Related papers: Continuous Modal Logical Neural Networks: Modal Re…

Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…

Foundation models have transformed language, vision, and time series data analysis, yet progress on dynamic predictions for physical systems remains limited. Given the complexity of physical constraints, two challenges stand out. $(i)$…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…

We present SplineNets, a practical and novel approach for using conditioning in convolutional neural networks (CNNs). SplineNets are continuous generalizations of neural decision graphs, and they can dramatically reduce runtime complexity…

Despite the significant progress of deep learning models in multitude of applications, their adaption in planning and policy related areas remains challenging due to the black-box nature of these models. In this work, we develop a set of…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…

Time Series Foundation Models (TSFMs) excel at numerical forecasting but operate as black boxes lacking qualitative reasoning. Conversely, applying LLMs directly to temporal data introduces a modality gap: text tokenizers fragment…

Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP,…

Backpropagation is the foundational algorithm for training neural networks and a key driver of deep learning's success. However, its biological plausibility has been challenged due to three primary limitations: weight symmetry, reliance on…

The growth of Massive Open Online Courses (MOOCs) presents significant challenges for personalized learning, where concept recommendation is crucial. Existing approaches typically rely on heterogeneous information networks or knowledge…

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many…

The human reasoning process is seldom a one-way process from an input leading to an output. Instead, it often involves a systematic deduction by ruling out other possible outcomes as a self-checking mechanism. In this paper, we describe the…

The explainability of recommendation systems is crucial for enhancing user trust and satisfaction. Leveraging large language models (LLMs) offers new opportunities for comprehensive recommendation logic generation. However, in existing…

Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…

We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity…

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural…

Deciphering brain function through non-invasive recordings requires synthesizing complementary high-frequency electromagnetic (EEG/MEG) and low-frequency metabolic (fMRI) signals. However, despite their shared neural origins, extreme…

We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…

Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the…