# MM++: Post-Hoc Scale-Invariant Multilayer OOD Detection via Top-K Gated Feature Fusion

arXiv: https://arxiv.org/abs/2606.17352 · HTML: https://mlsanity.com/paper/2606.17352/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 48 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 30 of 41)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [EVA-02: A Visual Representation for Neon Genesis](https://mlsanity.com/paper/2303.11331/) (2023)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluation](https://mlsanity.com/paper/2306.00826/) (2023)
- [PixMix: Dreamlike Pictures Comprehensively Improve Safety Measures](https://mlsanity.com/paper/2112.05135/) (2021)
- [Non-Parametric Outlier Synthesis](https://mlsanity.com/paper/2303.02966/) (2023)

## Abstract (arXiv)

We introduce MM++ (Multilayer Mahalanobis++), a strictly post-hoc, and scale-invariant framework for Out-of-Distribution (OOD) detection. To address the trade-off between scale invariance and hierarchical expressivity, MM++ constructs a principled joint feature space. It first identifies discriminative intermediate layers by measuring entropy density drops, which mark the boundaries of sharp semantic compression. By fusing these selected layers with the terminal representation, the framework captures latent cross-layer correlations while mitigating early-layer noise. Crucially, a Ledoit-Wolf regularized tied covariance matrix stabilizes this unified space, enabling reliable distance estimation. Requiring no auxiliary OOD data, classifier fine-tuning, or architectural modifications, MM++ delivers robust performance across distinct architectures for both near- and far-OOD detection.