# QPM: Discrete Optimization for Globally Interpretable Image Classification

arXiv: https://arxiv.org/abs/2502.20130 · HTML: https://mlsanity.com/paper/2502.20130/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 67 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 30 of 51)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [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)
- [Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks](https://mlsanity.com/paper/2103.14749/) (2021)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [TrivialAugment: Tuning-free Yet State-of-the-Art Data Augmentation](https://mlsanity.com/paper/2103.10158/) (2021)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers](https://mlsanity.com/paper/1604.00825/) (2016)

## Built on by (most cited first, 2 of 2)

- [Pruning by Block Benefit: Exploring the Properties of Vision Transformer Blocks during Domain Adaptation](https://mlsanity.com/paper/2506.23675/) (2025)
- [DINO-QPM: Adapting Visual Foundation Models for Globally Interpretable Image Classification](https://mlsanity.com/paper/2604.07166/) (2026)

## Abstract (arXiv)

Understanding the classifications of deep neural networks, e.g. used in safety-critical situations, is becoming increasingly important. While recent models can locally explain a single decision, to provide a faithful global explanation about an accurate model's general behavior is a more challenging open task. Towards that goal, we introduce the Quadratic Programming Enhanced Model (QPM), which learns globally interpretable class representations. QPM represents every class with a binary assignment of very few, typically 5, features, that are also assigned to other classes, ensuring easily comparable contrastive class representations. This compact binary assignment is found using discrete optimization based on predefined similarity measures and interpretability constraints. The resulting optimal assignment is used to fine-tune the diverse features, so that each of them becomes the shared general concept between the assigned classes. Extensive evaluations show that QPM delivers unprecedented global interpretability across small and large-scale datasets while setting the state of the art for the accuracy of interpretable models.