Compact Hadamard Latent Codes for Efficient Spectral Rendering

2026-02-21

AI Summary

Spectral rendering is challenging to integrate efficiently into existing RGB pipelines due to its requirement for extensive wavelength sampling and full spectral asset support. This work proposes Hadamard Spectral Encoding, which introduces, for the first time, a non-negative learnable latent code structure that exactly preserves linear scaling and addition while approximately preserving element-wise multiplication—thereby overcoming theoretical limitations of low-dimensional algebra-preserving representations. Built upon non-negative linear encoding/decoding, Hadamard product approximation, and lightweight neural upsampling, the method achieves significant chromatic error reduction with only two render passes (k=6) on a standard RGB renderer, substantially outperforming conventional approaches in speed. At k=9, it produces high-quality reference results with perceptually accurate color reproduction and seamless compatibility with legacy RGB assets.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Spectral rendering accurately reproduces wavelength-dependent appearance but is computationally expensive, as shading must be evaluated at many wavelength samples and scales roughly linearly with the number of samples. It also requires spectral textures and lights throughout the rendering pipeline. We propose Hadamard spectral codes, a compact latent representation that enables spectral rendering using standard RGB rendering operations. Spectral images are approximated with a small number of RGB rendering passes, followed by a decoding step. Our key requirement is latent linearity: scaling and addition in spectral space correspond to scaling and addition of codes, and the element-wise product of spectra (for example reflectance times illumination) is approximated by the element-wise product of their latent codes. We show that an exact low-dimensional algebra-preserving representation cannot exist for arbitrary spectra when the latent dimension k is smaller than the number of spectral samples n. We therefore introduce a learned non-negative linear encoder and decoder architecture that preserves scaling and addition exactly while encouraging approximate multiplicativity under the Hadamard product. With k = 6, we render k/3 = 2 RGB images per frame using an unmodified RGB renderer, reconstruct the latent image, and decode to high-resolution spectra or XYZ or RGB. Experiments on 3D scenes demonstrate that k = 6 significantly reduces color error compared to RGB baselines while being substantially faster than naive n-sample spectral rendering. Using k = 9 provides higher-quality reference results. We further introduce a lightweight neural upsampling network that maps RGB assets directly to latent codes, enabling integration of legacy RGB content into the spectral pipeline while maintaining perceptually accurate colors in rendered images.

Problem

• spectral rendering
• computational efficiency
• RGB compatibility
• latent representation
• color accuracy

Innovation

• Hadamard spectral codes
• spectral rendering
• latent linearity
• efficient rendering
• neural upsampling