PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications (1701.05517v1)

Abstract: PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.

• The paper introduces a discretized logistic mixture likelihood that significantly improves the modeling of pixel distributions in natural images.
• It adopts a multi-scale architecture with downsampling, upsampling, and residual connections to efficiently capture complex spatial dependencies.
• Empirical results on CIFAR-10 and ImageNet demonstrate competitive log-likelihood scores, validating its enhanced generative performance.

PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications

The paper "PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications" by Tim Salimans, Andrej Karpathy, Xi Chen, and Diederik P. Kingma presents a series of methodological advancements aimed at enhancing the existing PixelCNN architecture. This work addresses both the performance and complexity issues observed in earlier iterations of PixelCNN by incorporating several key improvements.

Methodological Enhancements

The authors introduce a discretized logistic mixture likelihood for modeling the output distribution of the network. This represents a significant shift from the conventional multinomial distribution previously used in PixelCNN. The new likelihood function is shown to yield a better fit for the pixel values in natural images, resulting in enhanced generative performance.

Further improvements include architectural modifications:

1. Hierarchical structure: The model adopts a multi-scale architecture that captures spatial dependencies across different resolutions, leading to more efficient learning of global structures.
2. Downsampling and upsampling blocks: These blocks are employed to reduce the computational overhead and memory requirements, enabling the model to handle higher-resolution images without a corresponding increase in complexity.
3. Residual connections: The integration of residual connections facilitates deeper architectures by mitigating the vanishing gradient problem, thus improving the model's ability to learn more complex representations.

Numerical Results

The paper provides empirical evidence supporting these modifications with several quantitative results. The enhanced PixelCNN++ achieves competitive log-likelihood scores on benchmark datasets such as CIFAR-10 and ImageNet downsampled to 32x32 and 64x64 resolutions. Notably, on the CIFAR-10 dataset:

• PixelCNN++ achieves a log-likelihood of 2.92 bits per dimension.
• This is an improvement over the original PixelCNN and comparable to other contemporary generative models, including autoregressive and variational autoencoders.

These results underscore the efficacy of the proposed methodological refinements in generating high-fidelity images.

Implications and Future Directions

The proposed enhancements to the PixelCNN architecture have significant implications for the field of generative modeling. By introducing a more accurate likelihood model and streamlining computational efficiency through architectural adjustments, PixelCNN++ represents a stronger candidate for applications requiring high-quality image synthesis.

From a theoretical perspective, the incorporation of discretized logistic mixture likelihood provides a new avenue for future research in pixel-level modeling. Practically, the model's efficient handling of high-resolution images opens the door to its deployment in areas such as data augmentation, image inpainting, and super-resolution, where maintaining high visual fidelity is crucial.

Future developments may explore the integration of adversarial training techniques to further refine the generative quality of PixelCNN++ models. Additionally, extending this architecture to other data modalities, such as videos or 3D point clouds, could yield compelling advancements in understanding and generating complex data structures.

In conclusion, this paper contributes valuable insights and practical improvements to generative modeling, enhancing the utility and performance of the PixelCNN framework.