# Make Deep Networks Shallow Again

arXiv: https://arxiv.org/abs/2309.08414 · HTML: https://mlsanity.com/paper/2309.08414/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [Efficient shallow learning as an alternative to deep learning](https://mlsanity.com/paper/2211.11106/) (2022)
- [Number of Attention Heads vs Number of Transformer-Encoders in Computer Vision](https://mlsanity.com/paper/2209.07221/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Data-Driven Approach to Support Clinical Renal Replacement Therapy](https://mlsanity.com/paper/2602.22902/) (2026)

## Abstract (arXiv)

Deep neural networks have a good success record and are thus viewed as the best architecture choice for complex applications. Their main shortcoming has been, for a long time, the vanishing gradient which prevented the numerical optimization algorithms from acceptable convergence. A breakthrough has been achieved by the concept of residual connections -- an identity mapping parallel to a conventional layer. This concept is applicable to stacks of layers of the same dimension and substantially alleviates the vanishing gradient problem. A stack of residual connection layers can be expressed as an expansion of terms similar to the Taylor expansion. This expansion suggests the possibility of truncating the higher-order terms and receiving an architecture consisting of a single broad layer composed of all initially stacked layers in parallel. In other words, a sequential deep architecture is substituted by a parallel shallow one. Prompted by this theory, we investigated the performance capabilities of the parallel architecture in comparison to the sequential one. The computer vision datasets MNIST and CIFAR10 were used to train both architectures for a total of 6912 combinations of varying numbers of convolutional layers, numbers of filters, kernel sizes, and other meta parameters. Our findings demonstrate a surprising equivalence between the deep (sequential) and shallow (parallel) architectures. Both layouts produced similar results in terms of training and validation set loss. This discovery implies that a wide, shallow architecture can potentially replace a deep network without sacrificing performance. Such substitution has the potential to simplify network architectures, improve optimization efficiency, and accelerate the training process.