# L-SR1: Learned Symmetric-Rank-One Preconditioning

arXiv: https://arxiv.org/abs/2508.12270 · HTML: https://mlsanity.com/paper/2508.12270/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 69 references that are in the map.
- First posted on arXiv 17 Aug 2025.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [OpenPose: Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1812.08008/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [Learning to Reconstruct 3D Human Pose and Shape via Model-fitting in the Loop](https://mlsanity.com/paper/1909.12828/) (2019)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [GRAB: A Dataset of Whole-Body Human Grasping of Objects](https://mlsanity.com/paper/2008.11200/) (2020)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [WHAM: Reconstructing World-grounded Humans with Accurate 3D Motion](https://mlsanity.com/paper/2312.07531/) (2023)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [STAR: Sparse Trained Articulated Human Body Regressor](https://mlsanity.com/paper/2008.08535/) (2020)
- [ContactDB: Analyzing and Predicting Grasp Contact via Thermal Imaging](https://mlsanity.com/paper/1904.06830/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Learned Optimizers that Scale and Generalize](https://mlsanity.com/paper/1703.04813/) (2017)
- [3D Human Pose Estimation via Intuitive Physics](https://mlsanity.com/paper/2303.18246/) (2023)
- [TRACE: 5D Temporal Regression of Avatars with Dynamic Cameras in 3D Environments](https://mlsanity.com/paper/2306.02850/) (2023)
- [Human Body Model Fitting by Learned Gradient Descent](https://mlsanity.com/paper/2008.08474/) (2020)
- [PromptHMR: Promptable Human Mesh Recovery](https://mlsanity.com/paper/2504.06397/) (2025)
- [Tasks, stability, architecture, and compute: Training more effective learned optimizers, and using them to train themselves](https://mlsanity.com/paper/2009.11243/) (2020)
- [VeLO: Training Versatile Learned Optimizers by Scaling Up](https://mlsanity.com/paper/2211.09760/) (2022)
- [Practical tradeoffs between memory, compute, and performance in learned optimizers](https://mlsanity.com/paper/2203.11860/) (2022)
- [SOMA: Solving Optical Marker-Based MoCap Automatically](https://mlsanity.com/paper/2110.04431/) (2021)
- [HUMAN4D: A Human-Centric Multimodal Dataset for Motions and Immersive Media](https://mlsanity.com/paper/2110.07235/) (2021)
- [ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection](https://mlsanity.com/paper/1905.10750/) (2019)

## Abstract (arXiv)

End-to-end deep learning has achieved impressive results but often relies on large labeled datasets, exhibits limited generalization to unseen scenarios, and incurs substantial computational cost. Classical optimization methods, in contrast, are more data-efficient and lightweight but frequently suffer from slow convergence. Learned optimizers aim to bridge this gap, yet existing approaches have focused primarily on first-order methods, while learned second-order optimization has received much less attention. We introduce L-SR1, a learned second-order optimizer inspired by the classical Symmetric Rank-One (SR1) method. At its core, L-SR1 employs a Projection-Guided Secant Mechanism (PGSM) that generates positive semi-definite preconditioners and biases meta-training toward the quasi-Newton secant relation. Through controlled analytic benchmarks, we study stability, generalization across problem dimensions, and search direction quality, and further evaluate L-SR1 on Monocular Human Mesh Recovery (HMR), where it outperforms both classical and learned optimization-based baselines. With a compact model and no reliance on task-specific fine-tuning or annotated data, L-SR1 demonstrates strong generalization and can be integrated into a broad range of iterative optimization problems to accelerate convergence and reduce the required number of iterations.