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Abby Bertics

Publications and source records attributed to Abby Bertics.

2 recordsLinked to original sources

Dynamic signatures of collective knowledge through navigation in a network with semantic structure

What distinguishes how humans navigate an information network like Wikipedia from what the underlying graph structure and language statistics alone predict? To study human collective navigation, we analyze 70,770 human trajectories through Wikispeedia, an online game where players navigate between articles to reach a target. To compare groups of trajectories rather than individual ones, we merge all trajectories leaving or entering a given article into a Flow Tree. Flow Trees compress collections of trajectories into hierarchies of group splits. We build forward and reverse Flow Trees for 815 of the most commonly traversed articles, representing divergence and convergence, respectively. We compare humans against four random-walker null models, either unweighted or weighted by graph structure, word frequency, or semantic similarity to target. Human Flow Trees are deeper with longer trunks and later splits, indicating players stay together longer than random walkers, whose Flow Trees tend to fan out immediately. An article's degree predicts 51.3-70.9% of the variation in Flow Tree branching factor for random walkers, but only 24.1-36.2% for humans. Taking what graph structure fails to predict as a two-dimensional coordinate system, we define four article types (beacons, funnels, forks, and corridors), distinguished by how humans enter and exit them. These human-defined types are not explained by out-degree or title-word frequency are, and are not recovered by any random walker. A fifth null model, built from first-order human click preferences, partially reproduces human Flow Tree shape but differs significantly in how much of that shape degree explains. We consider collective knowledge to be the structure shared by players who never communicate, beyond what graph structure imposes. It comprises first-order click preferences and a significant component that extends across clicks.

cs.SI↗

Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

cs.LG↗