aiqbench analysis
This research advances Neural Tangent Kernel (NTK) methods by introducing non-linear, meta-learnable approaches that enable efficient reconstruction from sparse data without relying on large generative priors. The proposed algorithms combine kernel interpolation with meta-learning to create reusable task priors, offering a lightweight alternative to diffusion models for few-shot inpainting in neural fields.
Kernel Reboot: Breaking the Boundaries of Neural Tangent Kernels for Neural Fields
arXiv:2609.03117v1 Announce Type: new Abstract: 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.
Abstract: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.
Published in IEEE TPAMI, vol. 48, no. 9, pp. 10940-10957, Sep. 2026. Author version adds related-work references and biography updates; Figures 12 and 13 were regenerated from the same locked hyperparameter sweep. Tabulated results, reported best points, scientific claims, and conclusions are unchanged
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2609.03117 [cs.LG]
(or arXiv:2609.03117v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.03117 arXiv-issued DOI via DataCite (pending registration)
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 48, no. 9, pp. 10940-10957, Sep. 2026
https://doi.org/10.1109/TPAMI.2026.3692624 DOI(s) linking to related resources
Full text under the publisher's open licence · 287 words
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