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An EM Algorithm for Capsule Regression.

Lawrence K Saul1

  • 1Department of Computer Science and Engineering, University of California, San Diego, La Jolla, CA 92093-0404 saul@cs.ucsd.edu.

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We introduce a novel latent variable model for multinomial classification inspired by capsule networks. This model enables tractable inference and provides least-squares updates for capsule weight matrices, advancing machine learning capabilities.

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Area of Science:

  • Machine Learning
  • Computer Vision
  • Deep Learning

Background:

  • Capsule architectures encode visual object pose and presence using hidden unit activity vectors.
  • Understanding capsules as primitive computing elements is crucial for advancing deep learning models.
  • Existing models lack a comprehensive framework for capsule regression in multinomial classification.

Purpose of the Study:

  • To propose a latent variable model for multinomial classification inspired by capsule architectures.
  • To investigate capsule regression as a higher-dimensional analog of traditional regression techniques.
  • To develop a tractable inference method for capsule networks.

Main Methods:

  • A novel capsule architecture with one capsule per class is proposed.
  • Hidden unit activities are modeled as latent variables with a squashing nonlinearity.
  • An expectation-maximization procedure is used for deriving least-squares updates.

Main Results:

  • The proposed model enables normalized probabilities for multinomial classification from capsule vector magnitudes.
  • Exact inference is shown to be tractable despite non-Gaussian posterior terms.
  • Experimental results demonstrate the practical application of the developed capsule regression model.

Conclusions:

  • The study presents a significant advancement in understanding and applying capsule networks for multinomial classification.
  • The developed latent variable model offers a tractable approach to capsule regression.
  • This work paves the way for more sophisticated part-whole relationship modeling in complex objects.