# Deep Kronecker Network

arXiv: https://arxiv.org/abs/2210.13327 · HTML: https://mlsanity.com/paper/2210.13327/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions](https://mlsanity.com/paper/2105.09513/) (2021)
- [Constrained Factor Models for High-Dimensional Matrix-Variate Time Series](https://mlsanity.com/paper/1710.06075/) (2017)
- [Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process](https://mlsanity.com/paper/1604.03192/) (2016)
- [Brain MRI-based 3D Convolutional Neural Networks for Classification of Schizophrenia and Controls](https://mlsanity.com/paper/2003.08818/) (2020)
- [KoPA: Automated Kronecker Product Approximation](https://mlsanity.com/paper/1912.02392/) (2019)
- [Sparse Kronecker Product Decomposition: A General Framework of Signal Region Detection in Image Regression](https://mlsanity.com/paper/2210.09128/) (2022)

## Built on by (most cited first, 2 of 2)

- [Structured and Fast Optimization: The Kronecker SGD Algorithm](https://mlsanity.com/paper/2305.08001/) (2023)
- [Time Series Generative Learning with Application to Brain Imaging Analysis](https://mlsanity.com/paper/2407.14003/) (2024)

## Abstract (arXiv)

We propose Deep Kronecker Network (DKN), a novel framework designed for analyzing medical imaging data, such as MRI, fMRI, CT, etc. Medical imaging data is different from general images in at least two aspects: i) sample size is usually much more limited, ii) model interpretation is more of a concern compared to outcome prediction. Due to its unique nature, general methods, such as convolutional neural network (CNN), are difficult to be directly applied. As such, we propose DKN, that is able to i) adapt to low sample size limitation, ii) provide desired model interpretation, and iii) achieve the prediction power as CNN. The DKN is general in the sense that it not only works for both matrix and (high-order) tensor represented image data, but also could be applied to both discrete and continuous outcomes. The DKN is built on a Kronecker product structure and implicitly imposes a piecewise smooth property on coefficients. Moreover, the Kronecker structure can be written into a convolutional form, so DKN also resembles a CNN, particularly, a fully convolutional network (FCN). Furthermore, we prove that with an alternating minimization algorithm, the solutions of DKN are guaranteed to converge to the truth geometrically even if the objective function is highly nonconvex. Interestingly, the DKN is also highly connected to the tensor regression framework proposed by Zhou et al. (2010), where a CANDECOMP/PARAFAC (CP) low-rank structure is imposed on tensor coefficients. Finally, we conduct both classification and regression analyses using real MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to demonstrate the effectiveness of DKN.