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In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

Anomaly detection is the problem of recognizing abnormal inputs based on the seen examples of normal data. Despite recent advances of deep learning in recognizing image anomalies, these methods still prove incapable of handling complex…

A deep convolutional neural network (CNN) has been widely used in image classification and gives better classification accuracy than the other techniques. The softmax cross-entropy loss function is often used for classification tasks. There…

Surface anomaly detection plays an important quality control role in many manufacturing industries to reduce scrap production. Machine-based visual inspections have been utilized in recent years to conduct this task instead of human…

We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…

Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…

From a non-central panorama, 3D lines can be recovered by geometric reasoning. However, their sensitivity to noise and the complex geometric modeling required has led these panoramas being very little investigated. In this work we present a…

Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…

In deep metric learning, the Triplet Loss has emerged as a popular method to learn many computer vision and natural language processing tasks such as facial recognition, object detection, and visual-semantic embeddings. One issue that…

Understanding the structure of loss landscape of deep neural networks (DNNs)is obviously important. In this work, we prove an embedding principle that the loss landscape of a DNN "contains" all the critical points of all the narrower DNNs.…

Neuron reconstruction is essential to generate exquisite neuron connectivity map for understanding brain function. Despite the significant amount of effect that has been made on automatic reconstruction methods, manual tracing by…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

The fast growing deep learning technologies have become the main solution of many machine learning problems for medical image analysis. Deep convolution neural networks (CNNs), as one of the most important branch of the deep learning…

Image restoration, including image denoising, super resolution, inpainting, and so on, is a well-studied problem in computer vision and image processing, as well as a test bed for low-level image modeling algorithms. In this work, we…

Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision…

Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…

Thousands of people suffer from cranial injuries every year. They require personalized implants that need to be designed and manufactured before the reconstruction surgery. The manual design is expensive and time-consuming leading to…