# Leveraging Second-Order Curvature for Efficient Learned Image Compression: Theory and Empirical Evidence

arXiv: https://arxiv.org/abs/2601.20769 · HTML: https://mlsanity.com/paper/2601.20769/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 80 of its 117 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 30 of 80)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [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)
- [Video Enhancement with Task-Oriented Flow](https://mlsanity.com/paper/1711.09078/) (2017)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [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)
- [Deep Contextual Video Compression](https://mlsanity.com/paper/2109.15047/) (2021)
- [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)
- [Deep Information Propagation](https://mlsanity.com/paper/1611.01232/) (2016)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Feature Learning in Infinite-Width Neural Networks](https://mlsanity.com/paper/2011.14522/) (2020)
- [The Devil Is in the Details: Window-based Attention for Image Compression](https://mlsanity.com/paper/2203.08450/) (2022)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)

## Built on by (most cited first, 2 of 2)

- [Uni-LVC: A Unified Method for Intra- and Inter-Mode Learned Video Compression](https://mlsanity.com/paper/2603.05756/) (2026)
- [KD-NVC: A Search-and-Distill Framework to Accelerate Neural Video Coding](https://mlsanity.com/paper/2606.04595/) (2026)

## Abstract (arXiv)

Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with gradient conflicts arising from competing objectives, leading to slow convergence and suboptimal rate-distortion performance. In this work, we demonstrate that a simple utilization of a second-order quasi-Newton optimizer, SOAP, dramatically improves both training efficiency and final performance across diverse LICs. Our theoretical and empirical analyses reveal that Newton preconditioning inherently resolves the intra-step and inter-step update conflicts intrinsic to the R-D objective, facilitating faster, more stable convergence. Beyond acceleration, we uncover a critical deployability benefit: second-order trained models exhibit significantly fewer activation and latent outliers. This substantially enhances robustness to post-training quantization. Together, these results establish second-order optimization, achievable as a seamless drop-in replacement of the imported optimizer, as a powerful, practical tool for advancing the efficiency and real-world readiness of LICs.