通过调整梯度改善隐式神经表示的频谱偏差，提升纹理与边缘细节。
Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representations
- 基于eNTK矩阵设计可归纳的梯度调整方法
- 在多种架构上实现一致且显著的性能提升
- 适合追求高保真图像重建的研究者
隐式神经表示（INRs）在计算机视觉任务中表现优异，但其性能受限于原始多层感知机（MLP）的频谱偏差。本文深入分析了MLP的线性动态模型，理论证明经验神经正切核（eNTK）矩阵是连接频谱偏差与训练动态的关键纽带。基于此，提出一种实用的归纳梯度调整（IGA）方法，通过eNTK引导的梯度变换矩阵实现对频谱偏差的有目的优化。理论与实证分析验证了IGA对频谱偏差的影响。在不同INR任务与架构上评估，结果表明IGA相比现有训练技术具有显著且稳定的性能优势。借助该梯度调整方法，能从数据中学习到具备更丰富纹理细节和更锐利边缘的高质量INRs。
原文摘要 · Abstract (English)
Implicit Neural Representations (INRs), as a versatile representation paradigm, have achieved success in various computer vision tasks. Due to the spectral bias of the vanilla multi-layer perceptrons (MLPs), existing methods focus on designing MLPs with sophisticated architectures or repurposing training techniques for highly accurate INRs. In this paper, we delve into the linear dynamics model of MLPs and theoretically identify the empirical Neural Tangent Kernel (eNTK) matrix as a reliable link between spectral bias and training dynamics. Based on this insight, we propose a practical Inductive Gradient Adjustment (IGA) method, which could purposefully improve the spectral bias via inductive generalization of eNTK-based gradient transformation matrix. Theoretical and empirical analyses validate impacts of IGA on spectral bias. Further, we evaluate our method on different INRs tasks with various INR architectures and compare to existing training techniques. The superior and consistent improvements clearly validate the advantage of our IGA. Armed with our gradient adjustment method, better INRs with more enhanced texture details and sharpened edges can be learned from data by tailored impacts on spectral bias.
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