# Densely connected neural networks for nonlinear regression

arXiv: https://arxiv.org/abs/2108.00864 · HTML: https://mlsanity.com/paper/2108.00864/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 54 references that are in the map.
- First posted on arXiv 29 Jul 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [Crop Yield Prediction Using Deep Neural Networks](https://mlsanity.com/paper/1902.02860/) (2019)
- [Real-time Intent Prediction of Pedestrians for Autonomous Ground Vehicles via Spatio-Temporal DenseNet](https://mlsanity.com/paper/1904.09862/) (2019)

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

- [Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient](https://mlsanity.com/paper/2506.04375/) (2025)
- [Explainable Bayesian deep learning through input-skip Latent Binary Bayesian Neural Networks](https://mlsanity.com/paper/2503.10496/) (2025)
- [A least distance estimator for a multivariate regression model using deep neural networks](https://mlsanity.com/paper/2401.03123/) (2024)

## Abstract (arXiv)

Densely connected convolutional networks (DenseNet) behave well in image processing. However, for regression tasks, convolutional DenseNet may lose essential information from independent input features. To tackle this issue, we propose a novel DenseNet regression model where convolution and pooling layers are replaced by fully connected layers and the original concatenation shortcuts are maintained to reuse the feature. To investigate the effects of depth and input dimension of proposed model, careful validations are performed by extensive numerical simulation. The results give an optimal depth (19) and recommend a limited input dimension (under 200). Furthermore, compared with the baseline models including support vector regression, decision tree regression, and residual regression, our proposed model with the optimal depth performs best. Ultimately, DenseNet regression is applied to predict relative humidity, and the outcome shows a high correlation (0.91) with observations, which indicates that our model could advance environmental data analysis.