# Hadamard-Domain Model Quantization for Learned Image Coding

arXiv: https://arxiv.org/abs/2608.01653 · HTML: https://mlsanity.com/paper/2608.01653/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 51 of its 94 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 30 of 51)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [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)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [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)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [The Devil Is in the Details: Window-based Attention for Image Compression](https://mlsanity.com/paper/2203.08450/) (2022)
- [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)
- [MLIC: Multi-Reference Entropy Model for Learned Image Compression](https://mlsanity.com/paper/2211.07273/) (2022)
- [Learning Convolutional Networks for Content-weighted Image Compression](https://mlsanity.com/paper/1703.10553/) (2017)
- [Towards Extreme Image Compression with Latent Feature Guidance and Diffusion Prior](https://mlsanity.com/paper/2404.18820/) (2024)
- [Efficient 8-Bit Quantization of Transformer Neural Machine Language Translation Model](https://mlsanity.com/paper/1906.00532/) (2019)
- [Lossy Compression for Lossless Prediction](https://mlsanity.com/paper/2106.10800/) (2021)
- [Contextformer: A Transformer with Spatio-Channel Attention for Context Modeling in Learned Image Compression](https://mlsanity.com/paper/2203.02452/) (2022)

## Abstract (arXiv)

Uniform INT8 quantization is attractive for deploying learned image coding (LIC), but its rate--distortion (R--D) performance is often limited by heavy-tailed tensors and large inter-channel variations. Existing methods mainly adapt the quantizer through mixed precision or non-uniform codebooks. We propose Hadamard-Transform-domain Quantization (HaTQ), which uses orthogonal Hadamard reparameterization before quantization to redistribute weight and activation responses in the original domain across channels. The reparameterization preserves the original function mapping of each linear operator, while making its weights and activations more amenable to uniform INT8 quantization. HaTQ provides two complementary forms. Double-Hadamard quantization transforms both the input activations and weights, whereas weight-only Hadamard quantization transforms only the weights. This distinction is important because the constant Hadamard basis can coherently accumulate a nonzero channel mean and enlarge the activation range in sensitive layers. We identify these sensitive layers through offline profiling and assign the appropriate form to each layer without input-dependent branching. HaTQ supports both post-training quantization (PTQ) and quantization-aware training (QAT), uses uniform INT8 quantizers, and is compatible with integer-only execution. Experiments on representative LIC architectures and datasets demonstrate consistent improvements across different quantization settings. The resulting QAT models further outperform competing mixed-precision and non-uniform quantization methods. TensorRT deployment results demonstrate practical INT8 inference efficiency. The source code will be publicly released.