Enhancing Implicit Neural Representations via Symmetric Power Transformation

TL;DR

The paper addresses the challenge of improving Implicit Neural Representations (INRs) without increasing training cost or storage. It introduces a reversible data transformation framework anchored by the Range-Defined Symmetric Hypothesis, and proposes the Symmetric Power Transformation $T_\mathrm{sym}$ to enforce range-bound and symmetric data distributions, together with deviation-aware calibration and adaptive soft boundary for robustness. Empirical results across 1D audio, 2D images, and 3D videos show consistent, substantial gains over existing transformations when used with SIREN and FINER backbones, with negligible overhead and the added benefit of lossless reversibility. The work suggests that aligning data range and symmetry can mitigate spectral bias in INRs and offers a practical, storage-free enhancement with potential for theoretical validation via Neural Tangent Kernel analysis in future work.

Abstract

We propose symmetric power transformation to enhance the capacity of Implicit Neural Representation~(INR) from the perspective of data transformation. Unlike prior work utilizing random permutation or index rearrangement, our method features a reversible operation that does not require additional storage consumption. Specifically, we first investigate the characteristics of data that can benefit the training of INR, proposing the Range-Defined Symmetric Hypothesis, which posits that specific range and symmetry can improve the expressive ability of INR. Based on this hypothesis, we propose a nonlinear symmetric power transformation to achieve both range-defined and symmetric properties simultaneously. We use the power coefficient to redistribute data to approximate symmetry within the target range. To improve the robustness of the transformation, we further design deviation-aware calibration and adaptive soft boundary to address issues of extreme deviation boosting and continuity breaking. Extensive experiments are conducted to verify the performance of the proposed method, demonstrating that our transformation can reliably improve INR compared with other data transformations. We also conduct 1D audio, 2D image and 3D video fitting tasks to demonstrate the effectiveness and applicability of our method.

Figures (4)

• Figure 1: Pipeline of Symmetric Power Transformation. We transform data with specific range and symmetry to enhance implicit neural representation without any additional time and spatial consumption. Integrating this simple nonlinear transformation can significantly improve the reconstruction quality. See comparison of "KBS" in reconstructed image.
• Figure 2: (a)&(b): Hypothesis verification from range and skewness perspectives; (c): Investigation of variance effects under zero-skewness distribution. Red arrows indicate performance degradation direction.
• Figure 3: Visualization for 2D natural image fitting. With symmetric power transformation in the SIREN and FINER backbones, texture details are reconstructed with greater fidelity.
• Figure 4: Visualization for 2D text image fitting. Symmetric Power Transformation can enhance the clarity and color fidelity of the synthesized text.