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We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicability to density…

Symbolic regression (SR) seeks to recover closed-form mathematical expressions that describe observed data. While existing methods have advanced the discovery of either explicit mappings (i.e., $y = f(\mathbf{x})$) or discovering implicit…

Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information.…

Recent progress on parse tree encoder for sentence representation learning is notable. However, these works mainly encode tree structures recursively, which is not conducive to parallelization. On the other hand, these works rarely take…

To improve the performance and explainability of LLM-based natural language reasoning, structured reasoning can be applied to generate explicitly structured proofs. Among different methods for structured reasoning, we specifically focus on…

Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…

Capturing the composition patterns of relations is a vital task in knowledge graph completion. It also serves as a fundamental step towards multi-hop reasoning over learned knowledge. Previously, several rotation-based translational methods…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

Planning remains a core challenge for large language models (LLMs), particularly in domains that require coherent multi-step action sequences grounded in external constraints. We introduce SymPlanner, a novel framework that equips LLMs with…

Learning implicit templates as neural fields has recently shown impressive performance in unsupervised shape correspondence. Despite the success, we observe current approaches, which solely rely on geometric information, often learn…

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…

When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…

Deep learning (DL) has advanced the field of dense prediction, while gradually dissolving the inherent barriers between different tasks. However, most existing works focus on designing architectures and constructing visual cues only for the…

Traditional language models, adept at next-token prediction in text sequences, often struggle with transduction tasks between distinct symbolic systems, particularly when parallel data is scarce. Addressing this issue, we introduce…

In continual learning, solving the catastrophic forgetting problem may make the models fall into the stability-plasticity dilemma. Moreover, inter-task confusion will also occur due to the lack of knowledge exchanges between different…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Despite numerous successes in Deep Reinforcement Learning (DRL), the learned policies are not interpretable. Moreover, since DRL does not exploit symbolic relational representations, it has difficulties in coping with structural changes in…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling.…

Elucidating the reasoning process with structured explanations from question to answer is crucial, as it significantly enhances the interpretability, traceability, and trustworthiness of question-answering (QA) systems. However, structured…