Implicit Neural Representations: A Signal Processing Perspective

2026-04-16

AI Summary

This work addresses the limitations of traditional signal modeling, which relies on discrete sampling and struggles to unify multimodal continuous signals or support analytical operations. Viewing implicit neural representations (INRs) through the lens of signal processing, the study models images, audio, 3D geometry, and other modalities as continuous coordinate-based functions, realized via differentiable neural networks. The authors systematically analyze the spectral properties, sampling theory, and multiscale mechanisms underlying INRs and propose structured representation strategies—integrating periodicity, localization, adaptive activation functions, and hash-grid encodings—to reshape the approximation space for enhanced spatial adaptivity and computational efficiency. The resulting framework demonstrates superior performance in inverse problems such as medical and radar imaging, signal compression, and 3D scene reconstruction, advancing both the theoretical understanding and practical applicability of INRs as learnable continuous signal models.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework for representing images, audio, video, 3D geometry, and beyond as continuous functions of their coordinates. This functional viewpoint enables signal operations such as differentiation to be carried out analytically through automatic differentiation rather than through discrete approximations. In this article, we examine the evolution of INRs from a signal processing perspective, emphasizing spectral behavior, sampling theory, and multiscale representation. We trace the progression from standard coordinate based networks, which exhibit a spectral bias toward low frequency components, to more advanced designs that reshape the approximation space through specialized activations, including periodic, localized, and adaptive functions. We also discuss structured representations, such as hierarchical decompositions and hash grid encodings, that improve spatial adaptivity and computational efficiency. We further highlight the utility of INRs across a broad range of applications, including inverse problems in medical and radar imaging, compression, and 3D scene representation. By interpreting INRs as learned signal models whose approximation spaces adapt to the underlying data, this article clarifies the field's core conceptual developments and outlines open challenges in theoretical stability, weight space interpretability, and large scale generalization.

Problem

• Implicit Neural Representations
• Signal Processing
• Spectral Bias
• Sampling Theory
• Multiscale Representation

Innovation

• Implicit Neural Representations
• Signal Processing
• Spectral Bias
• Multiscale Representation
• Hash Grid Encoding