Early Language Learning via Spreading Activation and Category Exploration in Complex Networks

Is word acquisition in children uneven with respect to semantic and lexical categories? To answer this question, we model early language learning as a search on a graph-based mental lexicon, driven by two interacting processes: spreading activation and an enforced exploration (rather than exploitation) of lexical categories. We evaluate model performance on four languages (German, English, Dutch, and Rioplatense Spanish), using CDIs as ground-truth data for lexical categories, normative ages derived from the Wordbank repository, and state-of-the-art resources for reconstructing graphs of word similarities. We find that spreading activation outperforms a shortest path baseline in simulating normative word acquisition. At the category level, we highlight complex transitions between CDIs. By studying their sequences in terms of burstiness and average persistence time within the same CDI, we find that spreading activation better captures the exploration dynamics observed empirically. Overall, our findings suggest that vocabulary development can be understood through the non-trivial interplay between activation dynamics and some degree of constraints regulating the visiting of lexical categories in complex networks.

Code evolution for link prediction in complex networks

The problem of predicting links in complex networks appears in different disciplines and has led to a variety of ingenious human-designed methods. We use this rich program space to explore the performance and behavior of automated code-evolution systems tasked to obtain machine-designed methods for link prediction. Despite being trained on limited data, algorithms evolved through code evolution outperform human-designed methods (with an average AUC score of 0.915 vs. 0.783, computed over 580 networks) and show improved computational efficiency, allowing them to be applied to networks with millions of links. The discovered methods follow approaches that have been employed in human-designed methods, but contain key innovations in the selection and combination of node- and link-features. This illustrates the role modern large language models and genetic algorithms can play in algorithmic innovation and scientific discovery more generally.

On the Entropy Formula for Real, Complex, and Quaternionic Deep Linear Networks

We extend the entropy formula of Menon and Yu for the real Deep Linear Network (DLN) to its complex and quaternionic analogues, obtaining a unified formula for DLNs over $\mathbb{R}$, $\mathbb{C}$, and $\mathbb{H}$.