Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters

2025-04-15

AI Summary

Traditional implicit neural representations (INRs) suffer from aliasing of multi-frequency visual information in the native spatial domain and rely on manually tuned hyperparameters—namely, the frequency parameter ω and tensor rank R—thereby limiting representational fidelity and cross-domain generalization. To address these limitations, we propose Cross-Frequency Implicit Neural Representations (CF-INR). First, input signals are decomposed into four distinct frequency bands via Haar wavelet transform. Second, each band is independently modeled in the wavelet domain, with cross-frequency tensor decomposition enabling data-adaptive band-specific encoding. Third, a self-evolving parameter mechanism dynamically optimizes both rank R and frequency ω per band, eliminating manual hyperparameter tuning. Extensive experiments on image regression, inpainting, denoising, and cloud removal demonstrate that CF-INR consistently surpasses state-of-the-art methods, achieving significant gains in reconstruction accuracy and robust generalization across diverse scenes.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Implicit neural representation (INR) has emerged as a powerful paradigm for visual data representation. However, classical INR methods represent data in the original space mixed with different frequency components, and several feature encoding parameters (e.g., the frequency parameter $omega$ or the rank $R$) need manual configurations. In this work, we propose a self-evolving cross-frequency INR using the Haar wavelet transform (termed CF-INR), which decouples data into four frequency components and employs INRs in the wavelet space. CF-INR allows the characterization of different frequency components separately, thus enabling higher accuracy for data representation. To more precisely characterize cross-frequency components, we propose a cross-frequency tensor decomposition paradigm for CF-INR with self-evolving parameters, which automatically updates the rank parameter $R$ and the frequency parameter $omega$ for each frequency component through self-evolving optimization. This self-evolution paradigm eliminates the laborious manual tuning of these parameters, and learns a customized cross-frequency feature encoding configuration for each dataset. We evaluate CF-INR on a variety of visual data representation and recovery tasks, including image regression, inpainting, denoising, and cloud removal. Extensive experiments demonstrate that CF-INR outperforms state-of-the-art methods in each case.

Problem

• Decouples data into four frequency components using Haar wavelet
• Automatically updates rank and frequency parameters via self-evolving optimization
• Enhances accuracy in visual data representation and recovery tasks

Innovation

• Haar wavelet transform for frequency decoupling
• Self-evolving cross-frequency tensor decomposition
• Automatic rank and frequency parameter optimization