# Towards Lossless Implicit Neural Representation via Bit Plane Decomposition

arXiv: https://arxiv.org/abs/2502.21001 · HTML: https://mlsanity.com/paper/2502.21001/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 30 of 30)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [Compression with Bayesian Implicit Neural Representations](https://mlsanity.com/paper/2305.19185/) (2023)
- [Polynomial Neural Fields for Subband Decomposition and Manipulation](https://mlsanity.com/paper/2302.04862/) (2023)
- [Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory](https://mlsanity.com/paper/2310.20360/) (2023)
- [Learning Local Implicit Fourier Representation for Image Warping](https://mlsanity.com/paper/2207.01831/) (2022)
- [RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations](https://mlsanity.com/paper/2309.17182/) (2023)
- [A Little Bit More: Bitplane-Wise Bit-Depth Recovery](https://mlsanity.com/paper/2005.01091/) (2020)
- [JDEC: JPEG Decoding via Enhanced Continuous Cosine Coefficients](https://mlsanity.com/paper/2404.05558/) (2024)
- [BitNet: Learning-Based Bit-Depth Expansion](https://mlsanity.com/paper/1910.04397/) (2019)

## Built on by (most cited first, 5 of 5)

- [Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features](https://mlsanity.com/paper/2603.01028/) (2026)
- [Error Aware Distribution Prediction for Lightweight Implicit Neural Representations](https://mlsanity.com/paper/2607.10068/) (2026)
- [Lossless-INR: Lossless Volumetric Implicit Neural Representations](https://mlsanity.com/paper/2607.18150/) (2026)
- [Recurrent Sinusoidal INRs for Efficient High-Fidelity Representation](https://mlsanity.com/paper/2607.21485/) (2026)
- [RAID: Towards Robust AI-Generated Image Detection with Bit-Reversed Images](https://mlsanity.com/paper/2607.28974/) (2026)

## Abstract (arXiv)

We quantify the upper bound on the size of the implicit neural representation (INR) model from a digital perspective. The upper bound of the model size increases exponentially as the required bit-precision increases. To this end, we present a bit-plane decomposition method that makes INR predict bit-planes, producing the same effect as reducing the upper bound of the model size. We validate our hypothesis that reducing the upper bound leads to faster convergence with constant model size. Our method achieves lossless representation in 2D image and audio fitting, even for high bit-depth signals, such as 16-bit, which was previously unachievable. We pioneered the presence of bit bias, which INR prioritizes as the most significant bit (MSB). We expand the application of the INR task to bit depth expansion, lossless image compression, and extreme network quantization. Our source code is available at https://github.com/WooKyoungHan/LosslessINR