FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation (2407.19434v1)

Abstract: Implicit Neural Representation (INR), which utilizes a neural network to map coordinate inputs to corresponding attributes, is causing a revolution in the field of signal processing. However, current INR techniques suffer from the "frequency"-specified spectral bias and capacity-convergence gap, resulting in imperfect performance when representing complex signals with multiple "frequencies". We have identified that both of these two characteristics could be handled by increasing the utilization of definition domain in current activation functions, for which we propose the FINER++ framework by extending existing periodic/non-periodic activation functions to variable-periodic ones. By initializing the bias of the neural network with different ranges, sub-functions with various frequencies in the variable-periodic function are selected for activation. Consequently, the supported frequency set can be flexibly tuned, leading to improved performance in signal representation. We demonstrate the generalization and capabilities of FINER++ with different activation function backbones (Sine, Gauss. and Wavelet) and various tasks (2D image fitting, 3D signed distance field representation, 5D neural radiance fields optimization and streamable INR transmission), and we show that it improves existing INRs. Project page: {https://liuzhen0212.github.io/finerpp/}

• The paper’s main contribution is the development of variable-periodic activation functions that mitigate spectral bias and enhance the performance of implicit neural representations.
• It presents a versatile framework applicable to diverse functions like Sine, Gaussian, and Wavelet, demonstrated across tasks such as 2D image fitting, 3D SDF, and 5D NeRF.
• An innovative initialization scheme extends bias vector ranges, significantly boosting both geometric representation and neural tangent kernel properties.

Overview of "FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation"

The paper introduces FINER++, an advanced framework designed to enhance the performance of Implicit Neural Representations (INRs) by employing variable-periodic activation functions. Despite the growing usage of INRs across various domains such as neural rendering and inverse imaging, existing techniques often confront limitations like spectral bias and a capacity-convergence gap. These limitations hinder the network's effectiveness in representing complex signals characterized by multiple frequencies.

Core Contributions and Methodology

1. Variable-periodic Activation Functions: The central innovation of FINER++ lies in its transformation of existing periodic and non-periodic activation functions into variable-periodic forms. This transformation widens the definition domain usage of activation functions, thereby enhancing the supported frequency set. Consequently, FINER++ facilitates tuning INRs' spectral bias, enabling better performance in high-frequency signal representation.
2. Framework Universality: The framework is applicable to various activation functions including Sine, Gaussian, and Wavelet. This versatility is demonstrated across different tasks such as 2D image fitting, 3D signed distance field representation, and 5D neural radiance field optimization. The results indicate a notable performance improvement over traditional INRs.
3. Innovative Initialization Scheme: FINER++ proposes a novel initialization approach for the bias vector in neural networks. By extending the initialization range, the framework enhances both the geometric representation and neural tangent kernel properties, allowing for superior handling of spectral bias and capacity-convergence issues.

Numerical Evaluation and Comparative Analysis

The FINER++ framework exhibits strong empirical performance across multiple benchmark tasks. For 2D image fitting, FINER++ achieves higher PSNR and SSIM metrics compared to its traditional counterparts, confirming its enhanced ability to capture high-frequency details. In 3D tasks, FINER++ demonstrates greater fidelity in signed distance field representation, improving both Chamfer distance and intersection over union (IOU) measures. Furthermore, in the context of neural radiance fields (NeRF), FINER++ enables the synthesis of more precise and visually appealing results.

Theoretical and Practical Implications

Theoretical implications of FINER++ suggest a shift in how activation functions in INRs are understood and utilized. By moving beyond traditional "frequency"-specified frameworks, FINER++ introduces a broader, variable-periodic functional expansion that can adaptively meet signal demands. Practically, the ability of FINER++ to adjust supported frequency sets makes it highly applicable in scenarios demanding incremental and streamable signal representations, such as high-resolution image transmission and streaming services.

Future Prospects

The development of FINER++ invites further research into creating INRs with adaptable spectral properties without pre-defining limitations. There is potential for exploring additional complex activation functions that could be extended into variable-periodic forms. Moreover, expanding the application domain of FINER++ to other signal processing and machine learning challenges where frequency representation plays a crucial role will be an interesting direction for future work. The paper sets a new benchmark in INR development, pushing boundaries towards more flexible and comprehensive signal representation techniques.