不用反向传播，用快速局部拟合实现高效隐式神经表示。
Escaping Spectral Bias without Backpropagation: Fast Implicit Neural Representations with Extreme Learning Machines
- 分块局部拟合，用闭式解替代迭代优化
- 重建速度提升显著，数值稳定性强
- 适合资源受限下需快速生成的场景
训练隐式神经表示（INRs）以捕捉细粒度细节通常依赖迭代反向传播，且在目标具有高度非均匀频谱内容时易受频谱偏差影响。我们提出 ELM-INR，一种无需反向传播的 INR，将定义域划分为重叠子域，每个子域使用极限学习机（ELM）进行闭式拟合，以稳定线性最小二乘解取代迭代优化。该设计通过单位分解组合局部预测器，实现快速且数值稳健的重建。为理解固定局部容量下的逼近难点，我们从谱 Barron 范数视角分析该方法，发现全局重建误差主要由高谱复杂度区域主导。基于此洞察，我们引入 BEAM 自适应网格细化策略，在容量受限情况下均衡各子域的谱复杂度，从而提升重建质量。
原文摘要 · Abstract (English)
Training implicit neural representations (INRs) to capture fine-scale details typically relies on iterative backpropagation and is often hindered by spectral bias when the target exhibits highly non-uniform frequency content. We propose ELM-INR, a backpropagation-free INR that decomposes the domain into overlapping subdomains and fits each local problem using an Extreme Learning Machine (ELM) in closed form, replacing iterative optimization with stable linear least-squares solutions. This design yields fast and numerically robust reconstruction by combining local predictors through a partition of unity. To understand where approximation becomes difficult under fixed local capacity, we analyze the method from a spectral Barron norm perspective, which reveals that global reconstruction error is dominated by regions with high spectral complexity. Building on this insight, we introduce BEAM, an adaptive mesh refinement strategy that balances spectral complexity across subdomains to improve reconstruction quality in capacity-constrained regimes.
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