to be extremely effective in causing misclassification. However, these…

Recent studies show that the state-of-the-art deep neural networks (DNNs) are vulnerable to adversarial examples, resulting from small-magnitude perturbations added to the input. Given that that emerging physical systems are using DNNs in…

We study the conjectured relationship between the implicit regularization in neural networks, trained with gradient-based methods, and rank minimization of their weight matrices. Previously, it was proved that for linear networks (of depth…

Adversarial attacks pose a severe security threat to the state-of-the-art speaker identification systems, thereby making it vital to propose countermeasures against them. Building on our previous work that used representation learning to…

Humans rely heavily on shape information to recognize objects. Conversely, convolutional neural networks (CNNs) are biased more towards texture. This is perhaps the main reason why CNNs are vulnerable to adversarial examples. Here, we…

In this paper, we consider malware classification using deep learning techniques and image-based features. We employ a wide variety of deep learning techniques, including multilayer perceptrons (MLP), convolutional neural networks (CNN),…

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training…

A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance…

Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima. The implicit bias refers to the limiting global minimum that is attained by a common optimization…

Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on training two-layer ReLU neural networks in a…

In this paper, we first identify activation shift, a simple but remarkable phenomenon in a neural network in which the preactivation value of a neuron has non-zero mean that depends on the angle between the weight vector of the neuron and…

With the Rise of Adversarial Machine Learning and increasingly robust adversarial attacks, the security of applications utilizing the power of Machine Learning has been questioned. Over the past few years, applications of Deep Learning…

This research project studies the impact of convolutional neural networks (CNN) in image classification tasks. We explore different architectures and training configurations with the use of ReLUs, Nesterov's accelerated gradient, dropout…

We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on $n$ data points. Our main contribution leverages the high dimensionality of the ambient space, which implies low correlation of the input samples, to…

Deep neural networks have shown to be very vulnerable to adversarial examples crafted by adding human-imperceptible perturbations to benign inputs. After achieving impressive attack success rates in the white-box setting, more focus is…

By adding carefully crafted perturbations to input images, adversarial examples (AEs) can be generated to mislead neural-network-based image classifiers. $L_2$ adversarial perturbations by Carlini and Wagner (CW) are among the most…

The convolutional neural network is the crucial tool for the recent success of deep learning based methods on various computer vision tasks like classification, segmentation, and detection. Convolutional neural networks achieved…

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…

The problem of quantizing the activations of a deep neural network is considered. An examination of the popular binary quantization approach shows that this consists of approximating a classical non-linearity, the hyperbolic tangent, by two…

We continue a long line of research aimed at proving convergence of depth 2 neural networks, trained via gradient descent, to a global minimum. Like in many previous works, our model has the following features: regression with quadratic…