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Methods of statistical physics for explaining neural networks performance
Get PDFIn this thesis we focus on understanding the impressive ability of neural networks to generalize on unseen data. When and why does this generalization occur, and how can it be predicted? We offer partial answers to these questions by analyzing the loss landscape of neural networks, drawing insights from the study of disordered systems.
The first chapter contains a study that addresses multiple phenomena in machine learning using a complexity measure of the function realized by a neural network. Specifically, we study how the generalization of a neural network evolves as we vary its size. We demonstrate that the location of the test error double descent of a network can be accurately predicted by studying the phase transitions of a new sensitivity metric for the neural networks that we call Boolean Mean Dimension (BMD). Focusing on a teacher-student setting for the random feature model, we derive a theoretical analysis based on the replica method that yields an interpretable expression for the BMD, in the high dimensional regime where the number of data points, the number of features, and the input size grow to infinity.
The second chapter delves into the relationship between the generalization capabilities of neural networks and the concept of flatness, which is evaluated through local entropy measures for different loss functions. Our goal is to enhance the understanding of how properties of the loss landscape connect with generalization.
We show that the generalization properties of a loss minimizer can be inferred by examining the empirical risk landscape around it. Specifically, we show that generalization correlates with the existence of clusters of near-minimal solutions nearby, which we refer to as flat minima. Conversely, isolated minimizers tend to overfit the model. Following this idea, we employ variants of gradient descent methods to train neural networks that specifically target these wide flat minima. We demonstrate that these algorithms improve generalization across different architectures, datasets, and loss functions.
In the third chapter we conduct a more precise study of the loss landscape in a simple model of shallow neural networks known as the perceptron problem. We analyze the Stochastic Localization (SL) algorithm, which employs a denoising diffusion process to sample from a known but intractable distribution. In our setting, the score function is provided by an oracle using Approximate Message Passing.
We consider different variants of non-convex perceptron problems: the negative spherical perceptron, the binary perceptron, and the binary perceptron with modified loss functions. We show that stochastic localization successfully samples solutions for any satisfiable parameter regime of the negative spherical perceptron and fails throughout an entire regime of parameters for the binary perceptron, but also that the latter issue can be overcome by adapting the loss function to target flat minima. Additionally, we provide numerical evidence for the uniformity of sampled solutions in case of the negative spherical perceptron.
Finally, the fourth chapter discusses the performance of the stochastic localization algorithm on sparse constraint satisfaction problems (CSPs). In particular, we focus on sampling solutions to linear equations over finite fields (k-XORSAT), Boolean formulas (k-SAT), and proper graph colorings (q-coloring). Previous works analyzing this sampling algorithm on CSPs rely on a certain contiguity assumption that does not hold in the entire replica-symmetric regime for the k-SAT problem. Instead, we propose a new population dynamics framework tailored to the localization process in order to analyze the limitations of stochastic localization beyond the contiguity regime. Lastly, we provide numerical evidence showing that stochastic localization achieves uniform sampling for the k-XORSAT problem
Efficiency in Firm Financing and Financial Markets
Get PDFEfficiency is a central tenet of classical finance theory, grounded in the assumption that agents act to eliminate profit opportunities. Real-world markets often deviate from these idealized predictions due to frictions. My dissertation examines such frictions from both corporate and investor perspectives, focusing on their origins, deviations from theoretical benchmarks, and broader impact on financial markets.
My first paper explores how information-free demand shocks affect stock prices. Under the efficient market hypothesis, stock prices reflect expected future cash flows discounted for systematic risk, implying nearly flat demand curves—meaning that non-informational demand shocks should not move prices. Yet, demonstrating this empirically requires isolating truly information-free shocks.
One prominent setting is the "index effect," where stocks added to or removed from major indices exhibit abnormal returns. If these changes contain no new fundamental information, they challenge the idea of flat demand curves and thus the efficient market hypothesis. However, as the magnitude of the index effect has declined over time despite growing passive investing flows, scholars have debated whether this reflects declining inefficiencies or information in index reconstitutions.
To address this, I propose a novel identification approach that shifts focus from the firms added or removed during reconstitution to those index members not directly involved in these events. Since the sizes of added and deleted firms generally differ, the portfolio weights of incumbent firms must adjust to keep the total at 100\%, requiring that passive index trackers alter their demand for incumbent stocks without any new information about them. Consequently, any abnormal returns on these stocks around reconstitution can be linked solely to passive demand shifts. By studying these information-free demand shifts on incumbents' prices, I can estimate what the abnormal returns would be for added and deleted stocks in the absence of an informational component. Comparing the realized abnormal returns on additions and deletions with these counterfactual scenarios enables me to isolate the role of information.
By estimating counterfactual abnormal returns for added and deleted stocks based on incumbent behavior, I isolate the informational component of the index effect. I find that post-2000, the index effect is largely driven by passive demand, with information playing a minor role. Specifically: (i) a simple demand-based counterfactual—accounting for time-varying elasticities—can replicate the average effect size and its decline over time; and (ii) the declining effect stems from increasingly flatter demand curves, not improved information efficiency. In contrast, pre-2000 effects were too large to be explained by passive demand alone, suggesting a stronger role for information in earlier periods.
My second paper, coauthored with Stefano Rossi and Lorenzo Bretscher, investigates how legal environments shape firms' financing strategies and creditors' responses. Using newly combined datasets, we reconstruct the debt structure of 10,136 firms across 51 countries. We find that debt ownership is most concentrated in civil law countries and most dispersed in common law countries.
In strong investor protection environments, firms borrow through both dispersed unsecured debt and concentrated secured bank lending. Where investor protection is weaker, firms respond by borrowing shorter-term and in USD-denominated debt. These patterns are most pronounced among small and medium-sized firms, while large firms tend to attract dispersed debt from international investors—effectively circumventing local institutional constraints. Our work illustrates how legal environments influence firm behavior and how creditors strategically structure ownership to manage the trade-off between strategic default and inefficient liquidation
Abuso del processo o «abuso tiranno»?
No full textLa nota mira a definire i limiti della pronuncia della Cass. SSUU n. 7299/2025, concentrandosi, in particolar modo, sulla smisurata estensione del concetto di interesse apprezzabile alla tutela frazionata; sull'indebito accostamento, in chiave sinonimica, dei medesimi o analoghi fatti costitutivi il cui accertamento separato si tradurrebbe in un inutile e ingiustificato dispendio dell’attività processuale; sull'incongruenza delle sanzioni nel caso di intervenuto giudicato della prima domanda frazionata proposta
Electoral Accountability for Illiberal Governments: Essays on Immigration, State-Sponsored Homophobia and Political Methodology
Get PDFFar-right parties have surged to power across democracies, but their electoral accountability remains poorly understood. Through a series of essays, this dissertation provides a comprehensive analysis of how voters respond to the policies and outcomes of far-right incumbents and how policy effects on different parties can be evaluated. The findings contribute to the literature on political behavior, illiberal and far-right politics, and political methodology.
In the first chapter, I empirically investigate to what extent performance in office affects support for the far right, and which voters hold them accountable. To answer these questions, I conducted a novel pre-registered survey experiment embedded in a representative survey of 2055 individuals in Italy. Respondents were randomly exposed to factual information about rising immigration or economic growth under the far-right government of Giorgia Meloni. I find that rising immigration erodes support towards the government, with an effect comparable to economic voting. The effect does not vary by partisanship, policy preferences, or issue salience, suggesting a broad-based valence reaction rather than a partisan or ideological one. These findings suggest that far-right governments are not insulated from electoral accountability, as immigration can influence voter support in a manner comparable to economic conditions.
In the second chapter, I study whether state-sponsored homophobia bolsters the support for the government. While a growing body of literature documents the increasing politicization of LGBTQ- and gender-related issues by illiberal elites, little is known about the electoral effects of these strategies. I address this important question by studying whether anti-LGBTQ mobilization pays off electorally for the initiating party. Empirically, I study the adoption of anti-LGBTQ resolutions in many Polish municipalities prior to the 2019 parliamentary election. Using a synthetic difference-in-differences design, I find that these resolutions significantly depressed turnout in affected municipalities, with opposition parties showing less mobilization capacity. By contrast, turnout for the incumbent Law and Justice Party increased substantially. Overall, this study's findings are relevant for understanding the electoral consequences of both elite-led mobilization against stigmatized and discriminated groups, and policies of subnational democratic backsliding.
In the third chapter, I address the methodological challenge of estimating causal effects on party vote shares by synthetic control methods. Synthetic control methods are widely used for causal inference in case studies and panel data settings, often applied to model counterfactuals for proportional outcomes. However, conventional synthetic control methods are designed for univariate outcomes, leading researchers to model counterfactuals for each proportion separately. This study introduces an extension to synthetic control methods to simultaneously handle multivariate outcomes in compositional data. The approach establishes constant control comparisons by using the same weights for each proportion, improving comparability while adhering to treatment constraints. Results from a simulation study and an empirical application of the method to the study from chapter 2 and another study on climate policy effects underscore the benefits of accounting for the interplay of proportional outcomes. This advancement extends the validity and reliability of synthetic control estimates to common outcomes in political science
Il fomento nel contesto italiano
No full textIl contributo, partendo da una disamina dottrinale sulla riflessione in materia di ruolo dello Stato nell’economia, affronta il problematico inserimento
della nozione di fomento, tipica degli ordinamenti di tradizione ispanica, nel contesto italiano. Sono quindi esaminate modalità e misure del fomento nell’ordinamento italiano, con alcune riflessioni finali a carattere comparatistico
Linking futures and options pricing in the natural gas market
Get PDFA robust model for natural gas prices should simultaneously capture the observed prices of both futures and options. While incorporating a seasonal factor in the convenience yield of the spot price effectively replicates forward curves, it proves insufficient for ac- curately modelling the options price surface. The latter is more sensitive to the volatility structure of the spot price process, which has a limited impact on futures pricing. In this paper, we analyse European natural gas spot, futures, and options prices throughout 2024 and propose a no-arbitrage model that integrates both a seasonal stochastic convenience yield and a local volatility factor. This framework enables a simultaneous and accurate fit of both forward curves and options prices
Le organizzazioni ibride come partner strategico per lo sviluppo della Pa
No full textIl capitolo inquadra le società in-house come società ibride, descrivendo sfide e opportunità di questa forma di gestione per sostenere la creazione di valore pubblico nei servizi di interesse generale
Methods and approaches in PA research on Italy
No full textThis chapter provides a comprehensive overview of the evolution of methods and approaches in Public Administration (PA) research on Italy. Drawing on a longitudinal database of 272 empirical articles published between 2000 and 2023 in major PA and Management journals, we systematically map the presence and evolution of qualitative and quantitative research perspectives. Utilizing bibliometric and thematic analyses, we identify and analyze five core research methods: single and multiple case studies, ethnographies, quantitative observational methods, survey methods, and experimental methods. Our findings reveal a balanced methodological pluralism with increasing sophistication in research design and analysis over time. We further discuss the diverse contributions of each method to different PA research topics, and the structure of collaborative networks on Italian PA
Random probability measures with fixed mean distributions
No full textLinear functionals, or means, of discrete random probability measures are a natural probabilistic object and the investigation of their properties have a long and rich history. They appear in several areas of mathematics, including statistics, combinatorics, special functions, excursions of stochastic processes and financial mathematics, among others. Most contributions have aimed at determining their distribution starting from a fully specified random probability. This work addresses the inverse problem: the identification of the base measure of a discrete random probability measure yielding a specific mean distribution. Available results concern only the Dirichlet case for specific choices of the concentration parameter. Here we address the problem in much greater generality and, besides considering new instances of Dirichlet processes, we cover the normalized stable process and the Pitman–Yor process. In addition to their theoretical interest, the results are of practical relevance to Bayesian nonparametric inference, where the law of a random probability measure acts as a prior distribution: often pre-experimental information is available about a finite-dimensional projection of the data generating distribution, such as the mean, rather than about an infinite-dimensional parameter. We further extend our findings to mixture models, ubiquitous in statistics and machine learning
Designing a green memorandum: central bankers, politicians, monetary policy, and macroprudential regulation
No full textIncorporating environmental aspects in monetary and macroprudential policies poses a series of questions in terms of central banks’ effectiveness, independence, neutrality, and legitimacy. Most analyses of
this matter rely on a purely economic approach, underestimating the trade-offs it entails and thus being
biased in favor of central banks’ interventions. We develop a political-economy setting based on a Walsh
contract, which can be interpreted as a memorandum that the government and central bank can implement. Through it, the former legitimizes, or pushes for, the intervention of the latter under the aegis of
an elected authority. This setting eliminates the bias, unveiling the trade-offs that could result: accounting
for and tackling climate risks could lead central banks to miss their policy targets, not necessarily making
“brown” firms greener, and result in welfare distortions. Yet, thanks to this memorandum, the possibility
of a green transition favored by the central bank is made possible. We conclude that central banks should
keep a cautious stance when deciding to enter the climate arena, and that different evaluations of these
risks can be interpreted as a reason why central banks around the world have adopted different degrees of
climate interventionis