# Prototype-based interpretation of the functionality of neurons in winner-take-all neural networks

arXiv: https://arxiv.org/abs/2008.08750 · HTML: https://mlsanity.com/paper/2008.08750/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 5 of 5)

- [DE3-BERT: Distance-Enhanced Early Exiting for BERT based on Prototypical Networks](https://mlsanity.com/paper/2402.05948/) (2024)
- [A Deep Positive-Negative Prototype Approach to Integrated Prototypical Discriminative Learning](https://mlsanity.com/paper/2501.02477/) (2025)
- [Towards interpreting ML-based automated malware detection models: a survey](https://mlsanity.com/paper/2101.06232/) (2021)
- [Deep Positive-Negative Prototypes for Adversarially Robust Discriminative Prototypical Learning](https://mlsanity.com/paper/2504.03782/) (2025)
- [Revisiting Classical Multiclass Linear Discriminant Analysis with a Novel Prototype-based Interpretable Solution](https://mlsanity.com/paper/2205.00668/) (2022)

## Abstract (arXiv)

Prototype-based learning (PbL) using a winner-take-all (WTA) network based on minimum Euclidean distance (ED-WTA) is an intuitive approach to multiclass classification. By constructing meaningful class centers, PbL provides higher interpretability and generalization than hyperplane-based learning (HbL) methods based on maximum Inner Product (IP-WTA) and can efficiently detect and reject samples that do not belong to any classes. In this paper, we first prove the equivalence of IP-WTA and ED-WTA from a representational point of view. Then, we show that naively using this equivalence leads to unintuitive ED-WTA networks in which the centers have high distances to data that they represent. We propose ±ED-WTA which models each neuron with two prototypes: one positive prototype representing samples that are modeled by this neuron and a negative prototype representing the samples that are erroneously won by that neuron during training. We propose a novel training algorithm for the ±ED-WTA network, which cleverly switches between updating the positive and negative prototypes and is essential to the emergence of interpretable prototypes. Unexpectedly, we observed that the negative prototype of each neuron is indistinguishably similar to the positive one. The rationale behind this observation is that the training data that are mistaken with a prototype are indeed similar to it. The main finding of this paper is this interpretation of the functionality of neurons as computing the difference between the distances to a positive and a negative prototype, which is in agreement with the BCM theory. In our experiments, we show that the proposed ±ED-WTA method constructs highly interpretable prototypes that can be successfully used for detecting outlier and adversarial examples.