FLAIR: Frequency- and Locality-Aware Implicit Neural Representations

arXiv 2025

Sukhun Ko Chung-Ang University Seokhyun Yoon Chung-Ang University Dahyeon Kye Chung-Ang University Kyle Min Oracle Chanho Eom Chung-Ang University Jihyong Oh† Chung-Ang University

Chung-Ang University Chung-Ang University, South Korea Creative Vision and Multimedia Lab Creative Vision and Multimedia Lab Oracle Oracle, USA

{looloo330, rpekgus, cheom, jihyongoh}@cau.ac.kr,   kylemin@umich.edu

Paper Paper Code Code

TL;DR: We introduce FLAIR, combining novel Band-Localized Actvation (BLA) and Wavelet-Energy-Guided Encoding (WEGE) to enable joint frequency selectivity and spatial localization, effectively mitigating spectral bias in implicit neural representations.

Abstract

Overall Architecture

Implicit Neural Representations (INRs) leverage neural networks to map coordinates to corresponding signals, enabling continuous and compact representations. This paradigm has driven significant advances in various vision tasks. However, existing INRs lack frequency selectivity and spatial localization leading to an over-reliance on redundant signal components. Consequently, they exhibit spectral bias, tending to learn low-frequency components early while struggling to capture fine high-frequency details.

To address these issues, we propose FLAIR (Frequency- and Locality-Aware Implicit Neural Representations), which incorporates two key innovations. The first is Band-Localized Activation (BLA), a novel activation designed for joint frequency selection and spatial localization under the constraints of the time-frequency uncertainty principle (TFUP). The second is Wavelet-Energy-Guided Encoding (WEGE), which leverages the discrete wavelet transform (DWT) to compute energy scores and explicitly guide frequency information to the network.

Our method consistently outperforms existing INRs in 2D image representation, as well as 3D shape reconstruction and novel view synthesis.

Restoration Demo

Super-Resolution

LR input SR output
Input
FLAIR

Upscaling factor: ×4

Denoising

Noisy input Denoised output
Input
FLAIR

Noise: Poisson(30.0) & Gaussian(2.0)

Method

Band-Localized Activation Visualization
Figure 1. Band-Localized Activation (BLA) as a component of FLAIR. In (a), BLA jointly modulates the frequency–time trade-off under TFUP through its learnable parameters (ζ, T, σ), achieving both precise frequency selectivity and time localization. In (b), the loss-landscape visualizations show that BLA yields a significantly flatter MSE loss surface than sinc, indicating smoother and more stable optimization behavior.
WEGE Details
Figure 2. WEGE Design and Guided Filter Analysis. The Wavelet-Energy-Guided Encoding (WEGE) module in (c) computes region-adaptive wavelet energy scores and integrates them into the network to enable precise frequency selection and adaptive band control. In (d), the Guided Filter hyperparameters affect the stability of the pixel-wise score map W̃b; without filtering, score discontinuities appear as visible artifacts in the final RGB output. Using r = 6 and ϵ = 1e-5 provides a balanced response, reducing discontinuities while retaining sharp structural information.

Quantitative Results

Quantitative Benchmarking Across Methods

Quantitative Table 1
Table 1. Per-scene quantitative image-fitting results on DIV2K (00–15).
Quantitative Table 2
Table 2. Quantitative evaluation on 3D representation. Left: SDF metrics (Chamfer↓, IoU↑). Right: NeRF reconstruction metrics (PSNR↑, SSIM↑, LPIPS↓). FLAIR achieves consistently strong performance across benchmarks.

Qualitative Results

Visual Comparisons Across Methods on Diverse Tasks

Qualitative Results Row 1
Figure 3. Qualitative comparison with other methods on the fitting task across the DIV2K and Kodak datasets. FLAIR produces the most faithful results without noise, enabled by the band-limited behavior of BLA, while other methods exhibit frequency leakage.
Qualitative Results Row 2
Figure 4. Under the challenging setting of using only 25 input views instead of the default 100, FLAIR reconstructs unseen views without artifacts and preserves fine details.
Qualitative Results Row 3
Figure 5. Qualitative comparison on representing signed distance fields. FLAIR recovers finer geometry and sharper surface details compared to other methods.

Analysis

Empirical NTK and Fourier Spectrum Analysis

NTK Analysis
Figure 6. Eigenvalue distribution of empirical NTKs (a) and frequency-specific error analysis (b)–(e). The frequency shifting term in BLA selectively redirects concentrated eigenmodes toward higher spectral regions, broadening the usable eigenvalue range during training. As shown in (e), this enables BLA to capture multiple frequency bands early, yielding fast convergence and accurate high-frequency detail representation.
FFT Analysis
Figure 7. Fast Fourier Transform visualization of learned neurons. Compared with FINER, whose frequency responses are mostly concentrated near low-frequency regions, FLAIR exhibits richer and more diverse spectra (left), enabling comparable evaluation scores with roughly half the hidden dimensionality and demonstrating greater efficiency (right).

BibTeX

@article{ko2025flair,
  title={FLAIR: Frequency-and Locality-Aware Implicit Neural Representations},
  author={Ko, Sukhun and Kye, Dahyeon and Min, Kyle and Eom, Chanho and Oh, Jihyong},
  journal={arXiv preprint arXiv:2508.13544},
  year={2025}
}