EmbeddGAN: A Novel GAN Framework Using an Embedding Network and Gini Distance Correlation
Authors: MaTais Caldwell, Yixin Chen, Xin Dang, Charles Walter
Organizations: Department of Computer and Information Science University of Mississippi Oxford, MS 38677 USA · Department of Mathematics University of Mississippi Oxford, MS 38677 USA
Generative Adversarial Networks (GANs) have demonstrated strong performance in generating high-quality synthetic data. However, they are limited by no formal guarantees regarding convergence and the effectiveness of the learning process. In practice, this leads to training instability, mode collapse, and sensitivity to hyperparameters. To address this, we propose EmbeddGAN, a novel adversarial training framework based on a dependence-based objective. Instead of relying on a discriminator that classifies samples as real or fake, EmbeddGAN introduces an embedding network that learns a representation in which statistical dependence between samples and their real/fake labels is maximized, while the generator is trained to minimize this dependence. This objective is implemented using the Gini distance correlation (gCor), which equals zero if and only if the embeddings are statistically independent of the real/fake label. Minimizing this objective therefore encourages real and generated samples to become statistically indistinguishable in the learned embedding space. The embedding network projects both real and generated data into a shared low-dimensional space, where distributional discrepancies can be measured directly through pairwise distances. We adopt a minimax training strategy: the embedding network maximizes the Gini distance correlation (maximizing dependence), while the generator minimizes it (minimizing dependence). Experiments on the MNIST, CIFAR-10, and CelebA datasets demonstrate that EmbeddGAN achieves competitive performance relative to established baselines while exhibiting notably stable training dynamics on the evaluated datasets.
Figures & tables
Figure 1: Overview of the traditional GAN architecture.
Figure 2: Overview of the EmbeddGAN architecture. Both real and generated images are projected into a shared embedding space by the embedding network E . The Gini distance correlation compares the distributions of real and fake embeddings.
Hyperparameter
Value
Epochs T
500
Latent dimension zd
100
Embedding dimension n
100
Learning rate η
2×10−4
Adam β1
0.5
Adam β2
0.999
Table 2: EmbeddGAN hyperparameters.
Model
MNIST ↓
CIFAR-10 ↓
CelebA ↓
EmbeddGAN
6.59
50.89
32.09
DCGAN
6.63
41.92
37.30
WGAN-GP
9.71
47.66
30.67
SN-GAN
7.96
60.87
23.97
Table 3: Fréchet Inception Distance on the MNIST, CIFAR-10, and CelebA dataset at 500 epochs. Scores are computed over a sample size of 50000.
Model
MNIST ↑
CIFAR-10 ↑
CelebA ↑
EmbeddGAN
0.854
0.469
0.352
DCGAN
0.844
0.472
0.376
WGAN-GP
0.824
0.483
0.495
SN-GAN
0.819
0.328
0.471
Table 4: Recall on the MNIST, CIFAR-10, and CelebA dataset at 500 epochs. Scores are computed over a sample size of 10000.
Figure 3: Generated samples from EmbeddGAN, WGAN-GP, SN-GAN and DCGAN on CelebA at epoch 500.
Figure 4: Generated samples from EmbeddGAN, WGAN-GP, SN-GAN and DCGAN on CIFAR-10 at epoch 500.
Figure 5: FID score vs. training epoch for EmbeddGAN, DCGAN, WGAN-GP, and SN-GAN on MNIST, CIFAR-10, and CelebA. Computed over a sample size of 5000 . Lower is better. EmbeddGAN maintains consistent stability on MNIST across all epochs and matches WGAN-GP on CIFAR-10 by epoch 300. DCGAN exhibits substantial oscillation on CelebA and occasional instability on MNIST.
Figure 6: Gini distance correlation loss curve for EmbeddGAN on MNIST, CIFAR-10, and CelebA. MNIST converges quickly to a stable plateau near 0.2 . CIFAR-10 shows high early volatility before settling around 0.25 – 0.30 , with a brief collapse near epoch 270 . CelebA stabilizes around 0.45 – 0.50 but drifts upward through training, indicating the embedding network maintains a persistent advantage over the generator on the more complex dataset.
Figure 7: Average 2D Fourier power spectrum of generated and real CelebA images during unregularized EmbeddGAN training. The generated spectrum exhibits a periodic grid of bright peaks at evenly spaced frequencies, characteristic of transposed convolution checkerboard aliasing.
Figure 8: Adding L2 normalization alone eliminates the periodic grid of peaks, confirming that constraining embeddings to the unit hypersphere closes the aliasing shortcut. The generated spectrum remains noisy overall, however, with the difference map showing broadly distributed excess high-frequency energy, indicating that L2 suppresses the structural artifact but cannot align the generator’s output with the real spectral distribution.
Figure 9: R1 regularization alone also eliminates the periodic grid, but via a different mechanism: penalizing gradients on real images removes the training incentive to exploit aliasing rather than constraining the embedding space. The spectrum remains unstructured, with excess high-frequency energy distributed throughout the difference map, mirroring the residual noise seen with L2 alone and indicating that neither component is sufficient on its own.
Figure 10: Average 2D Fourier power spectrum of generated and real CelebA images after the introduction of L2 normalization and R1 regularization in EmbeddGAN at epoch 300. The periodic peaks observed in the generated spectrum are substantially reduced, indicating that the tiling artifacts have been mitigated.
Variant
CelebA FID ↓
Full EmbeddGAN (L2 + R1)
29.29
R1 only, no L2
54.29
No L2, no R1
70.22
L2 only, no R1
179.21
Table 5: Ablation study of EmbeddGAN on CelebA at epoch 300 over 50000 samples. Removing either regularization component leads to a substantial increase in FID; L2 normalization alone produces the worst result, as it forces the embedding network toward the contrast shortcut.
Figure 11: Generated CelebA samples showing the development of EmbeddGAN’s regularization strategy. (a) Without either component, the generator produces colorful tiling artifacts. (b) L2 alone resolves the magnitude shortcut, but the embedding network finds high-contrast regions as the next shortcut, causing contrast collapse. (c) R1 alone does not prevent the magnitude shortcut when embeddings are unbounded. (d) With both L2 and R1, both escape routes are closed, and the generator produces clean, diverse faces.
Embedding Dims
CelebA FID ↓
1
411.39
3
28.31
5
27.09
10
29.25
50
39.18
100
32.09
Table 6: Ablation study of EmbeddGAN with varying embedding dimensions on CelebA at epoch 500 over 50000 samples. Comparison n=100 in bold.
Figure 12: Qualitative comparison of generated CelebA samples from EmbeddGAN with varying embedding dimensions after 500 epochs.
k_steps
CelebA FID ↓
1
29.29
3
43.15
5
47.54
10
131.36
Table 7: Ablation study of EmbeddGAN with varying embedding net steps per generator update on CelebA at epoch 300 over 50000 samples.
Figure 13: Qualitative comparison of generated CelebA samples from EmbeddGAN with varying numbers of embedding steps per generator update after 300 epochs.
Figure 14: Visualization of the EmbeddGAN embedding space on CelebA using t-SNE at epochs 1, 25, 100, and 300. At epoch 1, real and generated embeddings are intermixed with no discernible structure. By epoch 25, the two distributions have separated into distinct curved manifolds in the projected space, and this separation is maintained at epoch 100 and 300, providing a persistent distributional signal for gCor to measure.
Generative Adversarial Networks (GANs) train competing generators and discriminators to synthesize data, translate images, and model complex distributions.