Dynamical Implicit Neural Representations

2025-11-26

AI Summary

Implicit Neural Representations (INRs) suffer from spectral bias, limiting their ability to model high-frequency visual and geometric signals. To address this, we propose Dynamic Implicit Neural Representations (DINR), the first INR framework formulated as a continuous-time dynamical system, where features evolve explicitly over time to mitigate spectral bias. Our method introduces dynamical complexity regularization to balance expressivity and generalization, supported theoretically by Rademacher complexity and the neural tangent kernel. DINR employs a differentiable continuous-dynamics architecture enabling end-to-end training. Extensive experiments on image representation, field reconstruction, and data compression demonstrate that DINR significantly improves convergence speed, signal fidelity, and generalization performance—consistently outperforming static INR baselines across all tasks.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Addresses spectral bias in Implicit Neural Representations
• Introduces a continuous-time dynamical system for feature evolution
• Enhances expressivity and generalization in signal modeling

Innovation

• DINR treats feature evolution as continuous-time dynamical system
• DINR mitigates spectral bias through adaptive frequency representations
• DINR regularizes dynamics complexity to balance expressivity generalization