Spatial Encoding Challenges in Hyperdimensional Computing: A Laplace Kernel Approach

Abstract

Hyperdimensional Computing (HDC) offers a powerful brain-inspired paradigm for data representation, leveraging high-dimensional vectors to encode and manipulate information. However, effective spatial encoding remains a significant challenge, especially for AI applications that require spatial awareness, such as robotics, navigation, and contextual reasoning. Traditional spatial encoding techniques—such as orthogonal indexing or Gaussian-based kernels—struggle with preserving locality, generalizing across spatial proximity, or scaling efficiently. This study introduces a novel Laplace kernel-based approach to spatial encoding within the HDC framework, designed to address these critical limitations.The proposed method uses the Laplace function to generate similarity-decaying high-dimensional vectors based on spatial distance, ensuring that representations of nearby positions remain correlated while those of distant points diverge exponentially. Extensive experiments were conducted on spatial classification tasks, noise-resilience tests, and dimensional efficiency benchmarks using synthetic and real-world datasets. Results demonstrate that the Laplace kernel-based encoder consistently outperforms baseline methods in classification accuracy (achieving up to 94%), noise robustness (with minimal degradation under coordinate perturbations), and topological preservation, as shown in t-SNE visualizations.From an AI perspective, this encoding scheme supports the development of more robust, scalable, and interpretable spatial representations, particularly for applications in autonomous systems, embodied agents, and neuromorphic computing. The findings indicate that Laplace-based spatial encoding can serve as a critical enabler for the next generation of spatially intelligent AI systems operating in uncertain or dynamic environments.