Related papers: Probabilistically Tightened Linear Relaxation-base…
Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated…
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,…
In this paper, we focus on the relaxed proximal point algorithm (RPPA) for solving convex (possibly nonsmooth) optimization problems. We conduct a comprehensive study on three types of relaxation schedules: (i) constant schedule with…
The rapid growth of deep learning applications in real life is accompanied by severe safety concerns. To mitigate this uneasy phenomenon, much research has been done providing reliable evaluations of the fragility level in different deep…
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…
Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…
We show that for constraint satisfaction problems (CSPs), sub-exponential size linear programming relaxations are as powerful as $n^{\Omega(1)}$-rounds of the Sherali-Adams linear programming hierarchy. As a corollary, we obtain…
ReLU neural networks trained as surrogate models can be embedded exactly in mixed-integer linear programs (MILPs), enabling global optimization over the learned function. The tractability of the resulting MILP depends on structural…
Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to…
Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several neural network…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial input uncertainty, but researchers…
State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…
We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as…
Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…
Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…
Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend…
Post-hoc explanation methods are used with the intent of providing insights about neural networks and are sometimes said to help engender trust in their outputs. However, popular explanations methods have been found to be fragile to minor…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…
Verifiers are auxiliary models that assess the correctness of outputs generated by base large language models (LLMs). They play a crucial role in many strategies for solving reasoning-intensive problems with LLMs. Typically, verifiers are…