# Exploiting Local Structures with the Kronecker Layer in Convolutional Networks

arXiv: https://arxiv.org/abs/1512.09194 · HTML: https://mlsanity.com/paper/1512.09194/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2015.

## Built on by (most cited first, 7 of 7)

- [Convolutional Neural Network Compression through Generalized Kronecker Product Decomposition](https://mlsanity.com/paper/2109.14710/) (2021)
- [Doping: A technique for efficient compression of LSTM models using sparse structured additive matrices](https://mlsanity.com/paper/2102.07071/) (2021)
- [Understanding MLP-Mixer as a Wide and Sparse MLP](https://mlsanity.com/paper/2306.01470/) (2023)
- [Investigating Temporal Convolutional Neural Networks for Satellite Image Time Series Classification: A survey](https://mlsanity.com/paper/2204.08461/) (2022)
- [Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective](https://mlsanity.com/paper/2105.13191/) (2021)
- [Weight Matrix Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures](https://mlsanity.com/paper/2204.04273/) (2022)
- [SeKron: A Decomposition Method Supporting Many Factorization Structures](https://mlsanity.com/paper/2210.06299/) (2022)

## Abstract (arXiv)

In this paper, we propose and study a technique to reduce the number of parameters and computation time in convolutional neural networks. We use Kronecker product to exploit the local structures within convolution and fully-connected layers, by replacing the large weight matrices by combinations of multiple Kronecker products of smaller matrices. Just as the Kronecker product is a generalization of the outer product from vectors to matrices, our method is a generalization of the low rank approximation method for convolution neural networks. We also introduce combinations of different shapes of Kronecker product to increase modeling capacity. Experiments on SVHN, scene text recognition and ImageNet dataset demonstrate that we can achieve 3.3 × speedup or 3.6 × parameter reduction with less than 1% drop in accuracy, showing the effectiveness and efficiency of our method. Moreover, the computation efficiency of Kronecker layer makes using larger feature map possible, which in turn enables us to outperform the previous state-of-the-art on both SVHN(digit recognition) and CASIA-HWDB (handwritten Chinese character recognition) datasets.