Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension $n=8$, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions $4-16$, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

Tree-of-Thought (ToT) reasoning boosts the problem-solving abilities of Large Language Models (LLMs) but is computationally expensive due to semantic redundancy, where distinct branches explore equivalent reasoning paths. We introduce Semantic Similarity-Based Dynamic Pruning (SSDP), a lightweight method that, to the best of our knowledge, is the first framework to integrate online semantic merging into parallelized tree search, enabling the clustering and pruning of redundant steps in real time. Across reasoning benchmarks, including GSM8K and MATH500, SSDP achieves up to a 2.3x speedup over state-of-the-art tree-search baselines while maintaining competitive accuracy (typically within 5% of the strongest baseline) and reducing the number of explored nodes by 85-90%, demonstrating a practical approach to efficient, scalable LLM reasoning. The implementation of SSDP is publicly available at https://github.com/kimjoonghokim/SSDP.

Designing effective algorithmic components remains a fundamental obstacle in tackling NP-hard combinatorial optimization problems (COPs), where solvers often rely on carefully hand-crafted strategies. Despite recent advances in using large language models (LLMs) to synthesize high-quality components, most approaches restrict the search to a single element - commonly a heuristic scoring function - thus missing broader opportunities for innovation. In this paper, we introduce a broader formulation of solver design as a multi-strategy optimization problem, which seeks to jointly improve a set of interdependent components under a unified objective. To address this, we propose Multi-strategy Optimization via Turn-based Interactive Framework (MOTIF) - a novel framework based on Monte Carlo Tree Search that facilitates turn-based optimization between two LLM agents. At each turn, an agent improves one component by leveraging the history of both its own and its opponent's prior updates, promoting both competitive pressure and emergent cooperation. This structured interaction broadens the search landscape and encourages the discovery of diverse, high-performing solutions. Experiments across multiple COP domains show that MOTIF consistently outperforms state-of-the-art methods, highlighting the promise of turn-based, multi-agent prompting for fully automated solver design.

Despite the integration of safety alignment and external filters, text-to-image (T2I) generative systems are still susceptible to producing harmful content, such as sexual or violent imagery. This raises serious concerns about unintended exposure and potential misuse. Red teaming, which aims to proactively identify diverse prompts that can elicit unsafe outputs from the T2I system, is increasingly recognized as an essential method for assessing and improving safety before real-world deployment. However, existing automated red teaming approaches often treat prompt discovery as an isolated, prompt-level optimization task, which limits their scalability, diversity, and overall effectiveness. To bridge this gap, in this paper, we propose DREAM, a scalable red teaming framework to automatically uncover diverse problematic prompts from a given T2I system. Unlike prior work that optimizes prompts individually, DREAM directly models the probabilistic distribution of the target system's problematic prompts, which enables explicit optimization over both effectiveness and diversity, and allows efficient large-scale sampling after training. To achieve this without direct access to representative training samples, we draw inspiration from energy-based models and reformulate the objective into a simple and tractable form. We further introduce GC-SPSA, an efficient optimization algorithm that provides stable gradient estimates through the long and potentially non-differentiable T2I pipeline. During inference, we also propose a diversity-aware sampling strategy to enhance prompt variety. The effectiveness of DREAM is validated through extensive experiments, demonstrating state-of-the-art performance across a wide range of T2I models and safety filters in terms of both prompt success rate and diversity. Our code is available at https://github.com/AntigoneRandy/DREAM

Resource allocation remains NP-hard due to combinatorial complexity. While deep reinforcement learning (DRL) methods, such as the Rainbow Deep Q-Network (DQN), improve scalability through prioritized replay and distributional heads, classical function approximators limit their representational power. We introduce Variational Quantum Rainbow DQN (VQR-DQN), which integrates ring-topology variational quantum circuits with Rainbow DQN to leverage quantum superposition and entanglement. We frame the human resource allocation problem (HRAP) as a Markov decision process (MDP) with combinatorial action spaces based on officer capabilities, event schedules, and transition times. On four HRAP benchmarks, VQR-DQN achieves 26.8% normalized makespan reduction versus random baselines and outperforms Double DQN and classical Rainbow DQN by 4.9-13.4%. These gains align with theoretical connections between circuit expressibility, entanglement, and policy quality, demonstrating the potential of quantum-enhanced DRL for large-scale resource allocation. Our implementation is available at: https://github.com/Analytics-Everywhere-Lab/qtrl/.

Partial Maximum Satisfiability (PMS) and Weighted Partial Maximum Satisfiability (WPMS) generalize Maximum Satisfiability (MaxSAT), with broad real-world applications. Recent advances in Stochastic Local Search (SLS) algorithms for solving (W)PMS have mainly focused on designing clause weighting schemes. However, existing methods often fail to adequately distinguish between PMS and WPMS, typically employing uniform update strategies for clause weights and overlooking critical structural differences between the two problem types. In this work, we present a novel clause weighting scheme that, for the first time, updates the clause weights of PMS and WPMS instances according to distinct conditions. This scheme also introduces a new initialization method, which better accommodates the unique characteristics of both instance types. Furthermore, we propose a decimation method that prioritizes satisfying unit and hard clauses, effectively complementing our proposed clause weighting scheme. Building on these methods, we develop a new SLS solver for (W)PMS named DeepDist. Experimental results on benchmarks from the anytime tracks of recent MaxSAT Evaluations show that DeepDist outperforms state-of-the-art SLS solvers. Notably, a hybrid solver combining DeepDist with TT-Open-WBO-Inc surpasses the performance of the MaxSAT Evaluation 2024 winners, SPB-MaxSAT-c-Band and SPB-MaxSAT-c-FPS, highlighting the effectiveness of our approach. The code is available at https://github.com/jmhmaxsat/DeepDist

Graph representation learning seeks to transform complex, high-dimensional graph structures into compact vector spaces that preserve both topology and semantics. Among the various strategies, subgraph-based methods provide an interpretable bridge between symbolic pattern discovery and continuous embedding learning. Yet, existing frequent or discriminative subgraph mining approaches often suffer from redundant multi-phase pipelines, high computational cost, and weak coupling between mined structures and their discriminative relevance. We propose DS-Span, a single-phase discriminative subgraph mining framework that unifies pattern growth, pruning, and supervision-driven scoring within one traversal of the search space. DS-Span introduces a coverage-capped eligibility mechanism that dynamically limits exploration once a graph is sufficiently represented, and an information-gain-guided selection that promotes subgraphs with strong class-separating ability while minimizing redundancy. The resulting subgraph set serves as an efficient, interpretable basis for downstream graph embedding and classification. Extensive experiments across benchmarks demonstrate that DS-Span generates more compact and discriminative subgraph features than prior multi-stage methods, achieving higher or comparable accuracy with significantly reduced runtime.

Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the matrix product, which improves interpretability and reduces the approximation error. It is also used in role mining and computer vision. In this paper, we first propose algorithms for BMF that perform alternating optimization (AO) of the factor matrices, where each subproblem is solved via integer programming (IP). We then design different approaches to further enhance AO-based algorithms by selecting an optimal subset of rank-one factors from multiple runs. To address the scalability limits of IP-based methods, we introduce new greedy and local-search heuristics. We also construct a new C++ data structure for Boolean vectors and matrices that is significantly faster than existing ones and is of independent interest, allowing our heuristics to scale to large datasets. We illustrate the performance of all our proposed methods and compare them with the state of the art on various real datasets, both with and without missing data, including applications in topic modeling and imaging.

Neural architecture search (NAS) in expressive search spaces is a computationally hard problem, but it also holds the potential to automatically discover completely novel and performant architectures. To achieve this we need effective search algorithms that can identify powerful components and reuse them in new candidate architectures. In this paper, we introduce two adapted variants of the Smith-Waterman algorithm for local sequence alignment and use them to compute the edit distance in a grammar-based evolutionary architecture search. These algorithms enable us to efficiently calculate a distance metric for neural architectures and to generate a set of hybrid offspring from two parent models. This facilitates the deployment of crossover-based search heuristics, allows us to perform a thorough analysis on the architectural loss landscape, and track population diversity during search. We highlight how our method vastly improves computational complexity over previous work and enables us to efficiently compute shortest paths between architectures. When instantiating the crossover in evolutionary searches, we achieve competitive results, outperforming competing methods. Future work can build upon this new tool, discovering novel components that can be used more broadly across neural architecture design, and broadening its applications beyond NAS.

The repetition problem, where Large Language Models (LLMs) continuously generate repetitive content without proper termination, poses a critical challenge in production deployments, causing severe performance degradation and system stalling. This paper presents a comprehensive investigation and multiple practical solutions for the repetition problem encountered in real-world batch code interpretation tasks. We identify three distinct repetition patterns: (1) business rule generation repetition, (2) method call relationship analysis repetition, and (3) PlantUML diagram syntax generation repetition. Through rigorous theoretical analysis based on Markov models, we establish that the root cause lies in greedy decoding's inability to escape repetitive loops, exacerbated by self-reinforcement effects. Our comprehensive experimental evaluation demonstrates three viable solutions: (1) Beam Search decoding with early_stopping=True serves as a universal post-hoc mechanism that effectively resolves all three repetition patterns; (2) presence_penalty hyperparameter provides an effective solution specifically for BadCase 1; and (3) Direct Preference Optimization (DPO) fine-tuning offers a universal model-level solution for all three BadCases. The primary value of this work lies in combining first-hand production experience with extensive experimental validation. Our main contributions include systematic theoretical analysis of repetition mechanisms, comprehensive evaluation of multiple solutions with task-specific applicability mapping, identification of early_stopping as the critical parameter for Beam Search effectiveness, and practical production-ready solutions validated in real deployment environments.