Related papers: Optimized Symbolic Interval Propagation for Neural…

Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning''…

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D…

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…

Deep neural networks have been widely adopted in many vision and robotics applications with visual inputs. It is essential to verify its robustness against semantic transformation perturbations, such as brightness and contrast. However,…

To create usable and deployable Artificial Intelligence (AI) systems, there requires a level of assurance in performance under many different conditions. Many times, deployed machine learning systems will require more classic logic and…

Deep neural networks (DNN) has received increasing attention in machine learning applications in the last several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN…

Formal verification has emerged as a promising method to ensure the safety and reliability of neural networks. However, many relevant properties, such as fairness or global robustness, pertain to the entire input space. If one applies…

Learning deep neural network (DNN) classifier with noisy labels is a challenging task because the DNN can easily over-fit on these noisy labels due to its high capability. In this paper, we present a very simple but effective training…

Deep Neural Networks (DNNs) have recently shown state of the art performance on semantic segmentation tasks, however, they still suffer from problems of poor boundary localization and spatial fragmented predictions. The difficulties lie in…

Deep neural networks (DNNs) have been introduced for designing wireless policies by approximating the mappings from environmental parameters to solutions of optimization problems. Considering that labeled training samples are hard to…

Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for…

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including…

The expressiveness of deep neural network (DNN) is a perspective to understandthe surprising performance of DNN. The number of linear regions, i.e. pieces thata piece-wise-linear function represented by a DNN, is generally used to…

Training neural networks to be certifiably robust is critical to ensure their safety against adversarial attacks. However, it is currently very difficult to train a neural network that is both accurate and certifiably robust. In this work…

Deep neural networks (DNNs) have become one of the enabling technologies in many safety-critical applications, e.g., autonomous driving and medical image analysis. DNN systems, however, suffer from various kinds of threats, such as…

In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP)…

Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty…

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…

Neuro-Symbolic Artificial Intelligence (NeSy AI) has emerged as a promising direction for integrating neural learning with symbolic reasoning. Typically, in the probabilistic variant of such systems, a neural network first extracts a set of…