发表机构
University of California Riverside（加州大学河滨分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Gram-Space压缩框架，通过格拉姆-施密特正交化保留VSA所需点积结构，可降低神经符号AI模型GPU内存使用与推理延迟，提升硬件利用率。
AI 中文摘要
向量符号架构（VSA）广泛应用于神经符号（NeSy）AI的推理任务，但高维码本常引发严重内存瓶颈，限制了模型的可扩展性与部署能力。本文提出Gram-Space压缩框架，该框架采用格拉姆-施密特正交化方法，将码本向量表示为紧凑的标准正交坐标系。Gram-Space保留了基于矩阵的VSA算子所需的点积结构，支持矩阵相似度、概率向量化及注意力分数计算的数值等价执行。我们通过正确性分析证明，在标准正交基表示下内积可被保留。在现代GPU硬件上，我们在标准神经符号推理数据集上对Gram-Space框架进行基准测试。对多个最先进VSA模型的实验评估显示，Gram-Space可将模型级GPU内存使用量最多降低15.75倍，并将推理延迟最多提升3.62倍。性能分析结果进一步表明，Gram-Space减少了码本相关阶段的高资源分配开销，提升了NeSy工作负载的硬件利用率。
英文摘要
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.
CommentsInternational Conference on Neuro-symbolic Systems (NeuS) 2026
