We study the deterministic global optimization of the K-Medoids clustering problem. This work proposes a branch and bound (BB) scheme, in which a tailored Lagrangian relaxation method proposed in the 1970s is used to provide a lower bound at each BB node. The lower bounding method already guarantees the maximum gap at the root node. A closed-form solution to the lower bound can be derived analytically without explicitly solving any optimization problems, and its computation can be easily parallelized. Moreover, with this lower bounding method, finite convergence to the global optimal solution can be guaranteed by branching only on the regions of medoids. We also present several tailored bound tightening techniques to reduce the search space and computational cost. Extensive computational studies on 28 machine learning datasets demonstrate that our algorithm can provide a provable global optimal solution with an optimality gap of 0.1% within 4 hours on datasets with up to one million samples. Besides, our algorithm can obtain better or equal objective values than the heuristic method. A theoretical proof of global convergence for our algorithm is also presented.

This paper presents IB-POMCP, a novel algorithm for online planning under partial observability. Our approach enhances the decision-making process by using estimations of the world belief's entropy to guide a tree search process and surpass the limitations of planning in scenarios with sparse reward configurations. By performing what we denominate as an information-guided planning process, the algorithm, which incorporates a novel I-UCB function, shows significant improvements in reward and reasoning time compared to state-of-the-art baselines in several benchmark scenarios, along with theoretical convergence guarantees.

Safety fine-tuning helps align Large Language Models (LLMs) with human preferences for their safe deployment. To better understand the underlying factors that make models safe via safety fine-tuning, we design a synthetic data generation framework that captures salient aspects of an unsafe input by modeling the interaction between the task the model is asked to perform (e.g., "design") versus the specific concepts the task is asked to be performed upon (e.g., a "cycle" vs. a "bomb").

All experiments are run on Intel Xeon ICX Platinum 8358 and GeForce RTX 3090.

Neural Information Processing Systems http://nips.cc/

Proof of Lemma 2. Let U be the data set associated to ν. Proof of Lemma 3. First, we prove that the property holds for the root node. We wish to prove the property for some unexplored leaf after the iteration. This is trivial if the leaf ν is not expanded in that iteration. Suppose the leaf ν is expanded. Proof of Lemma 5. From Lemma 2, we note that Q Consider any path from the root to a leaf whose length is mK for some integer K > 0. We note that for each node ν and any of its children ν (Lemma 5).

In this work, we ask two key questions. First, in a more realistic setting where only a CPU is available, is the GNN model still competitive?

Abstract--Diffusion models exhibit notable fragility when faced with adversarial prompts, and strengthening attack capabilities is crucial for uncovering such vulnerabilities and building more robust generative systems. Existing works often rely on white-box access to model gradients or hand-crafted prompt engineering, which is infeasible in real-world deployments due to restricted access or poor attack effect. In this paper, we propose CAHS-Attack, a CLIP-A ware Heuristic Search attack method. CAHS-Attack integrates Monte Carlo Tree Search (MCTS) to perform fine-grained suffix optimization, leveraging a constrained genetic algorithm to preselect high-potential adversarial prompts as root nodes, and retaining the most semantically disruptive outcome at each simulation rollout for efficient local search. Extensive experiments demonstrate that our method achieves state-of-the-art attack performance across both short and long prompts of varying semantics. Furthermore, we find that the fragility of SD models can be attributed to the inherent vulnerability of their CLIP-based text encoders, suggesting a fundamental security risk in current text-to-image pipelines. In recent years, advances in text-to-image generation have led to the emergence of powerful models such as Stable Diffusion (SD) [1], [2], FLUX [3], and MMaDA [4], enabling users to create high-quality images from natural language prompts.

To explore the relationship between dependency distance (DD) and hierarchical distance (HD) in Japanese, we compared the probability distributions of DD and HD with and without sentence length fixed, and analyzed the changes in mean dependency distance (MDD) and mean hierarchical distance (MHD) as sentence length increases, along with their correlation coefficient based on the Balanced Corpus of Contemporary Written Japanese. It was found that the valency of the predicates is the underlying factor behind the trade-off relation between MDD and MHD in Japanese. Native speakers of Japanese regulate the linear complexity and hierarchical complexity through the valency of the predicates, and the relative sizes of MDD and MHD depend on whether the threshold of valency has been reached. Apart from the cognitive load, the valency of the predicates also affects the probability distributions of DD and HD. The effect of the valency of the predicates on the distribution of HD is greater than on that of DD, which leads to differences in their probability distributions and causes the mean of MDD to be lower than that of MHD.