ScaLe-INR: Scale and Learn Implicit Neural Representations

2026-06-26

AI Summary

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).

Abstract

Implicit Neural Representations (INRs) parameterized by multilayer perceptrons excel at modeling continuous signals. However, a key challenge persists as INRs fundamentally suffer from spectral bias and information cross-talk. When a single network attempts to capture multi-scale phenomena, high-frequency weight updates destructively interfere with the underlying low-frequency structural approximation. We introduce Scale and Learn INR (ScaLe-INR), a novel multi-branch architecture that resolves these limitations by explicitly matching the signal's frequency spectrum with the optimal operating region of the INR. Drawing upon the Fourier inverse scaling theorem we demonstrate that applying directional coordinate scaling expands a network's representational bandwidth along specific spatial axes. To mathematically enforce functional disentanglement and minimize task-specific information leakage between branches, we propose a Directional Edge Guidance Loss, a spatially-conditioned sparsity prior derived from ground-truth gradients. By constraining the high-frequency branches to act as strict, localized edge-filters, ScaLe-INR eliminates spectral cross-talk, accelerates convergence, and achieves high-fidelity signal reconstruction on complex multi-scale topologies. We evaluate ScaLe-INR across diverse reconstruction and inverse tasks, demonstrating substantial performance gains over existing state-of-the-art (SOTA) methods. The proposed architecture improves upon the nearest baselines by +5.16 dB in image reconstruction and +0.65 dB in image denoising. Furthermore, it achieve an impressive figure of 50.02 dB on audio reconstruction and 0.999 IOU(Intersection Over Union) on 3D reconstruction which beats the all SOTA models.

Problem

• Implicit Neural Representations
• spectral bias
• information cross-talk
• multi-scale phenomena
• signal reconstruction

Innovation

• Implicit Neural Representations
• Multi-scale Modeling
• Spectral Bias
• Directional Coordinate Scaling
• Functional Disentanglement