NTK-Guided Implicit Neural Teaching

TL;DR

This work tackles the heavy computational cost of training high‑resolution implicit neural representations by introducing NTK‑Guided Implicit Neural Teaching (NINT). NINT selects training coordinates using the Neural Tangent Kernel to maximize the per‑iteration global functional update, incorporating both local fitting error and heterogeneous coordinate leverage via self‑leverage and cross‑coordinate coupling. Empirical results across 1D, 2D, and 3D tasks show NINT achieves up to nearly 50% faster training while maintaining or improving reconstruction fidelity, outperforming state‑of‑the‑art sampling baselines. The approach is model‑agnostic and scalable, with robust performance across network sizes and architectures, highlighting a practical route to accelerate INR training without architectural changes or additional data.

Abstract

Implicit Neural Representations (INRs) parameterize continuous signals via multilayer perceptrons (MLPs), enabling compact, resolution-independent modeling for tasks like image, audio, and 3D reconstruction. However, fitting high-resolution signals demands optimizing over millions of coordinates, incurring prohibitive computational costs. To address it, we propose NTK-Guided Implicit Neural Teaching (NINT), which accelerates training by dynamically selecting coordinates that maximize global functional updates. Leveraging the Neural Tangent Kernel (NTK), NINT scores examples by the norm of their NTK-augmented loss gradients, capturing both fitting errors and heterogeneous leverage (self-influence and cross-coordinate coupling). This dual consideration enables faster convergence compared to existing methods. Through extensive experiments, we demonstrate that NINT significantly reduces training time by nearly half while maintaining or improving representation quality, establishing state-of-the-art acceleration among recent sampling-based strategies.

Figures (8)

• Figure 1: NINT selection and reconstruction on kodim04 from Kodak kodak. Top: INR reconstructions at 0, 5, 20, 60 sec (final PSNR 30.78 dB). Bottom: NINT-selected coordinates (red), scored by NTK-augmented loss gradient norm to capture fitting errors and heterogeneous leverage (self-influence and cross-coupling).
• Figure 2: NTK visualization on the image 02 from DIV2K agustsson2017ntire. Two $9 \times 9$ NTK patches correspond to two $3 \times 3$ pixel regions (red). Strong off-diagonals show significant functional coupling between regions, while diverse diagonals indicate heterogeneous self-leverage. Color denotes magnitude.
• Figure 3: Visual comparison of image reconstructions using different sampling strategies on the kodim15 image from the Kodak dataset kodak, after a fixed training duration of 60 seconds.
• Figure 4: Trends in SSIM wang2004image and LPIPS zhang2018unreasonable metrics over 60 seconds of training across various sampling strategies.
• Figure 5: Visual comparison of reconstruction quality across various network sizes, after training for 150 seconds on image 07 from DIV2K agustsson2017ntire.