Third, we are the first to consider regularized monotone SCP (RMSCP).

Third, we are the first to consider regularized monotone SCP (RMSCP).

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In particular, we consider several variants of SCP including the general case, the case where $f$ is additionally assumed to be monotone, and finally the case where $f$ is a regularized monotone submodular function. Our most significant contributions are that: (i) We propose a scalable algorithm for monotone SCP that achieves nearly the same approximation guarantees as the standard greedy algorithm in significantly faster time; (ii) We are the first to develop an algorithm for general SCP that achieves a solution arbitrarily close to being feasible; and finally (iii) we are the first to develop algorithms for regularized SCP. Our algorithms are then demonstrated to be effective in an extensive experimental section on data summarization and graph cut, two applications of SCP.

The code generation capabilities of Large Language Models (LLMs) have transformed the field of software development. However, this advancement also presents significant security challenges, as LLM-generated code often contains vulnerabilities. One direction of research strengthens LLMs by injecting or refining security knowledge through curated datasets, model tuning, or static analyzers. While effective in certain settings, these methods can be resource-intensive, less adaptable to zero-day vulnerabilities, and often inapplicable to proprietary models. To address these challenges, we introduce GRASP, which explores a new direction that focuses on structured reasoning over Secure Coding Practices(SCPs) rather than additional training or external feedback. GRASP comprises two key ideas: (1) an SCP graph that organizes SCPs into a Directed Acyclic Graph (DAG) capturing dependencies and relationships, and (2) a graph-based reasoning process that systematically guides LLMs through relevant SCPs for code generation. This design enables interpretable, model-agnostic, and scalable security improvements, particularly for previously unseen vulnerabilities. Our evaluation shows that GRASP consistently achieves Security Rates (SR) exceeding 80% across multiple LLMs, and delivers up to 88% improvements over baselines on zero-day vulnerabilities.

In this paper, we investigate the semantic collapsing problem in generative personalization, an under-explored topic where the learned visual concept ($V$) gradually shifts from its original textual meaning and comes to dominate other concepts in multi-concept input prompts. This issue not only reduces the semantic richness of complex input prompts like "a photo of $V$ wearing glasses and playing guitar" into simpler, less contextually rich forms such as "a photo of $V$" but also leads to simplified output images that fail to capture the intended concept. We identify the root cause as unconstrained optimisation, which allows the learned embedding $V$ to drift arbitrarily in the embedding space, both in direction and magnitude. To address this, we propose a simple yet effective training-free method that adjusts the magnitude and direction of pre-trained embedding at inference time, effectively mitigating the semantic collapsing problem. Our method is broadly applicable across different personalization methods and demonstrates significant improvements in text-image alignment in diverse use cases. Our code is anonymously published at https://github.com/tuananhbui89/Embedding-Adjustment

In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming, second-order cone programming, and semidefinite programming. Our main contribution is a generic Gaussian mechanism for such functions, with sensitivity measured in $\ell_2$, $\ell_1$, and $\ell_\infty$ norms. Notably, this framework includes the important case where the function outputs are symmetric matrices, and sensitivity is measured in the Frobenius, nuclear, or spectral norm. We further derive private algorithms for solving symmetric cone programs under various settings, using a combination of the multiplicative weights update method and our generic Gaussian mechanism. As an application, we present differentially private algorithms for semidefinite programming, resolving a major open question posed by [Hsu, Roth, Roughgarden, and Ullman, ICALP 2014].