用连续动态系统提升神经隐式表示的高频建模能力
Dynamical Implicit Neural Representations
- 将特征演化视为连续时间动力系统，替代传统离散层堆叠
- 在图像、场重建等任务中实现更稳定收敛与更高保真度
- 适合需要高精度细节建模的视觉信号处理场景
隐式神经表示（INRs）为复杂视觉与几何信号建模提供了强大的连续框架，但频谱偏差仍是根本性挑战，限制了其对高频细节的捕捉能力。与现有修复策略正交，本文提出动态隐式神经表示（DINR），将特征演化建模为连续时间动力系统，而非离散层堆叠。该动态形式通过连续特征演化实现了更丰富、自适应的频率表示，缓解了频谱偏差。基于Rademacher复杂度与神经正切核的理论分析表明，DINR提升了模型表达能力并改善了训练动态。此外，对底层动力学复杂度的正则化提供了一种平衡表达能力与泛化性能的合理方法。在图像表示、场重建与数据压缩任务上的大量实验验证了DINR相较于传统静态INRs具有更稳定的收敛性、更高的信号保真度和更强的泛化能力。
原文摘要 · Abstract (English)
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.
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