内核重启：突破神经场的神经正切核边界
Kernel Reboot: Breaking the Boundaries of Neural Tangent Kernels for Neural Fields
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中文总结 AI 辅助
该研究针对神经场从稀疏观测重建的难题，提出NTK-KIP、MetaQuill、MetaQuill-KIP三种算法，实现了兼具非线性与元可学习性的神经场，提升了极稀疏观测下的重建与补全性能。
中文摘要 AI 辅助
神经场（NFs）将连续坐标映射为颜色或密度等信号，但从稀疏观测中快速高质量重建仍存在困难。经典神经正切核（NTK）回归可给出闭式拟合，但本质是线性的，无法积累可复用的任务先验。我们开发了三种算法来解决这些问题：NTK-KIP学习坐标（及可选标签）的蒸馏支持集，使有限NTK能从少量观测数据中补全大的缺失区域，生成紧凑的非线性表示而非原始核求解；MetaQuill元学习隐式神经表示（INR）的共享初始化，使新场景仅通过更新小的任务特定权重偏移即可适配，提供真正的特征学习和可复用先验；最后，MetaQuill-KIP融合了两种思路：以KIP式非线性预热启动任务，再仅优化元学习初始化周围的小偏移。MetaQuill-KIP在极稀疏观测下实现了高PSNR重建和语义合理的补全，且仅需轻量级的单实例适配，而扩散式基线通常依赖大型预训练生成先验和高成本的单图像调优。这表明，由NTK驱动的神经场可同时具备非线性和元可学习性，缩小了解析核与实际少样本重建之间的差距。
英文摘要
Neural fields (NFs) map continuous coordinates to signals such as color or density, but fast high-quality reconstruction from sparse observations remains difficult. Classical Neural Tangent Kernel (NTK) regression gives closed-form fits, yet it is fundamentally linear and cannot accumulate reusable task priors. We develop three algorithms that address these gaps. NTK-KIP learns a distilled support set of coordinates (and optional labels) so that a finite NTK can inpaint large missing regions from little observed data, yielding a compact non-linear representation instead of a raw kernel solve. MetaQuill meta-learns a shared initialization for an INR so that new scenes can be adapted by updating only a small task-specific weight offset, which provides true feature learning and a reusable prior. Finally, MetaQuill-KIP fuses both ideas: it seeds the task with a KIP-style non-linear warm start, then refines only that small offset around the meta-learned initialization. MetaQuill-KIP achieves high-PSNR reconstructions and semantically plausible inpainting under very sparse observations, while requiring only lightweight per-instance adaptation, whereas diffusion-style baselines typically depend on large pretrained generative priors and costly per-image tuning. This shows that NTK-driven neural fields can be made both non-linear and meta-learnable, narrowing the gap between analytic kernels and practical few-shot reconstruction.
发表机构
- University of Haifa（海法大学）
- Massachusetts Institute of Technology（麻省理工学院）
- Tel Aviv University（特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。
