multi-grade inr optimization

Existing implicit neural representations (INRs) are constrained by compact network architectures, limiting their ability to model multiscale structures, high-frequency components, and fine-grained textures prevalent in scientific data. To address this, we propose WIEN-INR—a wavelet-guided multiscale INR framework that integrates the discrete wavelet transform (DWT) as a structural prior into network design, enabling hierarchical feature decomposition across resolutions. At the finest scale, a lightweight, dedicated kernel network is introduced to precisely capture subtle textural details. Crucially, WIEN-INR achieves full-spectrum information encoding without increasing model parameter count. Experiments across multiple scientific datasets demonstrate that WIEN-INR significantly improves reconstruction fidelity for high-frequency details and complex structures, while reducing model size by 32%–57%, accelerating training by 1.8×–2.4×, and lowering storage overhead. This establishes a new paradigm for high-fidelity scientific data modeling under resource-constrained conditions.

This work addresses the limitations of traditional signal modeling, which relies on discrete sampling and struggles to unify multimodal continuous signals or support analytical operations. Viewing implicit neural representations (INRs) through the lens of signal processing, the study models images, audio, 3D geometry, and other modalities as continuous coordinate-based functions, realized via differentiable neural networks. The authors systematically analyze the spectral properties, sampling theory, and multiscale mechanisms underlying INRs and propose structured representation strategies—integrating periodicity, localization, adaptive activation functions, and hash-grid encodings—to reshape the approximation space for enhanced spatial adaptivity and computational efficiency. The resulting framework demonstrates superior performance in inverse problems such as medical and radar imaging, signal compression, and 3D scene reconstruction, advancing both the theoretical understanding and practical applicability of INRs as learnable continuous signal models.

Implicit neural representations (INRs) suffer from suboptimal performance due to the absence of systematic, joint design principles for activation functions and initialization parameters; existing approaches rely on heuristic tuning or exhaustive search, yielding inconsistent results across modalities. Method: We propose the first unified joint optimization framework for INR configuration, modeling discrete activation families (e.g., SIREN, WIRE, FINER) and continuous initialization scales as co-optimized variables, and employing Bayesian optimization for end-to-end automated configuration. Contribution/Results: Our method replaces ad hoc empirical practices with a data-driven, standardized configuration pipeline. Evaluated on multimodal signal reconstruction and 3D shape modeling tasks, it achieves significant improvements in reconstruction accuracy and training stability, demonstrating strong generalizability and cross-modal consistency.

Implicit Neural Representations (INRs) commonly suffer from mean regression bias, leading to loss of high-frequency details and poor noise robustness—limiting their effectiveness in signal reconstruction. To address this, we propose Iterative Implicit Neural Representations (I-INR), a plug-and-play differentiable iterative refinement framework that enables multi-step progressive optimization without modifying the backbone network. I-INR integrates residual learning with frequency-domain-aware strategies and is compatible with mainstream INR architectures—including SIREN, WIRE, and Gauss-based models. Extensive experiments demonstrate that I-INR consistently outperforms baseline methods across image restoration, denoising, and occupancy prediction tasks, achieving significant gains in PSNR and SSIM. Notably, I-INR is the first INR framework to jointly enhance high-frequency recovery capability and noise robustness while maintaining architectural lightness.

Implicit Neural Representations (INRs) suffer from the spectral bias of MLPs, hindering high-fidelity reconstruction of high-frequency details. To address this, we propose an inductive gradient adjustment method grounded in the empirical Neural Tangent Kernel (eNTK), which— for the first time—formally bridges spectral bias and training dynamics. Our approach dynamically designs a gradient transformation matrix to mitigate bias directionally, without altering network architecture. By establishing a linearized training dynamics model, it enables generalized gradient optimization across diverse INR architectures and tasks. Experiments demonstrate consistent improvements across multiple INR variants (e.g., SIREN, Fourier Features) and reconstruction tasks (images and videos): reconstructed outputs exhibit richer texture, sharper edges, and superior quantitative performance—achieving higher PSNR and lower LPIPS than state-of-the-art training strategies.

This work addresses the challenges of spectral bias and inter-branch interference in implicit neural representations (INRs) for multi-scale signal modeling, where high-frequency updates often corrupt low-frequency structures. The authors propose a multi-branch INR architecture that aligns the signal spectrum to each branch’s optimal operating range through directional coordinate scaling and incorporates a directional edge-guided loss to achieve functional disentanglement. By innovatively integrating the inverse Fourier scaling theorem with a gradient-based spatially conditioned sparsity prior, the method explicitly separates multi-scale features, effectively eliminating spectral crosstalk and accelerating convergence. Experiments demonstrate significant improvements over current state-of-the-art methods in image reconstruction (+5.16 dB), denoising (+0.65 dB), audio reconstruction (50.02 dB), and 3D reconstruction (IoU 0.999).

This work addresses the longstanding trade-off among memory efficiency, rendering speed, and image quality in traditional discrete texture representations. It presents the first systematic application of implicit neural representations (INRs) to continuous texture modeling, introducing a novel neural network architecture that achieves high-fidelity texture synthesis directly in UV coordinate space with low memory footprint and efficient inference. By transcending the discrete limitations of conventional textures, the proposed method enables new applications such as mipmap fitting and spatially coherent INR-based texture generation. Extensive experiments demonstrate that the approach significantly reduces both memory consumption and inference latency while preserving visual fidelity, thereby validating the practicality and potential of INRs for texture representation and downstream graphics tasks.

本文提出C²-INR方法，通过定制卷积核和激活函数选择机制解决图像表示中空间相关性利用不足的问题。

Implicit neural fields in 3D scientific simulation struggle to simultaneously achieve high fidelity and fast inference: deep MLPs offer strong expressivity but are computationally expensive, whereas embedded models are efficient yet limited in capacity. To address this trade-off, this work proposes a Decoupled Representation Refinement (DRR) architecture that leverages a deep refinement network and non-parametric transformations during an offline phase to compress high-capacity representations into compact embeddings, thereby decoupling expressiveness from inference efficiency. Additionally, a Variational Pairs data augmentation strategy is introduced to enhance representation performance on complex tasks. Experiments demonstrate that the proposed method achieves state-of-the-art fidelity across multiple ensemble simulation datasets, with inference speeds up to 27× faster than high-fidelity baselines while matching the efficiency of the fastest existing models.

This work addresses the problem of excessively large neural tangent kernel (NTK) variance in implicit neural representations (INRs), which leads to slow convergence, severe spectral bias, and poor recovery of high-frequency details. We first establish a closed-form decomposition framework for NTK variance, revealing its dependence on pairwise input similarity and scaling terms. Based on this analysis, we provide a unified theoretical explanation for how architectural components—including positional encoding, spherical normalization, and Hadamard modulation—jointly suppress NTK variance and improve condition number. Through rigorous NTK-theoretic analysis, spectral bias diagnostics, and multi-task reconstruction experiments (e.g., image and signed distance function reconstruction), we demonstrate that our variance-regulation mechanism significantly enhances training stability and convergence speed, while achieving superior reconstruction fidelity—particularly in capturing high-frequency structural details.