HOIN: High-Order Implicit Neural Representations

TL;DR

HOIN introduces a high-order implicit neural representation framework that enhances expressive power and mitigates spectral bias, leading to improved inverse problem solving and state-of-the-art results.

Contribution

The paper proposes a universal high-order framework for INRs that improves spectral bias mitigation and model expressiveness through high-order interactions and analysis of NTK properties.

Findings

Achieves 1-3 dB improvement in inverse problem recovery.

Establishes a new state-of-the-art in inverse problem solutions.

Provides theoretical validation of HOIN's effectiveness.

Abstract

Implicit neural representations (INR) suffer from worsening spectral bias, which results in overly smooth solutions to the inverse problem. To deal with this problem, we propose a universal framework for processing inverse problems called \textbf{High-Order Implicit Neural Representations (HOIN)}. By refining the traditional cascade structure to foster high-order interactions among features, HOIN enhances the model's expressive power and mitigates spectral bias through its neural tangent kernel's (NTK) strong diagonal properties, accelerating and optimizing inverse problem resolution. By analyzing the model's expression space, high-order derivatives, and the NTK matrix, we theoretically validate the feasibility of HOIN. HOIN realizes 1 to 3 dB improvements in most inverse problems, establishing a new state-of-the-art recovery quality and training efficiency, thus providing a new general paradigm for INR and paving the way for it to solve the inverse problem.