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One Filters All: A Generalist Filter For State Estimation
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Proposes LLM-Filter, a generalist state-estimation model that reprograms a frozen LLaMA-7B with trainable segment embedding/projection MLPs and a System-as-Prompt (SaP) context, outperforming learning-based and Bayesian filters and generalizing across systems without retraining.
Problem
Learning-based state estimation filters are task-specific and must be retrained when dynamical systems change or new systems appear; the paper asks whether pretrained LLMs can provide a general, in-context filter.
Approach
Embed noisy observation windows as segment tokens fed into the frozen core layers of an LLM (skipping its language embedding and output heads), add task-instruction and example text as a System-as-Prompt, and train only small MLP observation embedding and state projection layers to map LLM outputs to state estimates.
Key results
- LLM-Filter achieves average RMSE 0.6712 across seven classical systems versus 2.6097 for the best online Bayes filter (EnKF) and 0.8558 for the best learning-based filter (RStateNet) in the reported table.
- LLM-Filter improves over the top learning-based filter by 17.93% on average on low-dimensional systems and reports 11.7% average improvement on Lorenz96 and VL20.
- Replacing LLaMA-7B with MLP, RNN, or Transformer backbones increases RMSE by about 31-32% on average, and LoRA fine-tuning degrades performance.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add System-as-Prompt guidance (ablation) | LLM-Filter · Low-dimensional nonlinear systems | RMSE: 10.18% improvement | Helped |
| add System-as-Prompt guidance (ablation) | LLM-Filter · Cross-system scenarios | RMSE | Helped |
| apply LoRA fine-tuning (ablation) | LLM-Filter · Selkov, Oscillator, Hopf, Lorenz96, and VL20 | RMSE | Hurt |
| fully fine-tune the LLM (ablation) | LLM-Filter · Selkov, Oscillator, Hopf, Lorenz96, and VL20 | RMSE | Mixed |
| use an LLM rather than an MLP (ablation) | LLM-Filter · Selkov, Oscillator, Hopf, Lorenz96, and VL20 | RMSE: 31.66% | Helped |
| use an LLM rather than an RNN (ablation) | LLM-Filter · Selkov, Oscillator, Hopf, Lorenz96, and VL20 | RMSE: 32.43% | Helped |
| use an LLM rather than a Transformer (ablation) | LLM-Filter · Selkov, Oscillator, Hopf, Lorenz96, and VL20 | RMSE: 30.73% | Helped |
| increase LLM backbone size (ablation) | LLM-Filter · Low-dimensional nonlinear and high-dimensional chaotic systems | RMSE | Helped |
| increase LLM backbone size (ablation) | LLM-Filter · Low-dimensional nonlinear and high-dimensional chaotic systems | training time | Hurt |
| use LLM-Filter instead of the strongest baseline | state estimation · Low-dimensional nonlinear systems | RMSE: 17.93% | Helped |
| use LLM-Filter instead of the strongest baseline | state estimation · Lorenz96 and VL20 | RMSE: 11.7% | Helped |
Surprising findings
- LoRA adaptation of the LLM worsened RMSE relative to the frozen LLM on most systems.
- KalmanNet diverged during training on the high-dimensional Lorenz96 and VL20 systems.
Limitations
- Generalization is limited to systems with the same state dimensionality, as stated by the authors.
- Evaluation across diverse settings is limited, and no theoretical explanation is provided for why LLMs help filtering.
- Experiments use simulated ODE systems with Gaussian noise assumptions.
Experimental setup
Datasets: Tracking Selkov Oscillator Hopf Double Pendulum Lorenz96 VL20
Benchmarks: Selkov Oscillator Hopf Double Pendulum Lorenz96 VL20 Tracking
Metrics: RMSE runtime (ms/step)
Baselines: EnKF PF EnKFI EnKFS HubEnKF MEstimator RStateNet ProTran KalmanNet
Builds on: KalmanNet AutoTimes Time-LLM moving horizon estimation
Closest papers by meaning
- LongMamba: Enhancing Mamba's Long-Context Capabilities via Training-Free Receptive Field Enlargement (ICLR 2025 · similarity 0.86)
- Gated Inference Network: Inference and Learning State-Space Models (NeurIPS 2024 · similarity 0.85)
- Identifying latent state transitions in non-linear dynamical systems (ICLR 2025 · similarity 0.85)
- LLM-Empowered State Representation for Reinforcement Learning (ICML 2024 · similarity 0.85)
- Aligning Large Language Models with Representation Editing: A Control Perspective (NeurIPS 2024 · similarity 0.85)
- Quantifying Memory Utilization with Effective State-Size (ICML 2025 · similarity 0.85)
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