Polynomial function approximation and its application to deep generative models
File(s)
Author(s)
Chrysos, Grigorios
Type
Thesis
Abstract
Data are collected at an unprecedented rate owing to the ubiquitous existence of sensors. Modeling such data, especially high-dimensional data such as images or videos, is of paramount importance. Deep generative models, that are implemented as multilayer neural networks, have demonstrated success in modeling distributions of high-dimensional data.
In this thesis, we explore new structures, models and approximation methods for deep generative models.
We initially focus on conditional data generation and study the robustness of the popular conditional Generative Adversarial Nets (cGAN). The model assumes a conditional input, e.g., a corrupted image, is available and we want to transform it into a high-dimensional output. However, our experiments illustrate that cGAN is not robust to noise. To mitigate that, we propose a new, augmented model, called RoCGAN, which leverages structure in the output space of the model. RoCGAN exhibits robust behavior even under intense noise.
Sequentially, we turn our attention to the function approximation method used for implementing deep generative models, i.e., feedforward neural networks. Little attention has been given to the method of choice for function approximation. To that end, we model the data generator as a high-order polynomial. We conduct experiments with the polynomial generator using Generative Adversarial Nets (GANs). We illustrate that the polynomial expansion is a very expressive function approximator and natural signals, such as images, can be approximated without the use of activation functions (i.e., a cornerstone of the approximation with feedforward neural networks).
The polynomial function approximation is generalized from modeling the generator of a GAN to modeling both generative and discriminative methods in diverse tasks, such as image or audio classification or representation learning in non-euclidean domains.
Lastly, we focus on the type of generative model. Despite the stellar success of GANs, their complicated training dynamics, make the study of alternative models imperative. To that end, we introduce a decoder-only method that uses a polynomial expansion to approximate natural images.
In this thesis, we explore new structures, models and approximation methods for deep generative models.
We initially focus on conditional data generation and study the robustness of the popular conditional Generative Adversarial Nets (cGAN). The model assumes a conditional input, e.g., a corrupted image, is available and we want to transform it into a high-dimensional output. However, our experiments illustrate that cGAN is not robust to noise. To mitigate that, we propose a new, augmented model, called RoCGAN, which leverages structure in the output space of the model. RoCGAN exhibits robust behavior even under intense noise.
Sequentially, we turn our attention to the function approximation method used for implementing deep generative models, i.e., feedforward neural networks. Little attention has been given to the method of choice for function approximation. To that end, we model the data generator as a high-order polynomial. We conduct experiments with the polynomial generator using Generative Adversarial Nets (GANs). We illustrate that the polynomial expansion is a very expressive function approximator and natural signals, such as images, can be approximated without the use of activation functions (i.e., a cornerstone of the approximation with feedforward neural networks).
The polynomial function approximation is generalized from modeling the generator of a GAN to modeling both generative and discriminative methods in diverse tasks, such as image or audio classification or representation learning in non-euclidean domains.
Lastly, we focus on the type of generative model. Despite the stellar success of GANs, their complicated training dynamics, make the study of alternative models imperative. To that end, we introduce a decoder-only method that uses a polynomial expansion to approximate natural images.
Version
Open Access
Date Issued
2020-07
Date Awarded
2020-12
Copyright Statement
Creative Commons Attribution Non-Commercial No Derivatives license
Advisor
Zafeiriou, Stefanos
Glocker, Benjamin
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)