Research

Research Interests

My research interests include deep learning, high-dimensional probability, and trustworthy machine learning. I study the behavior of over-parameterized models trained on high-dimensional data, including implications for privacy and robustness.

Publications and Preprints

You can also find my publications on Google Scholar.

2025

• A Law of Data Reconstruction for Random Features (and Beyond)
  Leonardo Iurada, Simone Bombari, Tatiana Tommasi, Marco Mondelli.
  arXiv, 2025.

• Better Rates for Private Linear Regression in the Proportional Regime via Aggressive Clipping
  Simone Bombari, Inbar Seroussi, Marco Mondelli.
  arXiv, 2025.

• Spurious Correlations in High Dimensional Regression: The Roles of Regularization, Simplicity Bias and Over-Parameterization
  Simone Bombari, Marco Mondelli.
  ICML - best paper award at SCSL workshop at ICLR, 2025.

• Privacy for Free in the Overparameterized Regime
  Simone Bombari, Marco Mondelli.
  PNAS - contributed talk at DeepMath, 2025.

2024

• DP-KAN: Differentially Private Kolmogorov-Arnold Networks
  Nikita P. Kalinin, Simone Bombari, Hossein Zakerinia, Christoph H. Lampert.
  arXiv, 2024.

• Towards Understanding the Word Sensitivity of Attention Layers: A Study via Random Features
  Simone Bombari, Marco Mondelli.
  ICML, 2024.

• How Spurious Features Are Memorized: Precise Analysis for Random and NTK Features
  Simone Bombari, Marco Mondelli.
  ICML, 2024.

2023

• Beyond the Universal Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernels
  Simone Bombari, Shayan Kiyani, Marco Mondelli.
  ICML - selected for oral presentation, 2023.

2022

• Towards Differential Relational Privacy and its use in Question Answering
  Simone Bombari, Alessandro Achille, Zijian Wang, Yu-Xiang Wang, Yusheng Xie, Kunwar Yashraj Singh, Srikar Appalaraju, Vijay Mahadevan, Stefano Soatto.
  arXiv, 2022.

• Sharp asymptotics on the compression of two-layer neural networks
  Mohammad Hossein Amani, Simone Bombari, Marco Mondelli, Rattana Pukdee, Stefano Rini.
  Information Theory Workshop, 2022.

• Memorization and Optimization in Deep Neural Networks with Minimum Over-parameterization
  Simone Bombari, Mohammad Hossein Amani, Marco Mondelli.
  NeurIPS - contributed talk at DeepMath, 2022.

Download the bibliography (BibTeX)