LLM-SR: Scientific Equation Discovery via Programming with Large Language Models

Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the necessity of navigating extremely high-dimensional combinatorial and nonlinear hypothesis spaces. Traditional methods of equation discovery largely focus on extracting equations from data alone, often neglecting the rich domain-specific prior knowledge that scientists typically depend on. To bridge this gap, we introduce LLM-SR, a novel approach that leverages the extensive scientific knowledge and robust code generation capabilities of Large Language Models (LLMs) to discover scientific equations from data in an efficient manner. Specifically, LLM-SR treats equations as programs with mathematical operators and combines LLMs' scientific priors with evolutionary search over equation programs. The LLM iteratively proposes new equation skeletons, drawing from its physical understanding, which are then optimized against data to estimate skeleton parameters. We demonstrate LLM-SR's effectiveness across three diverse scientific domains, where it discovers physically accurate equations that provide significantly better fits to in-domain and out-of-domain data compared to the well-established equation discovery baselines

SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training

In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic unified understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training, which employs joint contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the pre-trained embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in few-shot learning scenarios where available data is limited.

Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecasting

There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal correlations observed in traffic networks. Current works primarily rely on road networks with graph structures and learn representations using graph neural networks (GNNs), but this approach suffers from over-smoothing problem in deep architectures. To tackle this problem, recent methods introduced the combination of GNNs with residual connections or neural ordinary differential equations (ODE). However, current graph ODE models face two key limitations in feature extraction: (1) they lean towards global temporal patterns, overlooking local patterns that are important for unexpected events; and (2) they lack dynamic semantic edges in their architectural design. In this paper, we propose a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE) which is designed with multiple connective ODE-GNN modules to learn better representations by capturing different views of complex local and global dynamic spatio-temporal dependencies. We also add some techniques like shared weights and divergence constraints into the intermediate layers of distinct ODE-GNN modules to further improve their communication towards the forecasting task. Our extensive set of experiments conducted on six real-world datasets demonstrate the superior performance of GRAM-ODE compared with state-of-the-art baselines as well as the contribution of different components to the overall performance. The code is available at https://github.com/zbliu98/GRAM-ODE

Transformer-based Planning for Symbolic Regression

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the efficacy of pretrained transformer-based models for generating equations as sequences, which benefit from large-scale pretraining on synthetic datasets and offer considerable advantages over GP-based methods in terms of inference time. However, these models focus on supervised pretraining goals borrowed from text generation and ignore equation-specific objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. TPSR, as opposed to conventional decoding strategies, allows for the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise. We also demonstrate that the utilization of various caching mechanisms can further enhance the efficiency of TPSR.

Execution-based Code Generation using Deep Reinforcement Learning

The utilization of programming language (PL) models, pretrained on large-scale code corpora, as a means of automating software engineering processes has demonstrated considerable potential in streamlining various code generation tasks such as code completion, code translation, and program synthesis. However, current approaches mainly rely on supervised fine-tuning objectives borrowed from text generation, neglecting specific sequence-level features of code, including but not limited to compilability as well as syntactic and functional correctness. To address this limitation, we propose PPOCoder, a new framework for code generation that combines pretrained PL models with Proximal Policy Optimization (PPO) deep reinforcement learning and employs execution feedback as the external source of knowledge into the model optimization. PPOCoder is transferable across different code generation tasks and PLs. Extensive experiments on three code generation tasks demonstrate the effectiveness of our proposed approach compared to SOTA methods, improving the success rate of compilation and functional correctness over different PLs. Our code can be found at https://github.com/reddy-lab-code-research/PPOCoder .

Adaptively Weighted Top-N Recommendation for Organ Matching

Reducing the shortage of organ donations to meet the demands of patients on the waiting list has being a major challenge in organ transplantation. Because of the shortage, organ matching decision is the most critical decision to assign the limited viable organs to the most suitable patients. Currently, organ matching decisions were only made by matching scores calculated via scoring models, which are built by the first principles. However, these models may disagree with the actual post-transplantation matching performance (e.g., patient's post-transplant quality of life (QoL) or graft failure measurements). In this paper, we formulate the organ matching decision-making as a top-N recommendation problem and propose an Adaptively Weighted Top-N Recommendation (AWTR) method. AWTR improves performance of the current scoring models by using limited actual matching performance in historical data set as well as the collected covariates from organ donors and patients. AWTR sacrifices the overall recommendation accuracy by emphasizing the recommendation and ranking accuracy for top-N matched patients. The proposed method is validated in a simulation study, where KAS [60] is used to simulate the organ-patient recommendation response. The results show that our proposed method outperforms seven state-of-the-art top-N recommendation benchmark methods.