"equiconnected", which is a stronger result that we will define and introduce later in the paper.

We present an application of the connectedness of these superlevel sets to the derivation of minimax theorems for robust reinforcement learning.

"equiconnected", which is a stronger result that we will define and introduce later in the paper.

This paper addresses the question of which of these tasks are asymptotically solved by sorting by decreasing order of expected utility, for some suitable notion of utility, or, equivalently, when is square loss regression consistent for ranking via score-and-sort?

This paper addresses the question of which of these tasks are asymptotically solved by sorting by decreasing order of expected utility, for some suitable notion of utility, or, equivalently, when is square loss regression consistent for ranking via score-and-sort?

Neural network minima are often connected by curves along which train and test loss remain nearly constant, a phenomenon known as mode connectivity. While this property has enabled applications such as model merging and fine-tuning, its theoretical explanation remains unclear. We propose a new approach to exploring the connectedness of minima using parameter space symmetry. By linking the topology of symmetry groups to that of the minima, we derive the number of connected components of the minima of linear networks and show that skip connections reduce this number. We then examine when mode connectivity and linear mode connectivity hold or fail, using parameter symmetries which account for a significant part of the minimum. Finally, we provide explicit expressions for connecting curves in the minima induced by symmetry. Using the curvature of these curves, we derive conditions under which linear mode connectivity approximately holds. Our findings highlight the role of continuous symmetries in understanding the neural network loss landscape.

This paper investigates the risk spillovers among AI ETFs, AI tokens, and green markets using the R2 decomposition method. We reveal several key insights. First, the overall transmission connectedness index (TCI) closely aligns with the contemporaneous TCI, while the lagged TCI is significantly lower. Second, AI ETFs and clean energy act as risk transmitters, whereas AI tokens and green bond function as risk receivers. Third, AI tokens are difficult to hedge and provide limited hedging ability compared to AI ETFs and green assets. However, multivariate portfolios effectively reduce AI tokens investment risk. Among them, the minimum correlation portfolio outperforms the minimum variance and minimum connectedness portfolios.

Selecting an appropriate book is crucial for fostering reading habits in children. While children exhibit varying levels of complexity when generating oral narratives, the question arises: do children's books also differ in narrative complexity? This study explores the narrative dynamics of literary texts used in schools, focusing on how their complexity evolves across different grade levels. Using Word-Recurrence Graph Analysis, we examined a dataset of 1,627 literary texts spanning 13 years of education. The findings reveal significant exponential growth in connectedness, particularly during the first three years of schooling, mirroring patterns observed in children's oral narratives. These results highlight the potential of literary texts as a tool to support the development of literacy skills.