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Explainability of machine learning models: A systematic review and a case study on BERT
No full textDespite AI and Neural Networks model had an overwhelming evolution during the past decade, their applications must be subject to strong constraints due to their extensive uses in everyday human life. Nowadays, the results provided by these models are always filtered by humans be- cause of the difficulty of relying on an unexplainable machine, that, provided the inputs, bakes out the outputs without revealing the recipe behind that. This thesis aims to investigate deeper the functioning of Neural models, trying to whiten these black-boxes. I will use state-of-the-art eXplainable Artificial Intelligence (XAI) libraries and maths analysis of the
algorithms behind these libraries, in an attempt to whiten the models and
make them readable from a human point of view. To comprehend and exploit what the interpretation of deep learning models can do, I carried out two example applications. The first example uses an advance natural language processing model to detect if a sentence is a fake news or not, then the SHapely Additive exPlaination library is employed in order to comprehend deeply the relations between the sentence and the label and in which extent the model is understanding the required task. With the second example, I present an analysis of a classification model using SHAP library in order to understand which pixels are the key points for a class activation. Moreover, I will try to employ SHAP values to create defences to different type of adversarial attacks. So through a theoretical and practical analysis of the interpretation algorithms with a cue for their alternative use to simple analysis, with this thesis I give a complete overview of the poten- tial of XAI and its need for use as an integrated part in the production of artificial intelligence models
La dualità di Pontryagin-van Kampen nella categoria dei gruppi abeliani localmente compatti
No full textL'obiettivo di questa tesi è presentare la dualità di Pontryagin-van Kampen
nel caso generale dei gruppi abeliani topologici localmente compatti con il
linguaggio più elegante e attuale della teoria delle categorie. Viene
dimostrato che la categoria dei gruppi abeliani localmente compatti è una
categoria quasi-abeliana e che in essa esiste un funtore controvariante che
ad ogni gruppo associa il suo gruppo dei caratteri e ad ogni morfismo
associa il suo morfismo trasposto. Tale funtore dà origine a una dualità di
categorie, detta dualità di Pontryagin-van Kampen. Si conclude poi con
alcune applicazioni significative, tra cui un teorema di struttura per i
gruppi abeliani localmente compatti
p-adic Modular Forms
No full textThe aim of this thesis is to study p-adic modular forms, which are, roughly
speaking, p-adic limits of classical modular forms. In particular, we give a
self-contained and detailed overview of Serre’s p-adic modular forms, the objects introduced in the foundational paper "Formes modulaires et fonctions zêta p-adiques", [18]. Additionally, a brief introduction to the work of Haruzo Hida on ∧-adic forms will be give
Il teorema di Riemann-Roch per curve algebriche proiettive
No full textIn questo lavoro si vuole studiare il Teorema di Riemann-Roch e la sua
dimostrazione nel contesto delle curve algebriche proiettive, oggetti fondamentali nello studio della geometria algebrica. Il teorema studia opportuni sottospazi dello spazio delle funzioni razionali su una curva fissata e dà una formula esplicita per il calcolo della dimensione di tali spazi
Programmazione della produzione e della qualità: un problema di controllo ottimo con parametri
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A rigorous derivation of the Bogoliubov-Gross-Pitaevskii equation for superfluids
Get PDFIn the present Thesis, a rigorous derivation of the Bogoliubov-Gross-Pitaevskii (BGP) equation, which completely describes the dynamics of the condensed phase of a boson fluid at zero temperature, is presented. The problem is dealt within the formalism of second quantization, with an external trapping potential working as a vessel, the well amplitude size ruling the large size limit of the system (at a fixed density).
To begin with, in the First Chapter, the minimal necessary scaling hypotheses are discussed and compared with both the theoretical and the experimental ones existing in the literature. This is relevant in a problem where the existence of an effective equation in the thermodynamic limit almost always requires to let some physical parameters characterizing the system (e.g. the range of the two body potential) to depend on the size of the latter.
Once determined the right scaling regime, one is left with a problem in dimensionless form where, essentially, the dynamics of the boson quantum field is proven to be close to that of a problem where the two-body potential is delta-like, multiplied by a coupling constant that is explicitly computed in terms of all the parametres of the system (such as number density, two-body interaction, and so on). On the other hand, the fundamental boson commutation rules satisfied by the rescaled quantum field are of the semi-classical form, with a commutator that vanishes in the large size limit.
At this stage, by analogy with what has been done for the finite version of the problem, i.e. for Bose-Hubbard models, in the Second Chapter we take the expectation of the quantum field on a coherent state distributed according to a quantum invariant Gaussian thermal measure. Such an expectation, or Wick symbol, defines the scalar field that satisfies the BGP equation in a suitable infrared limit.
Finally, the convergence of the time-dependent Wick symbol defined above to the solution of the scalar BGP equation, in measure norm, is proven; specifically, the bounding constant of the distance is found to be depending linearly on time. Further, it is shown that such constant goes to zero in the thermodynamic limit, thus ensuring the exact convergence to BGP scalar dynamics at zero temperature, though a condition needs to be satisfied by the trapping potential