Related papers: A Neuro-Symbolic Method for Solving Differential a…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a…

Deep Neural Networks have achieved great success in some of the complex tasks that humans can do with ease. These include image recognition/classification, natural language processing, game playing etc. However, modern Neural Networks fail…

Deep Learning (DL) models have become popular for solving complex problems, but they have limitations such as the need for high-quality training data, lack of transparency, and robustness issues. Neuro-Symbolic AI has emerged as a promising…

Discrete and continuous representations of content (e.g., of language or images) have interesting properties to be explored for the understanding of or reasoning with this content by machines. This position paper puts forward our opinion on…

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic…

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Navigating the complexities of physics reasoning has long been a difficult task for Large Language Models (LLMs), requiring a synthesis of profound conceptual understanding and adept problem-solving techniques. In this study, we investigate…

We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…

To create usable and deployable Artificial Intelligence (AI) systems, there requires a level of assurance in performance under many different conditions. Many times, deployed machine learning systems will require more classic logic and…

We introduce Neuro-Symbolic Continual Learning, where a model has to solve a sequence of neuro-symbolic tasks, that is, it has to map sub-symbolic inputs to high-level concepts and compute predictions by reasoning consistently with prior…

Neural models and symbolic algorithms have recently been combined for tasks requiring both perception and reasoning. Neural models ground perceptual input into a conceptual vocabulary, on which a classical reasoning algorithm is applied to…

Solving symbolic mathematics has always been of in the arena of human ingenuity that needs compositional reasoning and recurrence. However, recent studies have shown that large-scale language models such as transformers are universal and…

We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian…

This paper addresses the problem of modeling and estimating dynamic multi-valued mappings. While most mathematical models provide a unique solution for a given input, real-world applications often lack deterministic solutions. In such…

Deep reinforcement learning (DRL) has led to a wide range of advances in sequential decision-making tasks. However, the complexity of neural network policies makes it difficult to understand and deploy with limited computational resources.…

Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…

Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform…