Juan Zhang

Da Li, Junping Yin, Jin Xu et al.

Extracting simple mathematical expression from an observational dataset to describe complex natural phenomena is one of the core objectives of artificial intelligence (AI). This field is known as symbolic regression (SR). Traditional SR models are based on genetic programming (GP) or reinforcement learning (RL), facing well-known challenges, such as low efficiency and overfitting. Recent studies have integrated SR with large language models (LLMs), enabling fast zero-shot inference by learning mappings from millions of dataset-expression pairs. However, since the input and output are inherently different modalities, such models often struggle to converge effectively. In this paper, we introduce ViSymRe, a vision-guided multimodal SR model that incorporates the third resource, expression graph, to bridge the modality gap. Different from traditional multimodal models, ViSymRe is trained to extract vision, termed virtual vision, from datasets, without relying on the global availability of expression graphs, which addresses the essential challenge of visual SR, i.e., expression graphs are not available during inference. Evaluation results on multiple mainstream benchmarks show that ViSymRe achieves more competitive performance than the state-of-the-art dataset-only baselines. The expressions predicted by ViSymRe not only fit the dataset well but are also simple and structurally accurate, goals that SR models strive to achieve.

Yangguang He, Wenhao Li, Minzhe Li et al.

Learning-based filtering has demonstrated strong performance in non-linear dynamical systems, particularly when the statistics of noise are unknown. However, in real-world deployments, environmental factors, such as changing wind conditions or electromagnetic interference, can induce unobserved noise-statistics drift, leading to substantial degradation of learning-based methods. To address this challenge, we propose OTAKNet, the first online solution to noise-statistics drift within learning-based adaptive Kalman filtering. Unlike existing learning-based methods that perform offline fine-tuning using batch pointwise matching over entire trajectories, OTAKNet establishes a connection between the state estimate and the drift via one-step predictive measurement likelihood, and addresses it using optimal transport. This leverages OT's geometry - aware cost and stable gradients to enable fully online adaptation without ground truth labels or retraining. We compare OTAKNet against classical model-based adaptive Kalman filtering and offline learning-based filtering. The performance is demonstrated on both synthetic and real-world NCLT datasets, particularly under limited training data.