SETAREH：基于Haar小波的排序辅助稀疏化方法，用于近似内积计算
SETAREH Transform: A Sorting-Assisted Haar-Wavelet Sparsification Method for Approximate Inner-Product Computation
一篇降低向量内积计算和传输成本的方法论文，用排序加Haar小波截断保留少量系数对，还在APPA-REAL年龄估计任务上做了验证。
arXiv 论文提出 SETAREH（Sorting-assisted Energy-concentrating Transform for Approximate Representation using Haar wavelets）变换，用于近似固定高维系数向量与输入向量之间的内积。方法对两个向量施加相同的置换序列与 Haar 变换，截断前保持内积精确，再只保留部分系数-输入对以降低存储与传输开销，并引入可控近似误差。实验在合成高斯向量基线和 APPA-REAL 数据集上的表观年龄估计 CNN 任务上进行，结果表明所需变换后系数-输入对数量明显少于原始向量维度。论文指出实际收益取决于近似精度与置换元数据的存储传输成本。
SETAREH Transform: A Sorting-Assisted Haar-Wavelet Sparsification Method for Approximate Inner-Product Computation
Modern deep learning systems increasingly rely on high-dimensional vector operations, in which large input and parameter vectors are repeatedly stored, transferred, and processed. Although substantial research has focused on reducing neural-network model size through pruning, quantization, knowledge distillation, and efficient architectures, the storage, memory-traffic, and communication costs associated with repeatedly presented high-dimensional input vectors remain important practical considerations, particularly in distributed and edge-computing environments. This paper proposes the SETAREH (Sorting-assisted Energy-concentrating Transform for Approximate Representation using Haar wavelets) transform, a Haar-wavelet-based sparsification approach for approximating the inner product between a fixed high-dimensional coefficient vector and successive input vectors. By applying the same sequence of permutations and Haar transforms to both vectors, SETAREH preserves the exact inner product before truncation. It then retains only a subset of the transformed coefficient-input pairs, reducing their representation cost while introducing a controllable approximation error. To evaluate SETAREH, we consider two complementary experimental settings: a synthetic Gaussian-vector baseline and a real apparent-age estimation task using a convolutional neural network on the APPA-REAL dataset. The results show that SETAREH can approximate the evaluated inner products using substantially fewer transformed coefficient-input pairs than the original vector dimension. The findings support its use as a potential structured data-representation method for repeated inner products with fixed weights, while the practical benefit depends on approximation accuracy and the cost of storing or transmitting permutation metadata.
