# Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data

arXiv: https://arxiv.org/abs/2606.26763 · HTML: https://mlsanity.com/paper/2606.26763/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [Polynomial Neural Fields for Subband Decomposition and Manipulation](https://mlsanity.com/paper/2302.04862/) (2023)
- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [BANF: Band-limited Neural Fields for Levels of Detail Reconstruction](https://mlsanity.com/paper/2404.13024/) (2024)
- [Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representations](https://mlsanity.com/paper/2410.13271/) (2024)
- [Superpixel-informed Implicit Neural Representation for Multi-Dimensional Data](https://mlsanity.com/paper/2411.11356/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [SASNet: Spatially-Adaptive Sinusoidal Networks for INRs](https://mlsanity.com/paper/2503.09750/) (2025)

## Built on by (most cited first, 3 of 3)

- [Temporal and Cross-Modal Alignment for Enhanced Audiovisual Video Captioning](https://mlsanity.com/paper/2607.01667/) (2026)
- [FlowPainter: Inpainting Optical Flow via Confidence-Guided Completion](https://mlsanity.com/paper/2607.10140/) (2026)
- [What We Talk About When We Talk About Emotion Editing](https://mlsanity.com/paper/2610.13558/) (2026)

## Abstract (arXiv)

Implicit neural representation (INR) has emerged as a powerful prior for multi-dimensional data (e.g., multispectral images and videos). However, most INR methods employing periodic activation functions (e.g., Sine) predominantly rely on function composition. This mechanism introduces optimization instability as network depth increases, thereby limiting their performance. Meanwhile, these methods fail to incorporate proper physical priors to effectively alleviate spectrum bias. To address these issues, inspired by the commonalities between deep periodic networks and generalized Fourier series, we propose a novel Calibrated Harmonic Overlaid Implicit Neural Representation (CHOIR). Specifically, we utilize Coordinated Harmonic Superposition (CHS) to replace the conventional function composition used in most INRs, thereby ensuring optimization stability when scaling network depth. Furthermore, we introduce a Perceptual Spectrum Calibration (PSC) to mitigate spectrum bias. This calibration embeds the ubiquitous power-law spectrum prior of natural images and adjusts the globally fixed spectrum towards a physically plausible log-uniform distribution. Extensive experiments on various multidimensional data recovery problems demonstrate that our method achieves superior performance over state-of-the-art approaches. Code is available at https://github.com/chorl0229/CHOIR.