Giuseppe Bruno

Giuseppe Bruno, Federico Pasqualotto, Andrea Agazzi

We model the evolution of tokens within a deep stack of Transformer layers as a continuous-time flow on the unit sphere, governed by a mean-field interacting particle system, building on the framework introduced in (Geshkovski et al., 2023). Studying the corresponding mean-field Partial Differential Equation (PDE), which can be interpreted as a Wasserstein gradient flow, in this paper we provide a mathematical investigation of the long-term behavior of this system, with a particular focus on the emergence and persistence of meta-stable phases and clustering phenomena, key elements in applications like next-token prediction. More specifically, we perform a perturbative analysis of the mean-field PDE around the iid uniform initialization and prove that, in the limit of large number of tokens, the model remains close to a meta-stable manifold of solutions with a given structure (e.g., periodicity). Further, the structure characterizing the meta-stable manifold is explicitly identified, as a function of the inverse temperature parameter of the model, by the index maximizing a certain rescaling of Gegenbauer polynomials.

Giuseppe Bruno, Federico Pasqualotto, Andrea Agazzi

In this paper, we study the evolution of tokens through the depth of encoder-only transformer models at inference time by modeling them as a system of particles interacting in a mean-field way and studying the corresponding dynamics. More specifically, we consider this problem in the moderate interaction regime, where the number $N$ of tokens is large and the inverse temperature parameter $β$ of the model scales together with $N$. In this regime, the dynamics of the system displays a multiscale behavior: a fast phase, where the token empirical measure collapses on a low-dimensional space, an intermediate phase, where the measure further collapses into clusters, and a slow one, where such clusters sequentially merge into a single one. We provide a rigorous characterization of the limiting dynamics in each of these phases and prove convergence in the above mentioned limit, exemplifying our results with some simulations.

I. Bailo, F. Buonora, G. Ciarfaglia et al.

The energy transition is a key theme of the last decades to determine a future of eco-sustainability, and an area of such importance cannot disregard digitization, innovation and the new technological tools available. This is the context in which the Generative Artificial Intelligence models described in this paper are positioned, developed by Engineering Ingegneria Informatica SpA in order to automate the plant structures acquisition of SNAM energy infrastructure, a leading gas transportation company in Italy and Europe. The digitization of a gas plant consists in registering all its relevant information through the interpretation of the related documentation. The aim of this work is therefore to design an effective solution based on Artificial Intelligence techniques to automate the extraction of the information necessary for the digitization of a plant, in order to streamline the daily work of MGM users. The solution received the P&ID of the plant as input, each one in pdf format, and uses OCR, Vision LLM, Object Detection, Relational Reasoning and optimization algorithms to return an output consisting of two sets of information: a structured overview of the relevant design data and the hierarchical framework of the plant. To achieve convincing results, we extend a state-of-the-art model for Scene Graph Generation introducing a brand new Transformer architecture with the aim of deepening the analysis of the complex relations between the plant's components. The synergistic use of the listed AI-based technologies allowed to overcome many obstacles arising from the high variety of data, due to the lack of standardization. An accuracy of 91\% has been achieved in the extraction of textual information relating to design data. Regarding the plants topology, 93\% of components are correctly identified and the hierarchical structure is extracted with an accuracy around 80\%.