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Analyzing the Benefits of Prototypes for Semi-Supervised Category Learning

Liyi Zhang, Logan Nelson, Thomas L. Griffiths

TL;DR

The paper examines how prototype-based representations can benefit semi-supervised category learning by implementing a prototype-informed prior in a variational auto-encoder (VampPrior). Treating prototypes as latent cluster centers, the approach yields more clustered embeddings and improves downstream categorization on MNIST and CIFAR-10, even without labels during training. The authors show that the learned prototypes organize latent space into interpretable clusters and that prototype-based classification can approach supervised performance under certain conditions, especially when category boundaries are simpler or perturbed data is used. By linking cognitive models of categorization with deep generative models, the work highlights when abstract prototypes can enhance unsupervised representation learning and downstream tasks in naturalistic image domains.

Abstract

Categories can be represented at different levels of abstraction, from prototypes focused on the most typical members to remembering all observed exemplars of the category. These representations have been explored in the context of supervised learning, where stimuli are presented with known category labels. We examine the benefits of prototype-based representations in a less-studied domain: semi-supervised learning, where agents must form unsupervised representations of stimuli before receiving category labels. We study this problem in a Bayesian unsupervised learning model called a variational auto-encoder, and we draw on recent advances in machine learning to implement a prior that encourages the model to use abstract prototypes to represent data. We apply this approach to image datasets and show that forming prototypes can improve semi-supervised category learning. Additionally, we study the latent embeddings of the models and show that these prototypes allow the models to form clustered representations without supervision, contributing to their success in downstream categorization performance.

Analyzing the Benefits of Prototypes for Semi-Supervised Category Learning

TL;DR

The paper examines how prototype-based representations can benefit semi-supervised category learning by implementing a prototype-informed prior in a variational auto-encoder (VampPrior). Treating prototypes as latent cluster centers, the approach yields more clustered embeddings and improves downstream categorization on MNIST and CIFAR-10, even without labels during training. The authors show that the learned prototypes organize latent space into interpretable clusters and that prototype-based classification can approach supervised performance under certain conditions, especially when category boundaries are simpler or perturbed data is used. By linking cognitive models of categorization with deep generative models, the work highlights when abstract prototypes can enhance unsupervised representation learning and downstream tasks in naturalistic image domains.

Abstract

Categories can be represented at different levels of abstraction, from prototypes focused on the most typical members to remembering all observed exemplars of the category. These representations have been explored in the context of supervised learning, where stimuli are presented with known category labels. We examine the benefits of prototype-based representations in a less-studied domain: semi-supervised learning, where agents must form unsupervised representations of stimuli before receiving category labels. We study this problem in a Bayesian unsupervised learning model called a variational auto-encoder, and we draw on recent advances in machine learning to implement a prior that encourages the model to use abstract prototypes to represent data. We apply this approach to image datasets and show that forming prototypes can improve semi-supervised category learning. Additionally, we study the latent embeddings of the models and show that these prototypes allow the models to form clustered representations without supervision, contributing to their success in downstream categorization performance.
Paper Structure (24 sections, 3 equations, 3 figures, 4 tables)

This paper contains 24 sections, 3 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Models of Categorization
  3. Prototype Theory
  4. Exemplar Models
  5. Rational Analysis
  6. Analyzing Semi-Supervised Category Learning
  7. Variational Auto-Encoders
  8. Putting Prototypes in the Prior
  9. Summary
  10. Evaluating the Benefits of Prototypes
  11. Datasets
  12. Downstream Categorization
  13. K-nearest neighbor (KNN).
  14. Classification using prototypes.
  15. Dataset Perturbations
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Reproduced results from VampPrior VAE with $K=500$. On the left are the first 25 pseudo-inputs, which are vague versions of real digits. On the middle are generations from these pseudo-inputs (each generated by one pseudo-input). On the right is a random sample of the actual data. The classifier $f$ predicts generated images in the middle as: 2, 3, 5, 9, 7 | 3, 3, 4, 1, 4 | 5, 5, 5, 5, 4 | 9, 6, 3, 2, 3 | 9, 3, 3, 8, 8; the predictions are reasonable even though the generations may be different from the actual data that classifier $f$ was trained on.
  • Figure 2: t-SNE mapping of test datapoint embeddings for three VAE models. Each colored circle represents a datapoint, and circles are colored by real labels. Black squares are embeddings of pseudo-inputs (prototypes). VampPrior VAE with 20 or 500 pseudo-inputs show stronger demarcation between classes than vanilla VAE, even though no label was present in training.
  • Figure 3: Squared loss from k-means clustering on two VAEs' embeddings, versus the number of clusters used by k-means. Lower value means more clustered embeddings.