Paolo Albano

Paolo Albano, Piermarco Cannarsa, Khai Tien Nguyen et al.

It is a generally shared opinion that significant information about the topology of a bounded domain $Ω$ of a riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partialΩ}$, %, $d:Ω\rightarrow [0,\infty [$, from the boundary of $Ω$. To confirm such an idea we propose an approach based on the invariance of the singular set of the distance function with respect to the generalized gradient flow of of $d_{\partialΩ}$. As an application, we deduce that such a singular set has the same homotopy type as $Ω$.

Bernardo Magnini, Roberto Zanoli, Michele Resta et al.

We describe Evalita-LLM, a new benchmark designed to evaluate Large Language Models (LLMs) on Italian tasks. The distinguishing and innovative features of Evalita-LLM are the following: (i) all tasks are native Italian, avoiding issues of translating from Italian and potential cultural biases; (ii) in addition to well established multiple-choice tasks, the benchmark includes generative tasks, enabling more natural interaction with LLMs; (iii) all tasks are evaluated against multiple prompts, this way mitigating the model sensitivity to specific prompts and allowing a fairer and objective evaluation. We propose an iterative methodology, where candidate tasks and candidate prompts are validated against a set of LLMs used for development. We report experimental results from the benchmark's development phase, and provide performance statistics for several state-of-the-art LLMs.