# FMCE-Net++: Feature Map Convergence Evaluation and Training

arXiv: https://arxiv.org/abs/2508.06109 · HTML: https://mlsanity.com/paper/2508.06109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 8 Aug 2025.

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

- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [BEVFormer v2: Adapting Modern Image Backbones to Bird's-Eye-View Recognition via Perspective Supervision](https://mlsanity.com/paper/2211.10439/) (2022)
- [Explainability of deep vision-based autonomous driving systems: Review and challenges](https://mlsanity.com/paper/2101.05307/) (2021)
- [Explainable Artificial Intelligence for Autonomous Driving: A Comprehensive Overview and Field Guide for Future Research Directions](https://mlsanity.com/paper/2112.11561/) (2021)
- [Jointly Optimizing Preprocessing and Inference for DNN-based Visual Analytics](https://mlsanity.com/paper/2007.13005/) (2020)
- [A Scenario-Based Functional Testing Approach to Improving DNN Performance](https://mlsanity.com/paper/2307.07083/) (2023)
- [Quantitative Performance Assessment of CNN Units via Topological Entropy Calculation](https://mlsanity.com/paper/2103.09716/) (2021)
- [Feature Map Convergence Evaluation for Functional Module](https://mlsanity.com/paper/2405.04041/) (2024)

## Abstract (arXiv)

Deep Neural Networks (DNNs) face interpretability challenges due to their opaque internal representations. While Feature Map Convergence Evaluation (FMCE) quantifies module-level convergence via Feature Map Convergence Scores (FMCS), it lacks experimental validation and closed-loop integration. To address this limitation, we propose FMCE-Net++, a novel training framework that integrates a pretrained, frozen FMCE-Net as an auxiliary head. This module generates FMCS predictions, which, combined with task labels, jointly supervise backbone optimization through a Representation Auxiliary Loss. The RAL dynamically balances the primary classification loss and feature convergence optimization via a tunable Representation Abstraction Factor. Extensive experiments conducted on MNIST, CIFAR-10, FashionMNIST, and CIFAR-100 demonstrate that FMCE-Net++ consistently enhances model performance without architectural modifications or additional data. Key experimental outcomes include accuracy gains of +1.16 pp (ResNet-50/CIFAR-10) and +1.08 pp (ShuffleNet v2/CIFAR-100), validating that FMCE-Net++ can effectively elevate state-of-the-art performance ceilings.