# This Probably Looks Exactly Like That: An Invertible Prototypical Network

arXiv: https://arxiv.org/abs/2407.12200 · HTML: https://mlsanity.com/paper/2407.12200/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 88 references that are in the map.
- First posted on arXiv 16 Jul 2024.

## Builds on (most cited first, 30 of 58)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)
- [Manipulating and Measuring Model Interpretability](https://mlsanity.com/paper/1802.07810/) (2018)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [Deep Learning for Case-Based Reasoning through Prototypes: A Neural Network that Explains Its Predictions](https://mlsanity.com/paper/1710.04806/) (2017)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [HIVE: Evaluating the Human Interpretability of Visual Explanations](https://mlsanity.com/paper/2112.03184/) (2021)
- [Towards the first adversarially robust neural network model on MNIST](https://mlsanity.com/paper/1805.09190/) (2018)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [A Survey on Generative Adversarial Networks: Variants, Applications, and Training](https://mlsanity.com/paper/2006.05132/) (2020)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)

## Built on by (most cited first, 3 of 3)

- [This looks like what? Challenges and Future Research Directions for Part-Prototype Models](https://mlsanity.com/paper/2502.09340/) (2025)
- [Comprehensive Evaluation of Prototype Neural Networks](https://mlsanity.com/paper/2507.06819/) (2025)
- [Beyond L2: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architectures](https://mlsanity.com/paper/2608.16773/) (2026)

## Abstract (arXiv)

We combine concept-based neural networks with generative, flow-based classifiers into a novel, intrinsically explainable, exactly invertible approach to supervised learning. Prototypical neural networks, a type of concept-based neural network, represent an exciting way forward in realizing human-comprehensible machine learning without concept annotations, but a human-machine semantic gap continues to haunt current approaches. We find that reliance on indirect interpretation functions for prototypical explanations imposes a severe limit on prototypes' informative power. From this, we posit that invertibly learning prototypes as distributions over the latent space provides more robust, expressive, and interpretable modeling. We propose one such model, called ProtoFlow, by composing a normalizing flow with Gaussian mixture models. ProtoFlow (1) sets a new state-of-the-art in joint generative and predictive modeling and (2) achieves predictive performance comparable to existing prototypical neural networks while enabling richer interpretation.