# Variational meta-learning inference for low dimensional neural system identification

arXiv: https://arxiv.org/abs/2607.18965 · HTML: https://mlsanity.com/paper/2607.18965/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Mixtures of Laplace Approximations for Improved Post-Hoc Uncertainty in Deep Learning](https://mlsanity.com/paper/2111.03577/) (2021)
- [Can Transformers Learn Optimal Filtering for Unknown Systems?](https://mlsanity.com/paper/2308.08536/) (2023)
- [Enhanced Transformer architecture for in-context learning of dynamical systems](https://mlsanity.com/paper/2410.03291/) (2024)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Distributionally robust minimization in meta-learning for system identification](https://mlsanity.com/paper/2506.18074/) (2025)
- [Manifold meta-learning for reduced-complexity neural system identification](https://mlsanity.com/paper/2504.11811/) (2025)

## Abstract (arXiv)

Deep learning has proven highly effective for nonlinear system identification, but heavily parameterized neural networks are prone to overfitting in low-data regimes and lack reliable uncertainty quantification. The recently developed manifold meta-learning framework addresses the data efficiency problem by restricting the model parameters to a meta-learned low-dimensional manifold. However, that method is purely deterministic. We propose a fully probabilistic extension of the manifold meta-learning framework, based on amortized Variational Inference, where a generative prior over the low-dimensional parameter manifold is learned. During task-specific adaptation, we combine Maximum A Posteriori estimation with the Laplace approximation to yield a mathematically grounded posterior approximation. Evaluated on a static regression task and the Bouc--Wen dynamical system benchmark, the proposed approach achieves predictive accuracy comparable to its deterministic counterpart while successfully providing calibrated uncertainty bounds in severely low-data regimes.