# Low-rank extended Kalman filtering for online learning of neural networks from streaming data

arXiv: https://arxiv.org/abs/2305.19535 · HTML: https://mlsanity.com/paper/2305.19535/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 83 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Towards Continual Reinforcement Learning: A Review and Perspectives](https://mlsanity.com/paper/2012.13490/) (2020)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Continual Prototype Evolution: Learning Online from Non-Stationary Data Streams](https://mlsanity.com/paper/2009.00919/) (2020)
- [Continual World: A Robotic Benchmark For Continual Reinforcement Learning](https://mlsanity.com/paper/2105.10919/) (2021)
- [Continual Learning for Robotics: Definition, Framework, Learning Strategies, Opportunities and Challenges](https://mlsanity.com/paper/1907.00182/) (2019)
- [A Wholistic View of Continual Learning with Deep Neural Networks: Forgotten Lessons and the Bridge to Active and Open World Learning](https://mlsanity.com/paper/2009.01797/) (2020)
- [Continual Backprop: Stochastic Gradient Descent with Persistent Randomness](https://mlsanity.com/paper/2108.06325/) (2021)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Streaming Variational Bayes](https://mlsanity.com/paper/1307.6769/) (2013)
- [SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient](https://mlsanity.com/paper/1811.04504/) (2018)
- [Task Agnostic Continual Learning Using Online Variational Bayes with Fixed-Point Updates](https://mlsanity.com/paper/2010.00373/) (2020)
- [Fast Predictive Uncertainty for Classification with Bayesian Deep Networks](https://mlsanity.com/paper/2003.01227/) (2020)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [Lifelong Incremental Reinforcement Learning with Online Bayesian Inference](https://mlsanity.com/paper/2007.14196/) (2020)
- [Gaussian variational approximation with a factor covariance structure](https://mlsanity.com/paper/1701.03208/) (2017)
- [Cold Posteriors and Aleatoric Uncertainty](https://mlsanity.com/paper/2008.00029/) (2020)

## Built on by (most cited first, 23 of 23)

- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Non-Stationary Learning of Neural Networks with Automatic Soft Parameter Reset](https://mlsanity.com/paper/2411.04034/) (2024)
- [Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching](https://mlsanity.com/paper/2405.20799/) (2024)
- [Kalman Filter for Online Classification of Non-Stationary Data](https://mlsanity.com/paper/2306.08448/) (2023)
- [Bayesian Online Natural Gradient (BONG)](https://mlsanity.com/paper/2405.19681/) (2024)
- [Temporal Test-Time Adaptation with State-Space Models](https://mlsanity.com/paper/2407.12492/) (2024)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Implicit Maximum a Posteriori Filtering via Adaptive Optimization](https://mlsanity.com/paper/2311.10580/) (2023)
- [Stragglers-Aware Low-Latency Synchronous Federated Learning via Layer-Wise Model Updates](https://mlsanity.com/paper/2403.18375/) (2024)
- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)
- [Numerically Robust Fixed-Point Smoothing Without State Augmentation](https://mlsanity.com/paper/2409.20004/) (2024)
- [KOALA++: Efficient Kalman-Based Optimization with Gradient-Covariance Products](https://mlsanity.com/paper/2506.04432/) (2025)
- [Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?](https://mlsanity.com/paper/2408.07588/) (2024)
- [LoKO: Low-Rank Kalman Optimizer for Online Fine-Tuning of Large Models](https://mlsanity.com/paper/2410.11551/) (2024)
- [Bayesian Natural Gradient Fine-Tuning of CLIP Models via Kalman Filtering](https://mlsanity.com/paper/2511.01694/) (2025)
- [Gradient Regularized Natural Gradients](https://mlsanity.com/paper/2601.18420/) (2026)
- [The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling](https://mlsanity.com/paper/2605.31547/) (2026)
- [Noise misleads rotation invariant algorithms on sparse targets](https://mlsanity.com/paper/2403.02697/) (2024)
- [Staying Alive: Online Neural Network Maintenance and Systemic Drift](https://mlsanity.com/paper/2503.17681/) (2025)
- [Using the SEKF to Transfer NN Models of Dynamical Systems with Limited Data](https://mlsanity.com/paper/2603.02439/) (2026)
- [Infinite-Parameter LLMs: Generating and Adapting Weights from Live Data](https://mlsanity.com/paper/2609.18842/) (2026)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)

## Abstract (arXiv)

We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a novel low-rank plus diagonal decomposition of the posterior precision matrix, which gives a cost per step which is linear in the number of model parameters. In contrast to methods based on stochastic variational inference, our method is fully deterministic, and does not require step-size tuning. We show experimentally that this results in much faster (more sample efficient) learning, which results in more rapid adaptation to changing distributions, and faster accumulation of reward when used as part of a contextual bandit algorithm.