# This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse

arXiv: https://arxiv.org/abs/2603.08374 · HTML: https://mlsanity.com/paper/2603.08374/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 66 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 30 of 44)

- [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)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Deformable ProtoPNet: An Interpretable Image Classifier Using Deformable Prototypes](https://mlsanity.com/paper/2111.15000/) (2021)
- [Part-based R-CNNs for Fine-grained Category Detection](https://mlsanity.com/paper/1407.3867/) (2014)
- [Learning to Navigate for Fine-grained Classification](https://mlsanity.com/paper/1809.00287/) (2018)
- [Reducing Overfitting in Deep Networks by Decorrelating Representations](https://mlsanity.com/paper/1511.06068/) (2015)
- [Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks](https://mlsanity.com/paper/1709.06079/) (2017)
- [Fine-Grained Visual Classification via Progressive Multi-Granularity Training of Jigsaw Patches](https://mlsanity.com/paper/2003.03836/) (2020)
- [Fairwashing: the risk of rationalization](https://mlsanity.com/paper/1901.09749/) (2019)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [This Looks Like That... Does it? Shortcomings of Latent Space Prototype Interpretability in Deep Networks](https://mlsanity.com/paper/2105.02968/) (2021)

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

- [MedSynapse-V: Bridging Visual Perception and Clinical Intuition via Latent Memory Evolution](https://mlsanity.com/paper/2604.26283/) (2026)

## Abstract (arXiv)

Prototype networks provide an intrinsic case based explanation mechanism, but their interpretability is often undermined by prototype collapse, where multiple prototypes degenerate to highly redundant evidence. We attribute this failure mode to the terminal dynamics of Neural Collapse, where cross entropy optimization suppresses intra class variance and drives class conditional features toward a low dimensional limit. To mitigate this, we propose Adaptive Manifold Prototypes (AMP), a framework that leverages Riemannian optimization on the Stiefel manifold to represent class prototypes as orthonormal bases and make rank one prototype collapse infeasible by construction. AMP further learns class specific effective rank via a proximal gradient update on a nonnegative capacity vector, and introduces spatial regularizers that reduce rotational ambiguity and encourage localized, non overlapping part evidence. Extensive experiments on fine-grained benchmarks demonstrate that AMP achieves state-of-the-art classification accuracy while significantly improving causal faithfulness over prior interpretable models.