通过分层结构提升隐式神经表示的表达能力，不增加计算开销。
Split-Layer: Enhancing Implicit Neural Representation by Maximizing the Dimensionality of Feature Space
- 将MLP每层拆分为并行分支，用哈达玛积融合输出，构建高阶多项式空间。
- 在图像拟合、3D建模等任务中显著优于现有方法，5D新视角合成效果突出。
- 适合需要高精度表示但受限于计算资源的场景，如医学成像与三维重建。
隐式神经表示（INR）利用神经网络将信号建模为连续函数，在多个领域中为反问题提供高效且可微优化。然而，传统多层感知机（MLP）架构中低维特征空间限制了INR的表征能力。尽管拓宽MLP可线性提升特征空间维度，却导致计算和内存成本二次增长。为此，本文提出一种新型MLP重构方式——分层结构（split-layer），将每层分解为多个并行分支，通过哈达玛积整合输出，有效构建高阶多项式空间。该方法在不带来显著计算负担的前提下，大幅扩展特征空间维度，显著增强INR的表征能力。大量实验表明，分层结构在2D图像拟合、2D CT重建、3D形状表示及5D新视角合成等多项任务中均超越现有方法，性能全面提升。
原文摘要 · Abstract (English)
Implicit neural representation (INR) models signals as continuous functions using neural networks, offering efficient and differentiable optimization for inverse problems across diverse disciplines. However, the representational capacity of INR defined by the range of functions the neural network can characterize, is inherently limited by the low-dimensional feature space in conventional multilayer perceptron (MLP) architectures. While widening the MLP can linearly increase feature space dimensionality, it also leads to a quadratic growth in computational and memory costs. To address this limitation, we propose the split-layer, a novel reformulation of MLP construction. The split-layer divides each layer into multiple parallel branches and integrates their outputs via Hadamard product, effectively constructing a high-degree polynomial space. This approach significantly enhances INR's representational capacity by expanding the feature space dimensionality without incurring prohibitive computational overhead. Extensive experiments demonstrate that the split-layer substantially improves INR performance, surpassing existing methods across multiple tasks, including 2D image fitting, 2D CT reconstruction, 3D shape representation, and 5D novel view synthesis.
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