Infeasibility Aware Large Language Models for Combinatorial Optimization

Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We propose an infeasibility-aware framework that combines certifiable dataset construction, supervised fine-tuning, and LLM-assisted downstream search. For the minor-embedding problem, we introduce a new mathematical programming formulation together with provable zero-phase infeasibility screening, which enables scalable construction of training instances labeled either as feasible with structured certificates or as certifiably infeasible. Using training data generated through this exact optimization pipeline, we show that an 8B-parameter LLM can be fine-tuned to jointly perform solution generation and infeasibility detection. We further utilize LLM outputs as warm starts for downstream local search, providing a practical way to accelerate optimization even when the LLM outputs are imperfect. Experiments show that our fine-tuned model improves overall accuracy by up to 30\% over GPT-5.2; meanwhile LLM-guided warm starts provide up to $2\times$ speedup compared with starting from scratch in downstream local search.

What's the Best Way to Retrieve Slides? A Comparative Study of Multimodal, Caption-Based, and Hybrid Retrieval Techniques

Slide decks, serving as digital reports that bridge the gap between presentation slides and written documents, are a prevalent medium for conveying information in both academic and corporate settings. Their multimodal nature, combining text, images, and charts, presents challenges for retrieval-augmented generation systems, where the quality of retrieval directly impacts downstream performance. Traditional approaches to slide retrieval often involve separate indexing of modalities, which can increase complexity and lose contextual information. This paper investigates various methodologies for effective slide retrieval, including visual late-interaction embedding models like ColPali, the use of visual rerankers, and hybrid retrieval techniques that combine dense retrieval with BM25, further enhanced by textual rerankers and fusion methods like Reciprocal Rank Fusion. A novel Vision-Language Models-based captioning pipeline is also evaluated, demonstrating significantly reduced embedding storage requirements compared to visual late-interaction techniques, alongside comparable retrieval performance. Our analysis extends to the practical aspects of these methods, evaluating their runtime performance and storage demands alongside retrieval efficacy, thus offering practical guidance for the selection and development of efficient and robust slide retrieval systems for real-world applications.