Lossy Compression for Lossless Prediction (2106.10800v5)

Abstract: Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations. Based on our theory, we design unsupervised objectives for training neural compressors. Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than $1000\times$ on ImageNet) compared to JPEG on 8 datasets, without decreasing downstream classification performance.

• The paper presents a novel approach that tailors lossy compression to preserve only the essential invariant information needed for machine learning predictions.
• It formulates a rate-invariance theorem linking minimal bit-rate requirements to the entropy of maximal invariants, ensuring high predictive performance.
• Experimental results demonstrate up to 1000x compression on ImageNet without sacrificing classification accuracy, highlighting practical scalability.

Understanding Lossy Compression for Predictive Performance

Introduction

Compressing data often involves a trade-off between reducing file sizes and retaining as much original information as possible. Traditional methods like JPEG prioritize human perception, but what if the goal is to ensure high performance in predictive tasks instead? The paper "Lossy Compression for Lossless Prediction" explores this idea, proposing a novel approach to compression that focuses on preserving only the critical information needed for downstream predictive tasks.

Key Concepts

Traditional vs. Task-Specific Compression

• Traditional Compression: Methods like JPEG reconstruct images focusing on human perceptual fidelity.
• Task-Specific Compression: This approach aims to retain only the data necessary for high predictive performance on downstream machine learning tasks.

Invariance and Maximal Invariants

The paper's central concept revolves around invariances and maximal invariants:

• Invariance Under Transformations: Predictive performance often remains invariant under certain data transformations (e.g., image rotations).
• Maximal Invariants: These are functions that capture the essence of these invariances, reducing data to its core components necessary for predictions.

Theoretical Foundations

Rate-Invariance Theorem

The authors formulate a rate-invariance theorem that describes the minimal bit-rate required for storing data while ensuring high predictive performance on any future task invariant to specified transformations. They show that if you know the invariances ahead of time, you can discard all other information, resulting in significant compression gains.

Key Result: For tasks invariant under certain transformations, the bit-rate required to maintain performance is tightly linked to the entropy of the maximal invariant—essentially the minimal information necessary to predict any relevant task.

Practical Implementations

The paper proposes two main unsupervised neural compressors:

1. Variational Invariant Compressor (VIC): This model uses a variational autoencoder modified to reconstruct canonical examples, focusing on invariant features.
2. Bottleneck InfoNCE (BINCE): This model leverages contrastive learning, transforming pre-trained self-supervised models into powerful compressors.

Experimental Results

ImageNet Compression

A highlight of the research is the impressive compression achieved on the ImageNet dataset:

• Compression Gains: The proposed methods achieve up to 1000 times better compression rates compared to JPEG without sacrificing classification performance, showing real-world applicability in large-scale settings.

Augmented MNIST

The VIC method was tested on augmented MNIST digits, and the results showed significant bit-rate reductions while maintaining high classification accuracy.

Implications and Future Directions

This research opens several avenues for exploration:

• Scalability to Other Tasks: Extending the approach to diverse predictive tasks beyond classification, such as object detection or segmentation.
• Impact on Storage and Transmission: Reduced bit-rates can lead to significant savings in storage and faster data transmission, which is critical for data-heavy fields like climate science or autonomous driving.
• Future Enhancements: Investigating improved augmentation methods and more sophisticated entropy models to enhance compression rates further.

Conclusion

The paper "Lossy Compression for Lossless Prediction" presents a paradigm shift in data compression tailored for machine learning. By focusing on preserving only the necessary information for predictive tasks and discarding redundant data, the proposed methods achieve remarkable compression gains without compromising performance. This approach holds great promise for various applications, from efficient data storage and transmission to enabling scalable machine learning in data-intensive fields.