Building a Telescope to Look Into High-Dimensional Image Spaces
By Mitch Hill, Erik Nijkamp, Song-Chun Zhu. 2018
10 citations recorded by the source corpus.
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join to form macroscopic image basins that represent pattern concepts. Recent works use neural networks that capture high-order image statistics to learn Gibbs models capable of synthesizing realistic images of many patterns. However, characterizing a learned probability density to uncover the Hopfield memories of the model, encoded by the structure of the local modes, remains an open challenge. In this work, we present novel computational experiments that map and visualize the local mode structure of Gibbs densities. Efficient mapping requires identifying the global basins without enumerating the countless modes. Inspired by Grenander's jump-diffusion method, we propose a new MCMC tool called Attraction-Diffusion (AD) that can capture the macroscopic structure of highly non-convex densities by measuring metastability of local modes. AD involves altering the target density with a magnetization potential penalizing distance from a known mode and running an MCMC sample of the altered density to measure the stability of the initial chain state. Using a low-dimensional generator network to facilitate exploration, we map image spaces with up to 12,288 dimensions (64 $\times$ 64 pixels in RGB). Our work shows: (1) AD can efficiently map highly non-convex probability densities, (2) metastable regions of pattern probability densities contain coherent groups of images, and (3) the perceptibility of differences between training images influences the metastability of image basins.
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Computer Vision and Pattern Recognition
In Representation & Self-Supervised Learning
Citations in the corpus
- On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models (2019, methodology): “On the other hand, the consistent appearance of long-run MCMC samples can actually be a useful feature of a learned potential because a metastable representation is needed for mapping applications such as [12].”
- Divergence Triangle for Joint Training of Generator Model, Energy-Based Model, and Inferential Model (2018, background): “To verify that (i) local minima of −fα(x) resemble {xi} and (ii) minima are separated by significant energy barriers, we shall follow the approach used in [55].”