[Paper Review] Adversarial Learning with Local Coordinate Coding

Jiezhang Cao, Yong Guo+4 more|arXiv (Cornell University)|Jun 13, 2018

Generative Adversarial Networks and Image Synthesis23 references21 citations

TL;DR

This paper proposes LCC-GANs, a generative adversarial network that uses Local Coordinate Coding (LCC) to sample from the latent manifold of real data, capturing local geometric structure for improved generation. By learning a data-driven latent distribution via autoencoders and applying LCC-based sampling, the method achieves strong generalization with low-dimensional inputs, outperforming state-of-the-art GANs even at d=30 while matching or exceeding performance at d=100.

ABSTRACT

Generative adversarial networks (GANs) aim to generate realistic data from some prior distribution (e.g., Gaussian noises). However, such prior distribution is often independent of real data and thus may lose semantic information (e.g., geometric structure or content in images) of data. In practice, the semantic information might be represented by some latent distribution learned from data, which, however, is hard to be used for sampling in GANs. In this paper, rather than sampling from the pre-defined prior distribution, we propose a Local Coordinate Coding (LCC) based sampling method to improve GANs. We derive a generalization bound for LCC based GANs and prove that a small dimensional input is sufficient to achieve good generalization. Extensive experiments on various real-world datasets demonstrate the effectiveness of the proposed method.

Motivation & Objective

• To address the limitation of standard GANs that rely on independent, pre-defined priors (e.g., Gaussian) which lose semantic and geometric structure.
• To develop a sampling method that leverages local manifold structure in the latent space to generate more semantically meaningful and diverse samples.
• To theoretically analyze the generalization performance of GANs in relation to the intrinsic dimensionality of the latent manifold.
• To demonstrate that a small-dimensional latent space is sufficient for good generalization when using LCC-based sampling.

Proposed method

• An autoencoder is trained to embed real data into a low-dimensional latent manifold, preserving semantic and geometric structure.
• Local Coordinate Coding (LCC) is applied to represent points on the latent manifold using a set of anchor points and adaptive weights.
• The LCC sampling method generates new latent codes by combining nearby anchor points with learned coefficients, enabling localized, structure-aware sampling.
• A generalization bound is derived using Rademacher complexity, linking discriminator error and intrinsic manifold dimensionality.
• The generator is trained adversarially using LCC-sampled latent vectors, improving data fidelity and diversity.
• The method is evaluated on MNIST, Oxford-102, LSUN, and CelebA using MS-SSIM and visual quality comparisons.

Experimental results

Research questions

• RQ1 Can LCC-based sampling from a data-driven latent manifold improve the quality and diversity of generated images in GANs compared to standard Gaussian priors?
• RQ2 What is the relationship between the intrinsic dimensionality of the latent manifold and the generalization performance of GANs?
• RQ3 Can a low-dimensional latent space (e.g., d=30) achieve better or comparable performance than high-dimensional spaces (e.g., d=100) when using LCC sampling?
• RQ4 How does LCC sampling compare to standard sampling in terms of preserving local structure and semantic content in generated samples?
• RQ5 Does the proposed method generalize well to unseen data without memorizing training samples?

Key findings

• LCC-GANs with d=30 outperform Progressive GANs with d=100 on all datasets in terms of image quality and diversity, as measured by MS-SSIM.
• On CelebA, LCC-GANs achieve an MS-SSIM of 0.305 at d=30, outperforming Progressive GANs (0.308) and WGANs (0.324) at d=100.
• The proposed method generates sharp, diverse digits on MNIST with varying orientations and styles, even when sampling from a fixed set of anchor points.
• Visual comparisons show that generated images are semantically similar to real images in the training set, indicating generalization rather than memorization.
• The theoretical analysis proves that a small-dimensional input is sufficient for good generalization, with performance bounded by the intrinsic dimension of the latent manifold.
• LCC sampling enables consistent generation of images with shared features (e.g., similar flower shapes or facial structures) while varying in color or style, confirming effective local structure exploitation.