Related papers: Computer Validation of Neural Network Dynamics: A …

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living…

Neural networks have achieved state-of-the-art performance in solving many problems, including many applications in safety/security-critical systems. Researchers also discovered multiple security issues associated with neural networks. One…

In recent years numerous methods have been developed to formally verify the robustness of deep neural networks (DNNs). Though the proposed techniques are effective in providing mathematical guarantees about the DNNs behavior, it is not…

Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many-body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign…

The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…

Despite their success in massive engineering applications, deep neural networks are vulnerable to various perturbations due to their black-box nature. Recent study has shown that a deep neural network can misclassify the data even if the…

Neural network pruning is an essential approach for reducing the computational complexity of deep models so that they can be well deployed on resource-limited devices. Compared with conventional methods, the recently developed dynamic…

This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…

This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…

We consider artificial neurons which will update their weight coefficients with an internal rule based on backpropagation, rather than using it as an external training procedure. To achieve this we include the backpropagation error estimate…

Knowledge tracing---where a machine models the knowledge of a student as they interact with coursework---is a well established problem in computer supported education. Though effectively modeling student knowledge would have high…

Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent…

The advent of recurrent neural networks for handwriting recognition marked an important milestone reaching impressive recognition accuracies despite the great variability that we observe across different writing styles. Sequential…

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…

With the rise of deep learning technology in practical applications, Convolutional Neural Networks (CNNs) have been able to assist humans in solving many real-world problems. To enhance the performance of CNNs, numerous network…

Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…

Training networks consisting of biophysically accurate neuron models could allow for new insights into how brain circuits can organize and solve tasks. We begin by analyzing the extent to which the central algorithm for neural network…

We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm…

Deep learning methods can be used to produce control policies, but certifying their safety is challenging. The resulting networks are nonlinear and often very large. In response to this challenge, we present OVERT: a sound algorithm for…