# Adaptive Depth Networks with Skippable Sub-Paths

arXiv: https://arxiv.org/abs/2312.16392 · HTML: https://mlsanity.com/paper/2312.16392/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 65 references that are in the map.
- First posted on arXiv 27 Dec 2023.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillation](https://mlsanity.com/paper/1905.08094/) (2019)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [GhostNet: More Features from Cheap Operations](https://mlsanity.com/paper/1911.11907/) (2019)
- [Dynamic Neural Networks: A Survey](https://mlsanity.com/paper/2102.04906/) (2021)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [AdaViT: Adaptive Tokens for Efficient Vision Transformer](https://mlsanity.com/paper/2112.07658/) (2021)
- [Rethinking Spatial Dimensions of Vision Transformers](https://mlsanity.com/paper/2103.16302/) (2021)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)

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

- [AnyDepth-DETR/-YOLO: Any-depth object detection with a single network](https://mlsanity.com/paper/2605.09407/) (2026)

## Abstract (arXiv)

Predictable adaptation of network depths can be an effective way to control inference latency and meet the resource condition of various devices. However, previous adaptive depth networks do not provide general principles and a formal explanation on why and which layers can be skipped, and, hence, their approaches are hard to be generalized and require long and complex training steps. In this paper, we present a practical approach to adaptive depth networks that is applicable to various networks with minimal training effort. In our approach, every hierarchical residual stage is divided into two sub-paths, and they are trained to acquire different properties through a simple self-distillation strategy. While the first sub-path is essential for hierarchical feature learning, the second one is trained to refine the learned features and minimize performance degradation if it is skipped. Unlike prior adaptive networks, our approach does not train every target sub-network in an iterative manner. At test time, however, we can connect these sub-paths in a combinatorial manner to select sub-networks of various accuracy-efficiency trade-offs from a single network. We provide a formal rationale for why the proposed training method can reduce overall prediction errors while minimizing the impact of skipping sub-paths. We demonstrate the generality and effectiveness of our approach with convolutional neural networks and transformers.