用正交化压缩符号向量库，大幅降低内存占用且不损失推理性能。
Gram-Space: Structure-Preserving Codebook Compression for Memory-Efficient Neuro-Symbolic AI
- 通过格拉姆-施密特正交化构建紧凑正交坐标系表示向量库。
- 在多个VSA模型上实现最高15.75倍内存压缩和3.62倍推理加速。
- 适合部署资源受限环境下的神经符号推理系统。
向量符号架构（VSA）广泛用于神经符号（NeSy）AI中的推理，但高维代码本常导致严重内存瓶颈，限制可扩展性和部署。本文提出Gram-Space，一种压缩框架，利用格拉姆-施密特正交化将代码本向量表示为紧凑的正交坐标系。该方法保持了矩阵型VSA算子所需的点积结构，支持矩阵相似性、概率向量化及注意力分数计算的数值等价执行。我们提供了正确性分析，证明在正交基表示下内积得以保留。使用现代GPU硬件，在标准神经符号推理数据集上进行基准测试。实验结果表明，跨多种先进VSA模型，Gram-Space使模型级GPU内存使用减少最多15.75倍，推理延迟提升最多3.62倍。性能剖析显示，该框架降低了代码本相关阶段的内存分配开销，提升了硬件利用率。
原文摘要 · Abstract (English)
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.
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