Related papers: A Symbolic Neural Network Representation and its A…
In this paper we present an alternative method to symbolic segmentation: we approach symbolic segmentation as an algorithm selection problem. That is, let there be a set A of available algorithms for symbolic segmentation, a set of input…
Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…
Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…
Deep learning models have achieved significant success in various image related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an efficient approach that…
To understand cognitive reasoning in the brain, it has been proposed that symbols and compositions of symbols are represented by activity patterns (vectors) in a large population of neurons. Formal models implementing this idea [Plate…
A common approach in neuroscience is to study neural representations as a means to understand a system -- increasingly, by relating the neural representations to the internal representations learned by computational models. However, a…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
This work theoretically investigates the performance of a composite neural network. A composite neural network is a rooted directed acyclic graph combining a set of pre-trained and non-instantiated neural network models, where a pre-trained…
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…
Computational context understanding refers to an agent's ability to fuse disparate sources of information for decision-making and is, therefore, generally regarded as a prerequisite for sophisticated machine reasoning capabilities, such as…
Recurrent Neural Networks are an effective and prevalent tool used to model sequential data such as natural language text. However, their deep nature and massive number of parameters pose a challenge for those intending to study precisely…
Deep neural networks are highly effective at a range of computational tasks. However, they tend to be computationally expensive, especially in vision-related problems, and also have large memory requirements. One of the most effective…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks)…
Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
Design representation is a common task in the design process to facilitate learning, analysis, redesign, communication, and other design activities. Traditional representation techniques rely on human expertise and manual construction and…
Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer…