# Model-Free Neural Filtering: A Comparison with Classical Filters in Nonlinear Systems

arXiv: https://arxiv.org/abs/2601.21266 · HTML: https://mlsanity.com/paper/2601.21266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Can a Transformer Represent a Kalman Filter?](https://mlsanity.com/paper/2312.06937/) (2023)
- [DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup](https://mlsanity.com/paper/2306.03897/) (2023)
- [Can Transformers Learn Optimal Filtering for Unknown Systems?](https://mlsanity.com/paper/2308.08536/) (2023)
- [Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction](https://mlsanity.com/paper/1901.08096/) (2019)
- [DynaNet: Neural Kalman Dynamical Model for Motion Estimation and Prediction](https://mlsanity.com/paper/1908.03918/) (2019)
- [Action-Conditional Recurrent Kalman Networks For Forward and Inverse Dynamics Learning](https://mlsanity.com/paper/2010.10201/) (2020)
- [Transformers Can Solve Non-Linear and Non-Markovian Filtering Problems in Continuous Time For Conditionally Gaussian Signals](https://mlsanity.com/paper/2310.19603/) (2023)
- [Explainable Gated Bayesian Recurrent Neural Network for Non-Markov State Estimation](https://mlsanity.com/paper/2310.17187/) (2023)

## Abstract (arXiv)

Neural network models are increasingly used for state estimation in control and decision-making, yet it remains unclear to what extent they behave as principled filters in nonlinear dynamical systems. Unlike classical filters, which rely on explicit dynamics and noise models, neural estimators can be trained purely from data. We present a systematic comparison between model-free neural estimators and classical filtering methods across multiple nonlinear scenarios. On the neural side, we evaluate Transformer-based models, recurrent neural networks, and state-space models; on the classical side, we compare against particle filters and nonlinear Kalman filters. Results show that structured state-space models (SSMs), in particular Mamba and Mamba-2, are consistently strong among neural estimators. They approach strong classical filters in several nonlinear systems and outperform weaker classical baselines without access to system models, while the evaluated neural implementations achieve substantially higher inference throughput on the tested hardware. Accurate model-based filters can still dominate when their assumptions are well matched. We attribute the relative strength of SSMs to filtering-aligned inductive bias: recursive latent-state updates make them structurally closer to classical filters under fixed parameter budgets, finite data, and long-horizon evaluation.