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

TL;DR

SETAREH is a wavelet-based sparsification method that uses sorting and Haar transforms to reduce the number of elements needed to approximate inner products between fixed weight vectors and incoming inputs. It maintains exact inner product values before truncation and enables significant compression with controlled error. The approach is effective in both synthetic and real-world settings, particularly for repeated computations in resource-constrained environments.

Why It Matters

Reducing memory and communication costs in deep learning systems is critical for deployment on edge devices and in distributed settings. SETAREH offers a structured way to compress high-dimensional data without sacrificing computational fidelity, potentially improving efficiency in inference pipelines with fixed weights.

Key Findings

• The method preserves exact inner-product values prior to truncation by applying consistent permutations and Haar transforms to both vectors.
• Performance gains depend on the trade-off between approximation error and the overhead of storing permutation metadata.