An Iterative Closest Points Approach to Neural Generative Models

TL;DR

This paper introduces an ICP-inspired iterative method for training neural generative models by aligning transformed samples with target data through pairwise correspondences and neural network optimization.

Contribution

It adapts the ICP algorithm to neural generative modeling, enabling effective distribution mapping with a simple iterative procedure.

Findings

Works on synthetic and MNIST data

Handles continuous and discrete distributions

Capable of learning complex transformations

Abstract

We present a simple way to learn a transformation that maps samples of one distribution to the samples of another distribution. Our algorithm comprises an iteration of 1) drawing samples from some simple distribution and transforming them using a neural network, 2) determining pairwise correspondences between the transformed samples and training data (or a minibatch), and 3) optimizing the weights of the neural network being trained to minimize the distances between the corresponding vectors. This can be considered as a variant of the Iterative Closest Points (ICP) algorithm, common in geometric computer vision, although ICP typically operates on sensor point clouds and linear transforms instead of random sample sets and neural nonlinear transforms. We demonstrate the algorithm on simple synthetic data and MNIST data. We furthermore demonstrate that the algorithm is capable of handling distributions with both continuous and discrete variables.