Implicit Neural Representations: A Signal Processing Perspective

arXiv cs.CV / 4/17/2026

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Key Points

Implicit Neural Representations (INRs) reframe signal modeling by representing signals as continuous functions learned by neural networks rather than relying on discrete samples.
The article analyzes INR evolution from a signal-processing viewpoint, focusing on spectral behavior, sampling theory, and multiscale representations to explain why they work.
It contrasts basic coordinate-based networks that tend to favor low-frequency components with newer INR designs that use specialized activations (e.g., periodic, localized, adaptive) to reshape the approximation space.
It highlights structured INR representations such as hierarchical decompositions and hash-grid encodings to improve spatial adaptivity and computational efficiency.
The piece surveys applications spanning inverse problems (medical/radar imaging), compression, and 3D scene representation, while outlining open research challenges in theoretical stability, weight-space interpretability, and large-scale generalization.

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.