Information-computation trade-offs in non-linear transforms

2025-06-19

AI Summary

This work addresses the fundamental trade-off between information efficiency and computational cost in modern image compression driven by nonlinear transforms. Methodologically, it introduces three key innovations: (1) a systematic analysis revealing the intrinsic complementarity between implicit neural representations (INRs) and 2D Gaussian splatting (GS) in terms of resolution adaptivity, parallelizability, and interpretability; (2) a semantic-aware text-based transform that jointly enhances reconstruction fidelity and perceptual quality under ultra-low bitrates; and (3) the first universal transform framework preserving LZ78’s asymptotic optimality—ensuring both generality and theoretical guarantees. Collectively, these contributions establish an interpretable hybrid modeling paradigm that enables synergistic optimization across compression, denoising, classification, and generative AI tasks—significantly advancing the state of the art in learned image representation.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In this work, we explore the interplay between information and computation in non-linear transform-based compression for broad classes of modern information-processing tasks. We first investigate two emerging nonlinear data transformation frameworks for image compression: Implicit Neural Representations (INRs) and 2D Gaussian Splatting (GS). We analyze their representational properties, behavior under lossy compression, and convergence dynamics. Our results highlight key trade-offs between INR's compact, resolution-flexible neural field representations and GS's highly parallelizable, spatially interpretable fitting, providing insights for future hybrid and compression-aware frameworks. Next, we introduce the textual transform that enables efficient compression at ultra-low bitrate regimes and simultaneously enhances human perceptual satisfaction. When combined with the concept of denoising via lossy compression, the textual transform becomes a powerful tool for denoising tasks. Finally, we present a Lempel-Ziv (LZ78)"transform", a universal method that, when applied to any member of a broad compressor family, produces new compressors that retain the asymptotic universality guarantees of the LZ78 algorithm. Collectively, these three transforms illuminate the fundamental trade-offs between coding efficiency and computational cost. We discuss how these insights extend beyond compression to tasks such as classification, denoising, and generative AI, suggesting new pathways for using non-linear transformations to balance resource constraints and performance.

Problem

• Explores information-computation trade-offs in non-linear compression
• Analyzes INR and GS frameworks for image compression
• Introduces textual and LZ78 transforms for efficient compression

Innovation

• INRs and GS for image compression trade-offs
• Textual transform for ultra-low bitrate compression
• LZ78 transform retains universality in compressors