Hierarchical Navigable Small World Siyoyo: Empirical Approximate Nearest Neighbor Graph Comparison in .NET 9 with GPU Support Mateus Yonathan Software Developer & Independent Researcher https://www.linkedin.com/in/siyoyo/ Fig. 1: Structural comparison of Standard HNSW vs Siyoyo graph variants. The Standard HNSW maintains fixed neighbor constraints across all layers (4 neighbors per layer), while Siyoyo employs exponentially decaying neighbor constraints (4, 2, 1, 1 neighbors per layer respectively). This results in significant memory reduction while maintaining navigability, as demonstrated in our benchmarking results. Abstract—This paper presents an empirical comparison of two Hierarchical Navigable Small World (HNSW) graph imple- mentations in .NET 9, implementing a variant called HNSW Siyoyo that incorporates layer-adaptive neighbor constraints and vector normalization. We implement both standard HNSW and the Siyoyo variant using modern C# with GPU acceleration via ComputeSharp for similarity calculations. Our experimental eval- uation on three datasets (Synthetic-2K, Synthetic-10K, and Real- World) demonstrates that the Siyoyo variant achieves comparable recall performance while providing significant memory reductions of 12.6-19.9% and generally improved insertion times. Although GPU acceleration for similarity calculation is implemented and benchmarked, our results show that for the tested datasets and hardware, GPU support did not provide a speedup compared to the CPU due to data transfer overhead and the efficiency of modern CPUs for this workload. This highlights the importance of empirical evaluation when considering GPU acceleration for ANN search in production systems. The implementation leverages .NET 9’s performance improvements and demonstrates practical applications of GPU-accelerated similarity search in production environments. Our benchmarking results show that the Siyoyo variant maintains 96.3-100.0% recall at ef=256 while using 12- 20% less memory than standard HNSW implementations, making it particularly suitable for memory-constrained environments. I. I NTRODUCTION Imagine you’re organizing a massive library where every book has been converted into a unique fingerprint. When someone asks for books similar to a particular title, you need to find the closest matches quickly without checking every single book. This is the challenge that modern similarity search systems face in production environments, where speed and accuracy can make or break user experience. In today’s data-driven world, applications ranging from recommendation systems to fraud detection rely heavily on finding similar items in high-dimensional spaces. Whether it’s matching user preferences, detecting anomalous transactions, or retrieving relevant documents, the ability to perform fast and accurate similarity search has become a cornerstone of modern software architecture. This work is also inspired by the rapid development of modern vector databases such as Qdrant, Milvus, and others, which rely on efficient approximate nearest neighbor (ANN) algorithms like HNSW to enable scalable similarity search in production environments. The Hierarchical Navigable Small World (HNSW) algorithm has emerged as a leading solution for approximate nearest neighbor (ANN) search, offering an elegant balance between search speed and accuracy. However, as we’ve discovered through practical implementation, the standard HNSW ap- proach has limitations when deployed in real-world scenarios with varying data distributions and performance constraints. Our work implements HNSW Siyoyo, a variant that applies layer-adaptive neighbor constraints and vector normalization to the standard HNSW algorithm. The name "Siyoyo" serves dual purposes: it is both the author’s nickname and draws inspiration from the Indonesian phrase "Si Yoyo," reflecting the top- down traversal behavior of the algorithm, much like a yoyo’s motion from top to bottom and back. This personal naming convention reflects the author’s background and the algorithm’s characteristic traversal pattern. This implementation provides a practical modification to the standard HNSW approach. The motivation for this work stems from the increasing demand and practical challenges of deploying similarity search