SETAREH Transform: A Sorting-Assisted Haar-Wavelet Sparsification Method for Approximate Inner-Product Computation
SETAREH uses Haar-wavelet sparsification to approximate repeated inner products with fewer stored pairs.
The paper proposes SETAREH, a sorting-assisted Haar-wavelet sparsification method for approximating inner products between a fixed high-dimensional coefficient vector and repeated input vectors. Matching permutations and Haar transforms on both vectors preserve the exact inner product before truncation, after which fewer coefficient-input pairs are stored. Experiments on synthetic Gaussian vectors and a convolutional age-estimation model on APPA-REAL show substantial reductions versus the original dimension. Practical savings depend on the approximation error and the overhead of permutation metadata.
- SETAREH applies shared permutations and Haar transforms, preserving the exact inner product before truncation.
- Only a subset of transformed pairs is kept, trading representation cost for controllable error.
- Tests use synthetic Gaussian vectors and age estimation on APPA-REAL.
- Benefit depends on accuracy and the cost of storing or sending permutation metadata.
From the original article
1 min read at arxiv.orgModern deep learning systems increasingly rely on high-dimensional vector operations, in which large input and parameter vectors are repeatedly stored, transferred, and processed.
By Seyed Kamaledin Setarehdan · arxiv.org
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