Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds

In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on $S^3$ with ${\rm Ric} = 2 F^2$, ${\rm Ric}=0$ and ${\rm Ric}=- 2 F^2$, respectively. This family of metrics provide an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not

Confidence bands for a log-concave density

We present a new approach for inference about a log-concave distribution: Instead of using the method of maximum likelihood, we propose to incorporate the log-concavity constraint in an appropriate nonparametric confidence set for the cdf $F$. This approach has the advantage that it automatically provides a measure of statistical uncertainty and it thus overcomes a marked limitation of the maximum likelihood estimate. In particular, we show how to construct confidence bands for the density that have a finite sample guaranteed confidence level. The nonparametric confidence set for $F$ which we introduce here has attractive computational and statistical properties: It allows to bring modern tools from optimization to bear on this problem via difference of convex programming, and it results in optimal statistical inference. We show that the width of the resulting confidence bands converges at nearly the parametric $n^{-\frac{1}{2}}$ rate when the log density is $k$-affine.Comment: Added more experiments, other minor change

In ChatGPT We Trust? Measuring and Characterizing the Reliability of ChatGPT

The way users acquire information is undergoing a paradigm shift with the advent of ChatGPT. Unlike conventional search engines, ChatGPT retrieves knowledge from the model itself and generates answers for users. ChatGPT's impressive question-answering (QA) capability has attracted more than 100 million users within a short period of time but has also raised concerns regarding its reliability. In this paper, we perform the first large-scale measurement of ChatGPT's reliability in the generic QA scenario with a carefully curated set of 5,695 questions across ten datasets and eight domains. We find that ChatGPT's reliability varies across different domains, especially underperforming in law and science questions. We also demonstrate that system roles, originally designed by OpenAI to allow users to steer ChatGPT's behavior, can impact ChatGPT's reliability. We further show that ChatGPT is vulnerable to adversarial examples, and even a single character change can negatively affect its reliability in certain cases. We believe that our study provides valuable insights into ChatGPT's reliability and underscores the need for strengthening the reliability and security of large language models (LLMs)

Backdoor Attacks in the Supply Chain of Masked Image Modeling

Masked image modeling (MIM) revolutionizes self-supervised learning (SSL) for image pre-training. In contrast to previous dominating self-supervised methods, i.e., contrastive learning, MIM attains state-of-the-art performance by masking and reconstructing random patches of the input image. However, the associated security and privacy risks of this novel generative method are unexplored. In this paper, we perform the first security risk quantification of MIM through the lens of backdoor attacks. Different from previous work, we are the first to systematically threat modeling on SSL in every phase of the model supply chain, i.e., pre-training, release, and downstream phases. Our evaluation shows that models built with MIM are vulnerable to existing backdoor attacks in release and downstream phases and are compromised by our proposed method in pre-training phase. For instance, on CIFAR10, the attack success rate can reach 99.62%, 96.48%, and 98.89% in the downstream phase, release phase, and pre-training phase, respectively. We also take the first step to investigate the success factors of backdoor attacks in the pre-training phase and find the trigger number and trigger pattern play key roles in the success of backdoor attacks while trigger location has only tiny effects. In the end, our empirical study of the defense mechanisms across three detection-level on model supply chain phases indicates that different defenses are suitable for backdoor attacks in different phases. However, backdoor attacks in the release phase cannot be detected by all three detection-level methods, calling for more effective defenses in future research