# Hierarchical Feature-level Reverse Propagation for Post-Training Neural Networks

arXiv: https://arxiv.org/abs/2506.07188 · HTML: https://mlsanity.com/paper/2506.07188/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [DriveGPT4: Interpretable End-to-end Autonomous Driving via Large Language Model](https://mlsanity.com/paper/2310.01412/) (2023)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [BEVFormer v2: Adapting Modern Image Backbones to Bird's-Eye-View Recognition via Perspective Supervision](https://mlsanity.com/paper/2211.10439/) (2022)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [GenAD: Generative End-to-End Autonomous Driving](https://mlsanity.com/paper/2402.11502/) (2024)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [A Survey of End-to-End Driving: Architectures and Training Methods](https://mlsanity.com/paper/2003.06404/) (2020)
- [Decoupled Greedy Learning of CNNs](https://mlsanity.com/paper/1901.08164/) (2019)
- [Explainable AI for Safe and Trustworthy Autonomous Driving: A Systematic Review](https://mlsanity.com/paper/2402.10086/) (2024)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [VATLD: A Visual Analytics System to Assess, Understand and Improve Traffic Light Detection](https://mlsanity.com/paper/2009.12975/) (2020)
- [Shap-CAM: Visual Explanations for Convolutional Neural Networks based on Shapley Value](https://mlsanity.com/paper/2208.03608/) (2022)
- [CLIP-BEVFormer: Enhancing Multi-View Image-Based BEV Detector with Ground Truth Flow](https://mlsanity.com/paper/2403.08919/) (2024)
- [OccAM's Laser: Occlusion-based Attribution Maps for 3D Object Detectors on LiDAR Data](https://mlsanity.com/paper/2204.06577/) (2022)
- [Fully Decoupled Neural Network Learning Using Delayed Gradients](https://mlsanity.com/paper/1906.09108/) (2019)
- [Exploring intermediate representation for monocular vehicle pose estimation](https://mlsanity.com/paper/2011.08464/) (2020)
- [Explainable Action Prediction through Self-Supervision on Scene Graphs](https://mlsanity.com/paper/2302.03477/) (2023)
- [Boosting Monocular 3D Object Detection with Object-Centric Auxiliary Depth Supervision](https://mlsanity.com/paper/2210.16574/) (2022)
- [Feature Map Convergence Evaluation for Functional Module](https://mlsanity.com/paper/2405.04041/) (2024)
- [Layerwise Knowledge Extraction from Deep Convolutional Networks](https://mlsanity.com/paper/2003.09000/) (2020)

## Abstract (arXiv)

End-to-end neural networks have become a dominant paradigm in autonomous driving, where reliable deployment requires controllable post-training adaptation and improved transparency of model updates. In this paper, we propose Feature-level Reverse Propagation for Post-Training (FR-PT), a hierarchical framework that provides explicit intermediate supervision for upstream modules by reconstructing label-conditioned features backward through frozen downstream networks. For the first time, we formulate feature reconstruction via the Computation Consistency Principle (CCP) and Minimum Deviation Principle (MDP), and develop efficient operator-specific reverse computation algorithms with MDP-centered Tikhonov regularization to handle numerically unstable inverse problems. Specifically, FR-PT incorporates circular convolution theorem-based solvers for scalable convolutional reconstruction, nearest embedding for constructing continuous output targets from categorical labels, and iterative reverse propagation for composite residual and Transformer-style blocks. Extensive experiments on image classification and autonomous driving tasks demonstrate effective and stable adaptation across diverse architectures. Among 85 post-training settings, FR-PT achieves statistically significant improvements over task-level baselines in 63 cases, while the matched backpropagation reference outperforms reconstruction-supervised configurations in only 4 cases. Additional efficiency, conditioning, and favorable-condition analyses characterize the reliability and limitations of reconstructed targets, while feature-response analyses further demonstrate their diagnostic value. Code is available at https://github.com/Dingni2000/FR-PT .