Shicheng Wei | Searcharxiv

arXiv2026

Prime Quadruplets and Jump Conditions on Arithmetic Functions

We provide progress on the characterization of composite integers $n$ that satisfy the jump conditions $\varphi(n+12)=\varphi(n)+12$ and $\sigma(n+12)=\sigma(n)+12$ simultaneously. While it is known that prime quadruplets $(p,p+2,p+6,p+8)$ generate solutions $n=p(p+8)$, the complete characterization remains an open conjecture. We prove that this characterization is complete when $n$ and $n+12$ are both squarefree semiprimes, and that no solution $n$ can be a prime power. Furthermore, a complete search up to $10^{12}$ resulted in no counterexamples to the conjecture. If this conjecture is proven true, and there are infinitely many such solutions, then it can be proved that there are infinitely many prime quadruplets.

math.NT↗

arXiv2025

Deep Learning Model Inversion Attacks and Defenses: A Comprehensive Survey

The rapid adoption of deep learning in sensitive domains has brought tremendous benefits. However, this widespread adoption has also given rise to serious vulnerabilities, particularly model inversion (MI) attacks, posing a significant threat to the privacy and integrity of personal data. The increasing prevalence of these attacks in applications such as biometrics, healthcare, and finance has created an urgent need to understand their mechanisms, impacts, and defense methods. This survey aims to fill the gap in the literature by providing a structured and in-depth review of MI attacks and defense strategies. Our contributions include a systematic taxonomy of MI attacks, extensive research on attack techniques and defense mechanisms, and a discussion about the challenges and future research directions in this evolving field. By exploring the technical and ethical implications of MI attacks, this survey aims to offer insights into the impact of AI-powered systems on privacy, security, and trust. In conjunction with this survey, we have developed a comprehensive repository to support research on MI attacks and defenses. The repository includes state-of-the-art research papers, datasets, evaluation metrics, and other resources to meet the needs of both novice and experienced researchers interested in MI attacks and defenses, as well as the broader field of AI security and privacy. The repository will be continuously maintained to ensure its relevance and utility. It is accessible at https://github.com/overgter/Deep-Learning-Model-Inversion-Attacks-and-Defenses.

cs.CR↗