Related papers: Learning Syllogism with Euler Neural-Networks

The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable…

We introduce RelNet: a new model for relational reasoning. RelNet is a memory augmented neural network which models entities as abstract memory slots and is equipped with an additional relational memory which models relations between all…

The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we…

We describe a new algorithm for learning multi-class neural-network models from large-scale clinical electroencephalograms (EEGs). This algorithm trains hidden neurons separately to classify all the pairs of classes. To find best pairwise…

In this paper, a taxonomy for memory networks is proposed based on their memory organization. The taxonomy includes all the popular memory networks: vanilla recurrent neural network (RNN), long short term memory (LSTM ), neural stack and…

Structural equation models (SEMs) are widely used in sciences, ranging from economics to psychology, to uncover causal relationships underlying a complex system under consideration and estimate structural parameters of interest. We study…

We introduce a new model, the Recurrent Entity Network (EntNet). It is equipped with a dynamic long-term memory which allows it to maintain and update a representation of the state of the world as it receives new data. For language…

Brain network provides important insights for the diagnosis of many brain disorders, and how to effectively model the brain structure has become one of the core issues in the domain of brain imaging analysis. Recently, various computational…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…

Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify…

Deep neural networks (DNNs) deliver state-of-the-art accuracy on regression and classification tasks, yet two structural deficits persistently obstruct their deployment in safety-critical, resource-constrained settings: (i) opacity of the…

Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order…

A biological neural network is constituted by numerous subnetworks and modules with different functionalities. For an artificial neural network, the relationship between a network and its subnetworks is also important and useful for both…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

To effectively classify graph instances, graph neural networks need to have the capability to capture the part-whole relationship existing in a graph. A capsule is a group of neurons representing complicated properties of entities, which…

Network representation aims to represent the nodes in a network as continuous and compact vectors, and has attracted much attention in recent years due to its ability to capture complex structure relationships inside networks. However,…

In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph.…

Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs)…

Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent…