FLAIR: Frequency- and Locality-Aware Implicit Neural Representations

TL;DR

FLAIR addresses spectral bias and poor locality in implicit neural representations by introducing Band-Localized Activation (BLA) for adaptive frequency control and locality, and Wavelet-Energy-Guided Encoding (WEGE) for region-aware frequency guidance using a lightweight, plug-and-play wavelet prior. The approach is analyzed through TFUP and empirical NTK perspectives, and validated across 2D image fitting, 3D SDF reconstruction, and NeRF with strong, fast-converging performance and compact models. Ablations confirm the complementary benefits of BLA components and WEGE, while experiments demonstrate robustness in arbitrary-scale SR and limited-view NeRF. Limitations include performance gaps under extreme degradation and per-scene training requirements, suggesting future work on generalization and diffusion-based baselines for more extreme tasks.

Abstract

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). Through structured frequency control and spatially localized responses, BLA effectively mitigates spectral bias and enhances training stability. The second is Wavelet-Energy-Guided Encoding (WEGE), which leverages the discrete wavelet transform to compute energy scores and explicitly guide frequency information to the network, enabling precise frequency selection and adaptive band control. Our method consistently outperforms existing INRs in 2D image representation, as well as 3D shape reconstruction and novel view synthesis.

Figures (23)

• Figure 1: Overall architecture of FLAIR. FLAIR consists of two complementary components: Band-Localized Activation (BLA) and a Wavelet-Energy-Guided Encoding (WEGE) module. Right: WEGE computes normalized wavelet-energy scores $\tilde{w}_b$ over the input coordinates, highlighting spatial frequency characteristics by assigning lower wavelet-energy scores to homogeneous regions (green box) and higher scores to textured regions (red box). Left: Wavelet-energy scores $\tilde{w}_b$ are channel-wise concatenated with input coordinates and passed through Band-Localized Activation (BLA). BLA modulates the signal representation via learnable band-adaptive parameters ($\zeta, T, \sigma$), enabling frequency shifting and band-limiting across low- and high-frequency components.
• Figure 2: Qualitative comparisons of ×4 super-resolution.Red and blue denote the best and second-best performances, respectively.
• Figure 3: (a) MSE loss convergence. (b) Ground-truth. (c)–(g) Comparison between FLAIR and other methods on image fitting.
• Figure 4: Both precise frequency selection and time localization under the TFUP. In domain (i), Sinusoid (a) produces only two fixed frequency components, so representing composite signals with diverse spectra requires many hidden dimensions. Sinc (b) provides sharp band selectivity. Our BLA (c) retains similar selectivity to (b) and further introduces a learnable frequency shift parameter $\zeta$ to access higher frequency bands (red box). In domain (ii), while (a) and (b) exhibit global support and oscillations (blue box), BLA (c) yields localized responses and reduces oscillations, mitigating noise propagation. Finally, our BLA (c) jointly modulates the frequency–time trade-off under the TFUP through its learnable parameters $(\zeta, T, \sigma)$, achieving both precise frequency selectivity and time localization.
• Figure 5: Residual error heatmaps on Kodak 01. Per-pixel absolute errors (RGB-averaged) are normalized to [0, 1]. Blue indicates lower error, and red indicates higher error. FLAIR consistently achieves lower reconstruction error than other methods.