SETAREH Transform: A Sorting-Assisted Haar-Wavelet Sparsification Method for Approximate Inner-Product Computation

Seyed Kamaledin Setarehdan

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…