# Lossless-INR: Lossless Volumetric Implicit Neural Representations

arXiv: https://arxiv.org/abs/2607.18150 · HTML: https://mlsanity.com/paper/2607.18150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 24 of 24)

- [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)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [Binary Radiance Fields](https://mlsanity.com/paper/2306.07581/) (2023)
- [Fast Neural Representations for Direct Volume Rendering](https://mlsanity.com/paper/2112.01579/) (2021)
- [DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization](https://mlsanity.com/paper/2204.06504/) (2022)
- [NLI4VolVis: Natural Language Interaction for Volume Visualization via LLM Multi-Agents and Editable 3D Gaussian Splatting](https://mlsanity.com/paper/2507.12621/) (2025)
- [Interactive Volume Visualization via Multi-Resolution Hash Encoding based Neural Representation](https://mlsanity.com/paper/2207.11620/) (2022)
- [iVR-GS: Inverse Volume Rendering for Explorable Visualization via Editable 3D Gaussian Splatting](https://mlsanity.com/paper/2504.17954/) (2025)
- [ECNR: Efficient Compressive Neural Representation of Time-Varying Volumetric Datasets](https://mlsanity.com/paper/2311.12831/) (2023)
- [Adaptively Placed Multi-Grid Scene Representation Networks for Large-Scale Data Visualization](https://mlsanity.com/paper/2308.02494/) (2023)
- [Meta-INR: Efficient Encoding of Volumetric Data via Meta-Learning Implicit Neural Representation](https://mlsanity.com/paper/2502.09669/) (2025)
- [StyleRF-VolVis: Style Transfer of Neural Radiance Fields for Expressive Volume Visualization](https://mlsanity.com/paper/2408.00150/) (2024)
- [ViSNeRF: Efficient Multidimensional Neural Radiance Field Representation for Visualization Synthesis of Dynamic Volumetric Scenes](https://mlsanity.com/paper/2502.16731/) (2025)
- [TexGS-VolVis: Expressive Scene Editing for Volume Visualization via Textured Gaussian Splatting](https://mlsanity.com/paper/2507.13586/) (2025)
- [A Little Bit More: Bitplane-Wise Bit-Depth Recovery](https://mlsanity.com/paper/2005.01091/) (2020)
- [Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration](https://mlsanity.com/paper/2504.00904/) (2025)
- [Towards Lossless Implicit Neural Representation via Bit Plane Decomposition](https://mlsanity.com/paper/2502.21001/) (2025)
- [MC-INR: Efficient Encoding of Multivariate Scientific Simulation Data using Meta-Learning and Clustered Implicit Neural Representations](https://mlsanity.com/paper/2507.02494/) (2025)
- [VolSegGS: Segmentation and Tracking in Dynamic Volumetric Scenes via Deformable 3D Gaussians](https://mlsanity.com/paper/2507.12667/) (2025)

## Abstract (arXiv)

Implicit neural representation (INR) methods provide continuous coordinate-to-value mappings and integrate naturally with direct volume rendering, making them attractive for representing volumetric data. However, existing INR-based approaches for volumetric data are inherently lossy, and even small reconstruction errors can propagate through rendering and downstream analysis. In this work, we explore Lossless-INR, a lossless INR framework for 3D scientific volumetric data based on bit-plane decomposition. By decomposing each voxel value into binary bit-planes, we reformulate reconstruction as per-bit binary classification, so that exact recovery reduces to predicting every bit correctly. To make this optimization tractable while keeping the representation compact, we combine an octree block-partitioning strategy that adaptively subdivides complex regions with a ternary feature-grid network whose grid entries are parameterized by a ternary set of values. Experiments on diverse volumetric datasets show that this design can achieve zero bit-error rate and bit-exact reconstruction, enabling faithful rendering and downstream analysis with a compact representation. The code is available at https://github.com/TouKaienn/Lossless-INR.