# MLIC++: Linear Complexity Multi-Reference Entropy Modeling for Learned Image Compression

arXiv: https://arxiv.org/abs/2307.15421 · HTML: https://mlsanity.com/paper/2307.15421/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 81 references that are in the map.
- First posted on arXiv 28 Jul 2023.

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Learned Image Compression with Mixed Transformer-CNN Architectures](https://mlsanity.com/paper/2303.14978/) (2023)
- [Checkerboard Context Model for Efficient Learned Image Compression](https://mlsanity.com/paper/2103.15306/) (2021)
- [How Much Position Information Do Convolutional Neural Networks Encode?](https://mlsanity.com/paper/2001.08248/) (2020)
- [The Devil Is in the Details: Window-based Attention for Image Compression](https://mlsanity.com/paper/2203.08450/) (2022)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Density Modeling of Images using a Generalized Normalization Transformation](https://mlsanity.com/paper/1511.06281/) (2015)
- [Entroformer: A Transformer-based Entropy Model for Learned Image Compression](https://mlsanity.com/paper/2202.05492/) (2022)
- [Enhanced Invertible Encoding for Learned Image Compression](https://mlsanity.com/paper/2108.03690/) (2021)
- [Non-local Attention Optimized Deep Image Compression](https://mlsanity.com/paper/1904.09757/) (2019)
- [Asymmetric Gained Deep Image Compression With Continuous Rate Adaptation](https://mlsanity.com/paper/2003.02012/) (2020)
- [MLIC: Multi-Reference Entropy Model for Learned Image Compression](https://mlsanity.com/paper/2211.07273/) (2022)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)

## Built on by (most cited first, 30 of 58)

- [StableCodec: Taming One-Step Diffusion for Extreme Image Compression](https://mlsanity.com/paper/2506.21977/) (2025)
- [Learned Image Compression with Dictionary-based Entropy Model](https://mlsanity.com/paper/2504.00496/) (2025)
- [Compressed Image Generation with Denoising Diffusion Codebook Models](https://mlsanity.com/paper/2502.01189/) (2025)
- [Linear Attention Modeling for Learned Image Compression](https://mlsanity.com/paper/2502.05741/) (2025)
- [Learned Image Compression with Hierarchical Progressive Context Modeling](https://mlsanity.com/paper/2507.19125/) (2025)
- [MambaIC: State Space Models for High-Performance Learned Image Compression](https://mlsanity.com/paper/2503.12461/) (2025)
- [Large Language Model for Lossless Image Compression with Visual Prompts](https://mlsanity.com/paper/2502.16163/) (2025)
- [Generalized Gaussian Model for Learned Image Compression](https://mlsanity.com/paper/2411.19320/) (2024)
- [Ultra-Low Bitrate Perceptual Image Compression with Shallow Encoder](https://mlsanity.com/paper/2512.12229/) (2025)
- [GroupedMixer: An Entropy Model with Group-wise Token-Mixers for Learned Image Compression](https://mlsanity.com/paper/2405.01170/) (2024)
- [Content-Aware Mamba for Learned Image Compression](https://mlsanity.com/paper/2508.02192/) (2025)
- [DeepHQ: Learned Hierarchical Quantizer for Progressive Deep Image Coding](https://mlsanity.com/paper/2408.12150/) (2024)
- [Dual-Representation Image Compression at Ultra-Low Bitrates via Explicit Semantics and Implicit Textures](https://mlsanity.com/paper/2602.05213/) (2026)
- [DiT-IC: Aligned Diffusion Transformer for Efficient Image Compression](https://mlsanity.com/paper/2603.13162/) (2026)
- [Differentiable Vector Quantization for Rate-Distortion Optimization of Generative Image Compression](https://mlsanity.com/paper/2604.10546/) (2026)
- [Towards Task-Compatible Compressible Representations](https://mlsanity.com/paper/2405.10244/) (2024)
- [Diversify, Contextualize, and Adapt: Efficient Entropy Modeling for Neural Image Codec](https://mlsanity.com/paper/2411.05832/) (2024)
- [Customizable ROI-Based Deep Image Compression](https://mlsanity.com/paper/2507.00373/) (2025)
- [ProGIC: Progressive and Lightweight Generative Image Compression with Residual Vector Quantization](https://mlsanity.com/paper/2603.02897/) (2026)
- [Next-Frame Decoding for Ultra-Low-Bitrate Image Compression with Video Diffusion Priors](https://mlsanity.com/paper/2603.15129/) (2026)
- [What Matters in Practical Learned Image Compression](https://mlsanity.com/paper/2605.05148/) (2026)
- [TLIC: Learned Image Compression with ROI-Weighted Distortion and Bit Allocation](https://mlsanity.com/paper/2401.08154/) (2024)
- [Scaling Learned Image Compression Models up to 1 Billion](https://mlsanity.com/paper/2508.09075/) (2025)
- [LVC-LGMC: Joint Local and Global Motion Compensation for Learned Video Compression](https://mlsanity.com/paper/2402.00680/) (2024)
- [Few-Shot Domain Adaptation for Learned Image Compression](https://mlsanity.com/paper/2409.11111/) (2024)
- [An Information-Theoretic Regularizer for Lossy Neural Image Compression](https://mlsanity.com/paper/2411.16727/) (2024)
- [Learned Image Compression and Restoration for Digital Pathology](https://mlsanity.com/paper/2503.23862/) (2025)
- [Learning to Interfere in Non-Orthogonal Multiple-Access Joint Source-Channel Coding](https://mlsanity.com/paper/2504.03690/) (2025)
- [Generalized Gaussian Entropy Model for Point Cloud Attribute Compression with Dynamic Likelihood Intervals](https://mlsanity.com/paper/2506.09510/) (2025)
- [Uni-LVC: A Unified Method for Intra- and Inter-Mode Learned Video Compression](https://mlsanity.com/paper/2603.05756/) (2026)

## Abstract (arXiv)

The latent representation in learned image compression encompasses channel-wise, local spatial, and global spatial correlations, which are essential for the entropy model to capture for conditional entropy minimization. Efficiently capturing these contexts within a single entropy model, especially in high-resolution image coding, presents a challenge due to the computational complexity of existing global context modules. To address this challenge, we propose the Linear Complexity Multi-Reference Entropy Model (MEM++). Specifically, the latent representation is partitioned into multiple slices. For channel-wise contexts, previously compressed slices serve as the context for compressing a particular slice. For local contexts, we introduce a shifted-window-based checkerboard attention module. This module ensures linear complexity without sacrificing performance. For global contexts, we propose a linear complexity attention mechanism. It captures global correlations by decomposing the softmax operation, enabling the implicit computation of attention maps from previously decoded slices. Using MEM++ as the entropy model, we develop the image compression method MLIC++. Extensive experimental results demonstrate that MLIC++ achieves state-of-the-art performance, reducing BD-rate by 13.39% on the Kodak dataset compared to VTM-17.0 in Peak Signal-to-Noise Ratio (PSNR). Furthermore, MLIC++ exhibits linear computational complexity and memory consumption with resolution, making it highly suitable for high-resolution image coding. Code and pre-trained models are available at https://github.com/JiangWeibeta/MLIC. Training dataset is available at https://huggingface.co/datasets/Whiteboat/MLIC-Train-100K.