Pierfrancesco Beneventano


Hi, I'm Pier! I am a PhD student at Princeton University my interests lie in Machine Learning Theory and the mathematics to develop it. I'm fortunate to be advised by Prof. Boris Hanin and Prof. Jason D. Lee.


Previously, I got an MSc in math at ETH Zurich, where I worked with Prof. Arnulf Jentzen on high-dimensional functions approximation capabilities for Deep Neural Networks. I finished my BSc in math at Università di Pisa advised by Prof. Dario Andrea Bini. I have also spent time at Daedalean AG as a Machine Learning Research Intern.

  pierb at princeton dot edu  


            CV                        

Research

I am a mathematician working on the theory of machine learning. My work is motivated by the deployment of machine learning techniques in safety critical contexts. A theoretical understanding of deep learning is, in my opinion, key to assessing when its use is harmful and to what extent. So, my long term objective is to understand which machine learning model works in what setting, how well, and why. I work towards this goal by trying to develop theoretical guarantees for neural networks. Right now I'm investigating the implicit bias of SGD as I believe is crucial to comprehending the generalization guarantees of neural networks.

News

[Jan - May '22]    I'm the teaching assistant of Analysis of Big Data taught by Prof. Boris Hanin.
[15 Dec '21, 5pm UK]    I am chairing the event with Prof. Bin Yu, organized within the CEST-UCL Seminar series on responsible modelling.
[1 Dec '21, 5pm UK]    I will be a panelist at the event with Prof. Mary Morgan on the importance of the narrative in mathematical modelling. Organized within the CEST-UCL Seminar series on responsible modelling.
[3 Nov '21, 5pm UK]    I will be a panelist at the event with Prof. Cynthia Rudin on the relationship between the assumptions of a model and its interpretability. Organized within the CEST-UCL Seminar series on responsible modelling.
[Oct '21 - Apr '22]    With a group of friends at CEST I'm organizing series of seminars on "Responsible modelling in uncertain times: ethics of quantification in action" supported by INET and hosted by UCL IIPP. Please check out the website!
[Sep - Dec '21]    I'm the teaching assistant of Energy and Commodities Market taught by Prof. Ronnie Sircar.
[Jul '21']    I'm attending the Deep Learning Theory Summer School at Princeton organized by Prof. Boris Hanin.
[Jun '21']    With a group of friends at CEST I'm organizing a conference on "Forecasting the future for sustainable development: New Approaches to Modelling and the Science of Prediction" supported by INET and hosted by OECD. Please check out the website!
I will be chair for the session on Explainable and Interpretable ML" and I'm glad to announce that Prof. Cynthia Rudin will give us a keynote lecture on it. Moreover, AI Ethics - IBM will organize a workshop on XAI. We will have also many others amazing guests and interesting sessions, please check out!

Preprints
PontTuset
Deep neural network approximation theory for high-dimensional functions.
Pierfrancesco Beneventano, Prof. Patrick Cheridito, Robin Graeber, Prof. Arnulf Jentzen, and Benno Kuckuck.

We study the capacity of neural networks to approximate high-dimensional functions without suffering from the curse of dimensionality. We prove that they can, on any compact domain, for a vast and new class of functions.
PontTuset
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations.
Pierfrancesco Beneventano, Prof. Patrick Cheridito, Prof. Arnulf Jentzen, and Philippe von Wurstemberger.

We develop new machinery to study the capacity of neural networks to approximate high-dimensional functions without suffering from the curse of dimensionality. We prove that this is the case, for example, of a certain family of PDEs.

Teaching
Analysis of Big Data, Princeton University, Spring 2022.

Audience: Students from various bachelors.

Tasks: Teach the precepts, hold office hours, grade homeworks and exams.

Contents:This course is a theoretically oriented introduction to the statistical tools that underpin modern machine learning, whose hallmarks are large datasets and/or complex models. Topics include a rigorous analysis of dimensionality reduction, a survey of models ranging from regression to neural networks, and an analysis of learning algorithms.

Energy and Commodities Markets, Princeton University, Fall 2021.

Audience: Master in Finance and BSc in Operations Research and Financial Engineering.

Tasks: Teach the precepts, hold office hours, grade homeworks and exams (Python, Excel, and theory).

Contents: This course is an introduction to commodities markets (oil, gas, metals, electricity, etc.), and quantitative approaches to capturing uncertainties in their demand and supply. We start from a financial perspective, and traditional models of commodity spot prices and forward curves. Then we cover modern topics: game theoretic models of energy production (OPEC vs. fracking vs. renewables); quantifying the risk of intermittency of solar and wind output on the reliability of the electric grid (mitigating the duck curve); financialization of commodity markets; carbon emissions markets; cryptocurrencies as commodities. We also discuss economic and policy implications.

Numerical Methods for Partial Differential Equations, ETH Zurich, Spring 2020.

Audience: Master in Physics, Data Science, Computational Biology. Bachelor in Computational Science and Engineering.

Tasks: Teach the precepts and grade the homeworks (C++ and theory).

Contents: Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library.

Computational Methods for Engineering Applications, ETH Zurich, Fall 2019.
Audience: Bachelor in Mechanical Engineering.

Tasks: Teach the precepts and grade the homeworks (C++ and theory).

Contents: Introduction to the numerical methods for the solution of ordinary and partial differential equations that play a central role in engineering applications. Both basic theoretical concepts and implementation techniques necessary to understand and master the methods are addressed.








Last modified on January 20th 2022.

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