Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At the same time, they provide a natural framework for exploring edge-centric network measures as tools for pruning and optimization. In this study, we investigate three edge-centric network measures: Forman-Ricci curvature (FRC), Ollivier-Ricci curvature (ORC), and edge betweenness centrality (EBC), to compress RWNNs by selectively retaining important synapses (or edges) while pruning the rest. As a baseline, RWNNs are trained for COVID-19 chest x-ray image classification, aiming to reduce network complexity while preserving performance in terms of accuracy, specificity, and sensitivity. We extend prior work on pruning RWNN using ORC by incorporating two additional edge-centric measures, FRC and EBC, across three network generators: Erdös-Rényi (ER) model, Watts-Strogatz (WS) model, and Barabási-Albert (BA) model. We provide a comparative analysis of the pruning performance of the three measures in terms of compression ratio and theoretical speedup. A central focus of our study is to evaluate whether FRC, which is computationally more efficient than ORC, can achieve comparable pruning effectiveness. Along with performance evaluation, we further investigate the structural properties of the pruned networks through modularity and global efficiency, offering insights into the trade-off between modular segregation and network efficiency in compressed RWNNs. Our results provide initial evidence that FRC-based pruning can effectively simplify RWNNs, offering significant computational advantages while maintaining performance comparable to ORC.

Accurate labels are critical for deriving robust machine learning models. Labels are used to train supervised learning models and to evaluate most machine learning paradigms. In this paper, we model the accuracy and cost of a common weak labeling process where annotators assign presence or absence labels to fixed-length data segments for a given event class. The annotator labels a segment as "present" if it sufficiently covers an event from that class, e.g., a birdsong sound event in audio data. We analyze how the segment length affects the label accuracy and the required number of annotations, and compare this fixed-length labeling approach with an oracle method that uses the true event activations to construct the segments. Furthermore, we quantify the gap between these methods and verify that in most realistic scenarios the oracle method is better than the fixed-length labeling method in both accuracy and cost. Our findings provide a theoretical justification for adaptive weak labeling strategies that mimic the oracle process, and a foundation for optimizing weak labeling processes in sequence labeling tasks.

This paper provides evidence that weak crossover effects differ in nature between matrix and relative clauses. Fukushima et al. (2024) provided similar evidence, showing that, when various non-structural factors were eliminated English speakers never accepted matrix weak crossover cases, but often accepted relative weak crossover ones. Those results were limited, however, by English word order, which lead to uncertainty as to whether this difference was due to the effects of linear precedence or syntactic structure. In this paper, to distinguish between these two possibilities, we conduct an experiment using Japanese, which lacks the word-order confound that English had. We find results that are qualitatively in line with Fukushima et al. (2024) suggesting that the relevant distinction is structural and not based simply on precedence.

Curvature serves as a potent and descriptive invariant, with its efficacy validated both theoretically and practically within graph theory. We employ a definition of generalized Ricci curvature proposed by Ollivier, which Lin and Yau later adapted to graph theory, known as Ollivier-Ricci curvature (ORC). ORC measures curvature using the Wasserstein distance, thereby integrating geometric concepts with probability theory and optimal transport. Jost and Liu previously discussed the lower bound of ORC by showing the upper bound of the Wasserstein distance. We extend the applicability of these bounds to discrete spaces with metrics on integers, specifically hypergraphs. Compared to prior work on ORC in hypergraphs by Coupette, Dalleiger, and Rieck, which faced computational challenges, our method introduces a simplified approach with linear computational complexity, making it particularly suitable for analyzing large-scale networks. Through extensive simulations and application to synthetic and real-world datasets, we demonstrate the significant improvements our method offers in evaluating ORC.

We present a minimal phase oscillator model for learning quadrupedal locomotion. Each of the four oscillators is coupled only to itself and its corresponding leg through local feedback of the ground reaction force, which can be interpreted as an observer feedback gain. We interpret the oscillator itself as a latent contact state-estimator. Through a systematic ablation study, we show that the combination of phase observations, simple phase-based rewards, and the local feedback dynamics induces policies that exhibit emergent gait preferences, while using a reduced set of simple rewards, and without prescribing a specific gait. The code is open-source, and a video synopsis available at https://youtu.be/1NKQ0rSV3jU.

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or communities. Our method implements discrete Ricci curvatures and their associated geometric flows, under which the edge weights of the graph evolve to reveal its community structure. We consider several discrete curvature notions and analyze the utility of the resulting algorithms. In contrast to prior literature, we study not only single-membership community detection, where each node belongs to exactly one community, but also mixed-membership community detection, where communities may overlap. For the latter, we argue that it is beneficial to perform community detection on the line graph, i.e., the graph's dual. We provide both theoretical and empirical evidence for the utility of our curvature-based clustering algorithms. In addition, we give several results on the relationship between the curvature of a graph and that of its dual, which enable the efficient implementation of our proposed mixed-membership community detection approach and which may be of independent interest for curvature-based network analysis.

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction, for the first time. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local structures and to enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further used as weights for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and a series of simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negativecurvature ratios, network densities, and network sizes (when larger than 500).

Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of hypergraphs has remained largely unexplored. On graphs, the Ollivier-Ricci curvature measures differences between random walks via Wasserstein distances, thus grounding a geometric concept in ideas from probability theory and optimal transport. We develop ORCHID, a flexible framework generalizing Ollivier-Ricci curvature to hypergraphs, and prove that the resulting curvatures have favorable theoretical properties. Through extensive experiments on synthetic and real-world hypergraphs from different domains, we demonstrate that ORCHID curvatures are both scalable and useful to perform a variety of hypergraph tasks in practice.

Recently, I've spent quite a lot of time pondering what an orc would look like with an afro. This, naturally, led to contemplation of an axe-afro-comb combo, and whether such a contraption would fall under blacksmithing or engineering. That's because I've been playing Shadowlands, the eighth expansion to World of Warcraft. For Warcraft fans, there's a lot to be excited about: the new game allows players to explore the afterlife – reviving classic characters such as Kael'thas Sunstrider – and introduces a new style of play in Torghast, a deliciously punishing dungeon that changes each time you visit. There's also a clear recruiting drive for new players with a simplified introduction, more straightforward questing and reconfigured character growth, all aimed at making this venerable and complex game less daunting.

San Francisco (CNN Business)A new artificial intelligence system is so good at composing text that the researchers behind it said they won't release it for fear of how it could be misused. Created by nonprofit AI research company OpenAI (whose backers include Tesla CEO Elon Musk and Microsoft), the text-generating system can write page-long responses to prompts, mimicking everything from fantasy prose to fake celebrity news stories and homework assignments. It builds on an earlier text-generating system the company released last year. Researchers have used AI to generate text for decades with varying levels of success. In recent years, the technology has gotten particularly good.