The field of artificial intelligence is witnessing significant advancements in approximate nearest neighbor search and neural network verification. Researchers are focusing on developing efficient and scalable algorithms for approximate nearest neighbor search, which is a crucial component of many machine learning pipelines. Novel indexing structures and verification techniques are being proposed to improve the performance and accuracy of these algorithms. Noteworthy papers in this area include the introduction of a disk-based dynamic vector index that integrates hierarchical graph indexing with LSM-tree storage, and a novel graph-based indexing structure that combines strong theoretical guarantees with practical efficiency. These advancements have the potential to improve the performance and reliability of various AI applications, including recommendation systems, multimodal search, and neural network-based systems. Notable papers: LSM-VEC achieves higher recall, lower query and update latency, and reduces memory footprint by over 66.2%. HENN guarantees polylogarithmic worst-case query time while preserving high recall and incurring minimal implementation overhead.