Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations (1704.00648v2)

Abstract: We present a new approach to learn compressible representations in deep architectures with an end-to-end training strategy. Our method is based on a soft (continuous) relaxation of quantization and entropy, which we anneal to their discrete counterparts throughout training. We showcase this method for two challenging applications: Image compression and neural network compression. While these tasks have typically been approached with different methods, our soft-to-hard quantization approach gives results competitive with the state-of-the-art for both.

• The paper introduces a soft-to-hard quantization method that enables differentiable training by transitioning from soft continuous approximations to hard discrete assignments.
• It presents a unified approach to both image and model compression, accurately estimating entropy without relying on parametric distribution assumptions.
• Experimental results on a 32-layer ResNet for CIFAR-10 demonstrate competitive compression ratios and a test accuracy of 92.1%, supporting efficient deployment in resource-constrained environments.

Analysis of "Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations"

Overview

The paper presents a novel perspective on end-to-end learning of compressible representations within deep neural networks (DNNs). The central contribution of this work is a method that employs a soft-to-hard vector quantization framework, transitioning progressively from soft (continuous) approximations to hard (discrete) quantization through an annealing process during training. This approach addresses two significant challenges in learning compressible representations: the non-differentiability of quantization operations and the accurate estimation of entropy.

Methodology

The proposed method offers a unified approach to tackle compression in two distinct domains: image compression and DNN model compression. Utilizing a soft relaxation of quantization, the strategy allows for continuous optimization of the model parameters and entropy during the training process.

Key features of the proposed framework include:

1. Unified Compression Approach: The method provides a cohesive framework for both feature and model parameter compression, typically studied independently. The unified view enhances its applicability across various domains.
2. Direct Differentiability: By adopting a soft assignment strategy, the method ensures differentiability throughout the optimization process, contrasting with traditional rounding-based or stochastic quantization schemes.
3. Vector Quantization: The paper argues for the advantages of vector quantization in learned compression, showing its benefits over scalar quantization by enabling applications to a broader set of problems.
4. Entropy Estimation Without Parametric Assumptions: By employing a histogram-based probability distribution model, the method avoids common assumptions about the marginal distributions in the compressible representations.
5. Implementation and Results: The framework is effectively applied to DNN model compression and image compression. For a 32-layer ResNet model on CIFAR-10, the method achieves compression ratios competitive with state-of-the-art approaches while maintaining performance.

Numerical Results and Claims

The authors present compelling results across both major applications. The method achieves state-of-the-art compression ratios without compromising the performance of a 32-layer ResNet on CIFAR-10, maintaining a test accuracy of 92.1%. For image compression, the scheme shows performance comparable to leading methods like BPG, particularly when evaluated on high-compression scenarios. These results underscore the efficacy of the proposed soft-to-hard annealing approach in realistically compressible scenarios in both applications.

Implications and Future Directions

The implications of this research are significant both in theory and practice. By enabling end-to-end learning of compressible neural representations, this method facilitates more efficient deployment of DNNs in environments with constrained resources, such as mobile and embedded devices. The simplicity and generalizability of the proposed framework suggest potential extensions to diverse data types and DNN architectures.

Future research could explore the optimization of annealing schedules and the expansion of the quantization framework to handle additional data modalities. Further, integrating this approach with more sophisticated entropy coding techniques could enhance compression efficiency.

Overall, this paper contributes a versatile and effective tool to the toolbox of AI researchers and practitioners focused on compression, with evidence of competitive performance across multiple benchmarks and applications.