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Information-computation trade-offs in nonlinear transforms
Connor Ding1, Abhiram Gorle1, Jiwon Jeong1
1Stanford University , Stanford, CA, USA.
Summary
This study explores nonlinear transforms for efficient data compression, analyzing implicit neural representations, Gaussian splatting, and textual transforms. These methods balance coding efficiency and computational cost for AI tasks.
Area of Science:
- Information Theory
- Computer Science
- Artificial Intelligence
Background:
- Modern information processing demands efficient compression techniques.
- Nonlinear transformations offer novel approaches to data compression and representation.
Purpose of the Study:
- To investigate the interplay between information and computation in nonlinear transform-based compression.
- To analyze emerging nonlinear data transformation frameworks for image compression and other AI tasks.
Main Methods:
- Analysis of implicit neural representations (INRs) and 2D Gaussian splatting (GS) for image compression.
- Introduction of a textual transform for ultra-low bit rate compression and denoising.
- Description of a Lempel-Ziv (LZ78) transform for universal compression.
Main Results:
- Key trade-offs identified between INR's flexibility and GS's parallelizability.
- Textual transform enhances perceptual satisfaction and aids denoising.
- LZ78 transform ensures asymptotic universality for new compressor families.
Conclusions:
- Nonlinear transforms offer fundamental trade-offs between coding efficiency and computational cost.
- Insights extend to classification, denoising, and generative AI, guiding resource-constrained AI development.
- This work contributes to sustainable AI through efficient information processing.
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