Related papers: Implicit Bias and Invariance: How Hopfield Network…

We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…

Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the…

The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This…

Recent years have witnessed a surge of interest in machine learning on graphs and networks with applications ranging from vehicular network design to IoT traffic management to social network recommendations. Supervised machine learning…

An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of…

The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…

Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…

Graph neural networks (GNNs) have been demonstrated to achieve state-of-the-art for a number of graph-based learning tasks, which leads to a rise in their employment in various domains. However, it has been shown that GNNs may inherit and…

Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…

A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We…

With the widespread use of Graph Neural Networks (GNNs) for representation learning from network data, the fairness of GNN models has raised great attention lately. Fair GNNs aim to ensure that node representations can be accurately…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

Thermodynamics-informed neural networks employ inductive biases for the enforcement of the first and second principles of thermodynamics. To construct these biases, a metriplectic evolution of the system is assumed. This provides excellent…

Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…

It has been observed that message-passing graph neural networks (GNN) sometimes struggle to maintain a healthy balance between the efficient/scalable modeling of long-range dependencies across nodes while avoiding unintended consequences…

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in…

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical…