Gram-Space: Structure-Preserving Codebook Compression for Memory-Efficient Neuro-Symbolic AI

2026-08-02

AI Summary

This work addresses the severe memory bottleneck imposed by high-dimensional codebooks in neural-symbolic AI, which hinders system scalability and deployment efficiency. We propose the first application of Gram-Schmidt orthogonalization to Vector Symbolic Architectures (VSAs), compressing codebooks into a compact orthogonal coordinate system while strictly preserving dot-product structure and numerical equivalence. This approach enables memory-efficient inference representations without compromising representational fidelity. Experimental results demonstrate substantial improvements in hardware utilization, achieving up to a 15.75× reduction in GPU memory consumption and a 3.62× decrease in inference latency on standard benchmark datasets.

Abstract

Vector symbolic architectures (VSA) are widely used for reasoning in neuro-symbolic (NeSy) AI, yet high-dimensional codebooks often create severe memory bottlenecks that limit scalability and deployment. In this paper, we propose Gram-Space, a compression framework that applies Gram-Schmidt orthogonalization to represent codebook vectors in a compact orthonormal coordinate system. Gram-Space preserves the dot-product structure required by matrix-based VSA operators, which supports numerically equivalent execution of matrix similarity, probability vectorization, and attention score computations. We provide a correctness analysis showing that inner products are preserved under the orthonormal basis representation. Using modern GPU hardware, we benchmark the Gram-Space framework on standard neuro-symbolic reasoning datasets. Experimental evaluations across state-of-the-art VSA models show that Gram-Space reduces model-level GPU memory usage by up to 15.75x and improves inference latency by up to 3.62x. Profiling results further indicate that Gram-Space reduces allocation-heavy overhead in codebook-associated stages and improves hardware utilization for NeSy workloads.

Problem

• memory bottleneck
• codebook compression
• neuro-symbolic AI
• vector symbolic architectures
• scalability

Innovation

• Gram-Space
• codebook compression
• vector symbolic architectures
• orthonormal basis
• neuro-symbolic AI