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Compensaciones entre información y computación en transformaciones no lineales

Connor Ding¹, Abhiram Gorle¹, Jiwon Jeong¹

¹Stanford University , Stanford, CA, USA.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

|February 28, 2026

Resumen

Este resumen es generado por máquina.

Este estudio explora transformaciones no lineales para una compresión de datos eficiente, analizando representaciones neuronales implícitas, representación de salpicaduras gaussianas y transformaciones textuales. Estos métodos equilibran la eficiencia de codificación y el costo computacional para tareas de IA.

Palabras clave:

universalidad de Lempel-Ziv compensación compresión-computación IA generativa representaciones neuronales implícitas poda de modelos transformaciones no lineales teoría de la tasa de distorsión transformaciones textuales

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Área de la Ciencia:

Teoría de la Información
Ciencias de la Computación
Inteligencia Artificial

Sus antecedentes:

El procesamiento moderno de la información exige técnicas de compresión eficientes.
Las transformaciones no lineales ofrecen enfoques novedosos para la compresión y representación de datos.

Objetivo del estudio:

Investigar la interacción entre información y computación en la compresión basada en transformaciones no lineales.
Analizar marcos emergentes de transformación de datos no lineales para la compresión de imágenes y otras tareas de IA.

Principales métodos:

Análisis de representaciones neuronales implícitas (INR) y representación de salpicaduras gaussianas 2D (GS) para la compresión de imágenes.
Introducción de una transformación textual para compresión y eliminación de ruido de tasa de bits ultrabaja.
Descripción de una transformación de Lempel-Ziv (LZ78) para compresión universal.

Principales resultados:

Se identificaron compensaciones clave entre la flexibilidad de INR y la paralelización de GS.
La transformación textual mejora la satisfacción perceptual y ayuda a la eliminación de ruido.
La transformación LZ78 garantiza la universalidad asintótica para nuevas familias de compresores.

Conclusiones:

Las transformaciones no lineales ofrecen compensaciones fundamentales entre la eficiencia de codificación y el costo computacional.
Las ideas se extienden a la clasificación, la eliminación de ruido y la IA generativa, guiando el desarrollo de IA con recursos limitados.
Este trabajo contribuye a la IA sostenible a través del procesamiento eficiente de la información.