# An exploration of parameter redundancy in deep networks with circulant projections

arXiv: https://arxiv.org/abs/1502.03436 · HTML: https://mlsanity.com/paper/1502.03436/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2015.

## Built on by (most cited first, 3 of 3)

- [Universal approximation and model compression for radial neural networks](https://mlsanity.com/paper/2107.02550/) (2021)
- [Low-rank Tensor Decomposition for Compression of Convolutional Neural Networks Using Funnel Regularization](https://mlsanity.com/paper/2112.03690/) (2021)
- [Quiver neural networks](https://mlsanity.com/paper/2207.12773/) (2022)

## Abstract (arXiv)

We explore the redundancy of parameters in deep neural networks by replacing the conventional linear projection in fully-connected layers with the circulant projection. The circulant structure substantially reduces memory footprint and enables the use of the Fast Fourier Transform to speed up the computation. Considering a fully-connected neural network layer with d input nodes, and d output nodes, this method improves the time complexity from O(d^2) to O(dlogd) and space complexity from O(d^2) to O(d). The space savings are particularly important for modern deep convolutional neural network architectures, where fully-connected layers typically contain more than 90% of the network parameters. We further show that the gradient computation and optimization of the circulant projections can be performed very efficiently. Our experiments on three standard datasets show that the proposed approach achieves this significant gain in storage and efficiency with minimal increase in error rate compared to neural networks with unstructured projections.