[Paper Review] Gradient Layer: Enhancing the Convergence of Adversarial Training for Generative Models

Atsushi Nitanda, Taiji Suzuki|arXiv (Cornell University)|Jan 7, 2018

Model Reduction and Neural Networks4 citations

TL;DR

This paper introduces the gradient layer, a novel technique that enhances adversarial training convergence in generative models by enabling optimization in an infinite-dimensional function space via functional gradients. By treating the generator as a continuous function and using gradient flow discretization, the method escapes local optima in finite-dimensional models, achieving faster convergence and improved sample quality—demonstrated by improved inception scores on CIFAR-10 and STL-10 datasets.

ABSTRACT

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep network is expressed using a highly non-convex finite-dimensional model, and thus the parameter gets stuck in a local optimum. Because of this, methods often suffer not only from degeneration of the convergence speed but also from limitations in the representational power of the trained network. To overcome this issue, we propose an additional layer called the gradient layer to seek a descent direction in an infinite-dimensional space. Because the layer is constructed in the infinite-dimensional space, we are not restricted by the specific model structure of finite-dimensional models. As a result, we can get out of the local optima in finite-dimensional models and move towards the global optimal function more directly. In this paper, this phenomenon is explained from the functional gradient method perspective of the gradient layer. Interestingly, the optimization procedure using the gradient layer naturally constructs the deep structure of the network. Moreover, we demonstrate that this procedure can be regarded as a discretization method of the gradient flow that naturally reduces the objective function. Finally, the method is tested using several numerical experiments, which show its fast convergence.

Motivation & Objective

• To address the slow convergence and local optima issues in adversarial training of deep generative models.
• To overcome the representational limitations of finite-dimensional parameterized generators in GANs.
• To develop a method that escapes local optima by operating in an infinite-dimensional function space.
• To provide a theoretical justification for faster convergence using functional gradient methods.
• To demonstrate the effectiveness of the gradient layer through empirical evaluation on standard benchmarks.

Proposed method

• Introduces the gradient layer as a mechanism to compute functional gradients in an infinite-dimensional space, avoiding constraints of finite-dimensional parameterization.
• Uses the functional gradient method to find a descent direction that is not restricted to the tangent space of the finite-dimensional model.
• Treats the training process as a discretization of the gradient flow in the space of probability measures, minimizing the distance between generated and real data distributions.
• Stacks gradient layers sequentially, where each iteration corresponds to adding a new layer to the generator, naturally forming a deep architecture.
• Applies the method in the final training phase by inserting gradient layers below the generator's output activation (e.g., tanh).
• Employs ADAM for critic training and uses a modified learning rate schedule for the gradient layer updates to ensure stability and convergence.

Experimental results

Research questions

• RQ1 Can infinite-dimensional optimization via functional gradients improve convergence in adversarial training of GANs?
• RQ2 Does the gradient layer method escape local optima that constrain finite-dimensional models?
• RQ3 Can the gradient layer be interpreted as a discretization of the gradient flow in the space of probability measures?
• RQ4 How does the gradient layer affect the representational power and sample quality of the generator?
• RQ5 Does the method achieve faster convergence and better performance compared to standard GANs and WGANs?

Key findings

• On the CIFAR-10 dataset, the inception score improved from 6.32 (WGAN-GP) to 6.80 after applying the gradient layer, indicating faster convergence and better sample quality.
• On the STL-10 dataset, the inception score increased from 7.40 (WGAN-GP) to 7.71 using the gradient layer, demonstrating consistent performance gains.
• The method achieved high-quality sample generation on challenging toy datasets (e.g., 8-gaussian and 25-gaussian) within just 100 generator iterations, even without pre-training.
• The gradient layer method showed rapid improvement in inception scores during the final training phase, suggesting effective optimization of the generator's representational capacity.
• Theoretical analysis confirms that the gradient layer corresponds to a discretization of the gradient flow in the space of probability measures, providing a principled optimization framework.
• The method naturally constructs deep architectures by stacking gradient layers, with each iteration equivalent to adding a new layer to the generator.