The Kalman Evolve: Closing the Gap in Kalman Filtering via Interpretable Algorithm Discovery

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail in realistic sensing settings such as Doppler radar and LiDAR. In these cases, the optimal estimator is inherently nonlinear, which leads to systematic performance degradation. This creates a performance gap that cannot be eliminated by tuning the noise covariance parameters (i.e., the process and measurement noise in the Kalman Filter) alone. To address this limitation, we propose Kalman Evolve, a framework for discovering improved filtering algorithms by jointly optimizing both noise parameters and the update structure. Our approach leverages large language models (LLMs) as a structured prior over program space, enabling the generation of interpretable, non-affine modifications to the classical Kalman filter while preserving its recursive form. We provide analytical results establishing the suboptimality of affine estimators under common nonlinear sensing models, motivating the need for structure-aware updates. Across a range of synthetic and real-world tracking benchmarks, including Doppler radar, LiDAR-based localization, and pedestrian tracking, the discovered algorithms consistently improve over strong baselines such as the Optimized Kalman Filter, achieving up to 12\% reduction in RMSE. These results suggest that optimizing the structure of the Kalman filter, rather than only its parameters, provides a practical and interpretable way to improve state estimation.

The Large Language Model GreekLegalRoBERTa

We develop four versions of GreekLegalRoBERTa, which are four large language models trained on Greek legal and nonlegal text. We show that our models surpass the performance of GreekLegalBERT, Greek- LegalBERT-v2, and GreekBERT in two tasks involving Greek legal documents: named entity recognition and multi-class legal topic classification. We view our work as a contribution to the study of domain-specific NLP tasks in low-resource languages, like Greek, using modern NLP techniques and methodologies.