Information-computation trade-offs in non-linear transforms
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908413235036160 |
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| author | Ding, Connor Gorle, Abhiram Rao Jeong, Jiwon Sagan, Naomi Weissman, Tsachy |
| author_facet | Ding, Connor Gorle, Abhiram Rao Jeong, Jiwon Sagan, Naomi Weissman, Tsachy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information-computation trade-offs in non-linear transforms Ding, Connor Gorle, Abhiram Rao Jeong, Jiwon Sagan, Naomi Weissman, Tsachy Information Theory Image and Video Processing 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. |
| title | Information-computation trade-offs in non-linear transforms |
| topic | Information Theory Image and Video Processing |
| url | https://arxiv.org/abs/2506.15948 |