Abstract: Possessing a manipulable representation of the world is a requirement for intelligent machines to plan, reason, and act in the world. Endowing computational systems, e.g., deep networks (DNs ...

Homework policy: I anticipate assigning three to five problem sets. Collaboration policy: While you should first think about the problems on your own, you are encouraged to discuss the problems with ...

Spectral graph theory examines the structural and dynamical properties of graphs by analysing the spectra of associated matrices such as the adjacency matrix, Laplacian, normalised Laplacian and ...

Extremal graph theory seeks to determine the maximum or minimum values of graph invariants—such as edge count, degree sequence or subgraph density—subject to the exclusion of particular configurations ...

Ningyi Liao, Haoyu Liu, Zulun Zhu, Siqiang Luo, and Laks V.S. Lakshmanan. A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness. Proceedings of the ACM on ...

A graph is a mathematical structure used to model pairwise relationships between objects. A graph consists of a set of vertices (or nodes) and a set of edges, each of which connects a pair of vertices ...

In the age of information overload, it can be troublesome to go through painstakingly long PDFs or when time is of the essence. With the ever-growing state of LLMs, skimming through a PDF has been ...

Rafael Toral has returned to Earth. The jet plane on the cover of his 1994 debut, Sound Mind Sound Body, signaled his skyward trajectory, and he spent the rest of the decade surfing on clouds of ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices represent chemical species or molecular states, edges represent reactions or ...