Dynamical Implicit Neural Representations

TL;DR

Dynamical Implicit Neural Representations (DINR) introduce a continuous-time dynamical system approach to INRs, enhancing their ability to capture high-frequency details and improve stability, expressivity, and generalization.

Contribution

DINR models feature evolution as a continuous dynamical system, addressing spectral bias and improving INR performance over traditional discrete-layer methods.

Findings

Better high-frequency detail capture

More stable convergence and training dynamics

Enhanced generalization and signal fidelity

Abstract

Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, but spectral bias remains a fundamental challenge, limiting their ability to capture high-frequency details. Orthogonal to existing remedy strategies, we introduce Dynamical Implicit Neural Representations (DINR), a new INR modeling framework that treats feature evolution as a continuous-time dynamical system rather than a discrete stack of layers. This dynamical formulation mitigates spectral bias by enabling richer, more adaptive frequency representations through continuous feature evolution. Theoretical analysis based on Rademacher complexity and the Neural Tangent Kernel demonstrates that DINR enhances expressivity and improves training dynamics. Moreover, regularizing the complexity of the underlying dynamics provides a principled way to balance expressivity and generalization. Extensive experiments on image representation, field reconstruction, and data compression confirm that DINR delivers more stable convergence, higher signal fidelity, and stronger generalization than conventional static INRs.