Lina Yu

Yanjie Li, Jingyi Liu, Weijun Li et al.

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great challenge for artificial intelligence. This field is called symbolic regression (SR). Symbolic regression was originally formulated as a combinatorial optimization problem, and Genetic Programming (GP) and Reinforcement Learning algorithms were used to solve it. However, GP is sensitive to hyperparameters, and these two types of algorithms are inefficient. To solve this problem, researchers treat the mapping from data to expressions as a translation problem. And the corresponding large-scale pre-trained model is introduced. However, the data and expression skeletons do not have very clear word correspondences as the two languages do. Instead, they are more like two modalities (e.g., image and text). Therefore, in this paper, we proposed MMSR. The SR problem is solved as a pure multi-modal problem, and contrastive learning is also introduced in the training process for modal alignment to facilitate later modal feature fusion. It is worth noting that to better promote the modal feature fusion, we adopt the strategy of training contrastive learning loss and other losses at the same time, which only needs one-step training, instead of training contrastive learning loss first and then training other losses. Because our experiments prove training together can make the feature extraction module and feature fusion module wearing-in better. Experimental results show that compared with multiple large-scale pre-training baselines, MMSR achieves the most advanced results on multiple mainstream datasets including SRBench. Our code is open source at https://github.com/1716757342/MMSR

Yuchen Wu, Jiahe Li, Xiaohan Yu et al.

Monocular visual SLAM enables 3D reconstruction from internet video and autonomous navigation on resource-constrained platforms, yet suffers from scale drift, i.e., the gradual divergence of estimated scale over long sequences. Existing frame-to-frame methods achieve real-time performance through local optimization but accumulate scale drift due to the lack of global constraints among independent windows. To address this, we propose SCE-SLAM, an end-to-end SLAM system that maintains scale consistency through scene coordinate embeddings, which are learned patch-level representations encoding 3D geometric relationships under a canonical scale reference. The framework consists of two key modules: geometry-guided aggregation that leverages 3D spatial proximity to propagate scale information from historical observations through geometry-modulated attention, and scene coordinate bundle adjustment that anchors current estimates to the reference scale through explicit 3D coordinate constraints decoded from the scene coordinate embeddings. Experiments on KITTI, Waymo, and vKITTI demonstrate substantial improvements: our method reduces absolute trajectory error by 8.36m on KITTI compared to the best prior approach, while maintaining 36 FPS and achieving scale consistency across large-scale scenes.

Yanjie Li, Weijun Li, Lina Yu et al.

The mathematical formula is the human language to describe nature and is the essence of scientific research. Finding mathematical formulas from observational data is a major demand of scientific research and a major challenge of artificial intelligence. This area is called symbolic regression. Originally symbolic regression was often formulated as a combinatorial optimization problem and solved using GP or reinforcement learning algorithms. These two kinds of algorithms have strong noise robustness ability and good Versatility. However, inference time usually takes a long time, so the search efficiency is relatively low. Later, based on large-scale pre-training data proposed, such methods use a large number of synthetic data points and expression pairs to train a Generative Pre-Trained Transformer(GPT). Then this GPT can only need to perform one forward propagation to obtain the results, the advantage is that the inference speed is very fast. However, its performance is very dependent on the training data and performs poorly on data outside the training set, which leads to poor noise robustness and Versatility of such methods. So, can we combine the advantages of the above two categories of SR algorithms? In this paper, we propose \textbf{FormulaGPT}, which trains a GPT using massive sparse reward learning histories of reinforcement learning-based SR algorithms as training data. After training, the SR algorithm based on reinforcement learning is distilled into a Transformer. When new test data comes, FormulaGPT can directly generate a "reinforcement learning process" and automatically update the learning policy in context. Tested on more than ten datasets including SRBench, formulaGPT achieves the state-of-the-art performance in fitting ability compared with four baselines. In addition, it achieves satisfactory results in noise robustness, versatility, and inference efficiency.

Jingyi Liu, Yanjie Li, Lina Yu et al.

Noise ubiquitously exists in signals due to numerous factors including physical, electronic, and environmental effects. Traditional methods of symbolic regression, such as genetic programming or deep learning models, aim to find the most fitting expressions for these signals. However, these methods often overlook the noise present in real-world data, leading to reduced fitting accuracy. To tackle this issue, we propose \textit{\textbf{D}eep Symbolic Regression against \textbf{N}oise via \textbf{C}ontrastive \textbf{L}earning (DN-CL)}. DN-CL employs two parameter-sharing encoders to embed data points from various data transformations into feature shields against noise. This model treats noisy data and clean data as different views of the ground-truth mathematical expressions. Distances between these features are minimized, utilizing contrastive learning to distinguish between 'positive' noise-corrected pairs and 'negative' contrasting pairs. Our experiments indicate that DN-CL demonstrates superior performance in handling both noisy and clean data, presenting a promising method of symbolic regression.