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Paper

  • Title: Attend, Infer, Repeat: Fast Scene Understanding with Generative Models
  • Authors: S. M. Ali Eslami, Nicolas Heess, Theophane Weber, Yuval Tassa, Koray Kavukcuoglu, Geoffrey E. Hinton
  • Link: http://arxiv.org/abs/1603.08575
  • Tags: Neural Network, VAE, attention
  • Year: 2016

Summary

Architecture

Rough chapter-wise notes

  • (1) Introduction

    • Assumption: Images are made up of distinct objects. These objects have visual and physical properties.
    • They develop a framework for efficient inference in images (i.e. get from the image to a representation of the objects, i.e. inverse graphics).
    • Parts of the framework: High dimensional representations (e.g. object images), interpretable latent variables (e.g. for rotation) and generative processes (to combine object images with latent variables).
    • Contributions:
      • A scheme for efficient variational inference in latent spaces of variable dimensionality.
        • Idea: Treat inference as an iterative process, implemented via an RNN that looks at one object at a time and learns an appropriate number of inference steps. (Attent-Infer-Repeat, AIR)
        • End-to-end training via amortized variational inference (continuous variables: gradient descent, discrete variables: black-box optimization).
      • AIR allows to train generative models that automatically learn to decompose scenes.
      • AIR allows to recover objects and their attributes from rendered 3D scenes (inverse rendering).

  • (2) Approach

    • Just like in VAEs, the scene interpretation is viewed with a bayesdian approach.
    • There are latent variables z and images x.
    • Images are generated via a probability distribution p(x|z).
    • This can be reversed via bayes rule to p(x|z) = p(x)p(z|x) / p(z) which means that p(x|z)p(z) / p(x) = p(z|x).
    • The prior p(z) must be chosen and captures assumption about the distributions of the latent variables.
    • p(x|z) is the likelihood and represents the model that generates images from latent variables.
    • They assume that there can be multiple objects in an image.
    • Every object get its own latent variables.
    • A probability distribution p(x|z) then converts each object (on its own) from the latent variables to an image.
    • The number of objects follows a probability distribution p(n).
    • For the prior and likelihood they assume two scenarios:
      • 2D: Three dimensions for X, Y and scale. Additionally n dimensions for its shape.
      • 3D: Dimensions for X, Y, Z, rotation, object identity/category (multinomial variable). (No scale?)
    • Both 2D and 3D can be separated into latent variables for "where" and "what".
    • It is assumed that the prior latent variables are independent of each other.
    • (2.1) Inference
      • Inference for their model is intractable, therefore they use an approximation q(z,n|x), which minizes KL(q(z,n|x)||p(z,n|x)), i.e. KL(approximation||real) using amortized variational approximation.
      • Challanges for them:
        • The dimensionality of their latent variable layer is a random variable p(n) (i.e. No static size.).
        • Strong symmetries.
      • They implement inference via an RNN which encodes the image object by object.
      • The encoded latent variables can be gaussians.
      • They encode the latent layer length via n as a vector (instead of an integer). The vector has the form of n 1s followed by one 0.
      • If the length vector is #z then they want to approximate q(z,#z|x).
      • That can apparently be decomposed into <product> q(latent variable value i, #z is still 1 at i|x, previous latent variable values) * q(has length n|z,x).
    • (2.2) Learning
      • The parameters theta (p, latent variable -> image) and phi (q, image -> latent variables) are jointly optimized.
      • Optimization happens be maximizing a lower bound E[log(p(x,z,n) / q(z,n|x))] called the negative free energy.
      • (2.2.1) Parameters of the model theta *