publications

2025

1. ICML

   Persistent Topological Features in Large Language Models

   Yuri Gardinazzi, Karthik Viswanathan, Giada Panerai, and 3 more authors

   In International Conference of Machine Learning, 2025

   Abs Bib PDF Code Poster

   Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework—zigzag persistence from topological data analysis —with practical and easily applicable algorithms. Zigzag persistence is particularly effective for characterizing data as it dynamically transforms across model layers. Within this framework, we introduce topological descriptors that measure how topological features, p-dimensional holes, persist and evolve throughout the layers. Unlike methods that assess each layer individually and then aggregate the results, our approach directly tracks the full evolutionary path of these features. This offers a statistical perspective on how prompts are rearranged and their relative positions changed in the representation space, providing insights into the system’s operation as an integrated whole. To demonstrate the expressivity and applicability of our framework, we highlight how sensitive these descriptors are to different models and a variety of datasets. As a showcase application to a downstream task, we use zigzag persistence to establish a criterion for layer pruning, achieving results comparable to state-of-the-art methods while preserving the system-level perspective.

   @inproceedings{gardinazzi2025persistent,
     title = {Persistent Topological Features in Large Language Models},
     author = {Gardinazzi, Yuri and Viswanathan, Karthik and Panerai, Giada and Ansuini, Alessio and Cazzaniga, Alberto and Biagetti, Matteo},
     booktitle = {International Conference of Machine Learning},
     year = {2025},
   }

2. arXiv

   The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models

   Karthik Viswanathan, Yuri Gardinazzi, Giada Panerai, and 2 more authors

   arXiv preprint arXiv:2501.10573, 2025

   Abs Bib PDF Code

   We study the geometry of token representations at the prompt level in large language models through the lens of intrinsic dimension. Viewing transformers as mean-field particle systems, we estimate the intrinsic dimension of the empirical measure at each layer and demonstrate that it correlates with next-token uncertainty. Across models and intrinsic dimension estimators, we find that intrinsic dimension peaks in early to middle layers and increases under syntactic and semantic disruption (by shuffling tokens), and that it is strongly correlated with average surprisal, with a simple analysis linking logits geometry to entropy via softmax. As a case study in practical interpretability and safety, we train a linear probe on the per-layer intrinsic dimension profile to distinguish malicious from benign prompts before generation. This probe achieves accuracy of 90 to 95% in different datasets, outperforming widely used guardrails such as Llama Guard and Shield Gemma. We further compare against linear probes built from layerwise entropy derived via the Tuned Lens and find that the intrinsic dimension-based probe is competitive and complementary, offering a compact, interpretable signal distributed across layers. Our findings suggest that prompt-level geometry provides actionable signals for monitoring and controlling LLM behavior, and offers a bridge between mechanistic insights and practical safety tools.

   @article{viswanathan2025intrinsic,
     title = {The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models},
     author = {Viswanathan, Karthik and Gardinazzi, Yuri and Panerai, Giada and Cazzaniga, Alberto and Biagetti, Matteo},
     journal = {arXiv preprint arXiv:2501.10573},
     year = {2025},
   }

3. Geometry, Topology and Mechanistic Interpretability of Large Scale AI Models

   Alessio Ansuini, Lorenzo Basile, Federica Bazzocchi, and 8 more authors

   2025

2024

1. Range of validity of perturbative models for galaxy clustering and its uncertainty

   Giosuè Gambardella, Matteo Biagetti, Chiara Moretti, and 1 more author

   Physical Review D, 2024
2. Euclid preparation-XLI. Galaxy power spectrum modelling in real space

   Andrea Pezzotta, Chiara Moretti, Matteo Zennaro, and 8 more authors

   Astronomy & Astrophysics, 2024
3. Cosmology with persistent homology: a Fisher forecast

   Jacky HT Yip, Matteo Biagetti, Alex Cole, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2024

2023

1. Primordial non-Gaussianity and non-Gaussian covariance

   Thomas Flöss, Matteo Biagetti, and P Daniel Meerburg

   Physical Review D, 2023
2. High-redshift JWST observations and primordial non-Gaussianity

   Matteo Biagetti, Gabriele Franciolini, and Antonio Riotto

   The Astrophysical Journal, 2023
3. Euclid: modelling massive neutrinos in cosmology—a code comparison

   Julian Adamek, Raul E Angulo, H Kurki-Suonio, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2023

2022

1. The reach of next-to-leading-order perturbation theory for the matter bispectrum

   Davit Alkhanishvili, Cristiano Porciani, Emiliano Sefusatti, and 4 more authors

   Monthly Notices of the Royal Astronomical Society, 2022
2. The covariance of squeezed bispectrum configurations

   Matteo Biagetti, Lina Castiblanco, Jorge Noreña, and 1 more author

   Journal of Cosmology and Astroparticle Physics, 2022
3. Bispectrum-window convolution via Hankel transform

   Kevin Pardede, Federico Rizzo, Matteo Biagetti, and 3 more authors

   Journal of Cosmology and Astroparticle Physics, 2022
4. Inflation: theory and observations

   Ana Achúcarro, Matteo Biagetti, Matteo Braglia, and 8 more authors

   arXiv preprint arXiv:2203.08128, 2022
5. Fisher forecasts for primordial non-Gaussianity from persistent homology

   Matteo Biagetti, Juan Calles, Lina Castiblanco, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2022
6. arXiv: Inflation: Theory and Observations

   Ana Achúcarro, Gonzalo A Palma, Benjamin D Wandelt, and 8 more authors

   2022
7. Fitting covariance matrix models to simulations

   Alessandra Fumagalli, Matteo Biagetti, Alex Saro, and 4 more authors

   Journal of Cosmology and Astroparticle Physics, 2022
8. A Model for the Squeezed Bispectrum in the Non-Linear Regime

   Matteo Biagetti, Juan Calles, Lina Castiblanco, and 2 more authors

   arXiv preprint arXiv:2212.11940, 2022

2021

1. The persistence of large scale structures. Part I. Primordial non-Gaussianity

   Matteo Biagetti, Alex Cole, and Gary Shiu

   Journal of Cosmology and Astroparticle Physics, 2021
2. Primordial non-Gaussianity from biased tracers: likelihood analysis of real-space power spectrum and bispectrum

   Azadeh Moradinezhad Dizgah, Matteo Biagetti, Emiliano Sefusatti, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2021
3. The formation probability of primordial black holes

   Matteo Biagetti, Valerio De Luca, Gabriele Franciolini, and 2 more authors

   Physics Letters B, 2021
4. PHL: Persistent_Homology_LSS

   Matteo Biagetti and Alex Cole

   Astrophysics Source Code Library, 2021

2020

1. Measurement of void bias using separate universe simulations

   Kwan Chuen Chan, Yin Li, Matteo Biagetti, and 1 more author

   The Astrophysical Journal, 2020
2. Primordial gravitational waves from galaxy intrinsic alignments

   Matteo Biagetti and Giorgio Orlando

   Journal of Cosmology and Astroparticle Physics, 2020
3. Topological echoes of primordial physics in the universe at large scales

   Alex Cole, Matteo Biagetti, and Gary Shiu

   arXiv preprint arXiv:2012.03616, 2020
4. Inflation and Dark Energy from spectroscopy at $\backslashmathcal {z}> 2$

   Simone Ferraro, Michael J Wilson, Muntazir Abidi, and 8 more authors

   Bulletin of the American Astronomical Society, 2020

2019

1. Inflation and Dark Energy from spectroscopy at z> 2

   Simone Ferraro, Michael J Wilson, Muntazir Abidi, and 8 more authors

   arXiv preprint arXiv:1903.09208, 2019
2. Primordial features from linear to nonlinear scales

   Florian Beutler, Matteo Biagetti, Daniel Green, and 2 more authors

   Physical Review Research, 2019
3. The hunt for primordial interactions in the large-scale structures of the Universe

   Matteo Biagetti

   Galaxies, 2019
4. Constraint of void bias on primordial non-Gaussianity

   Kwan Chuen Chan, Nico Hamaus, and Matteo Biagetti

   Physical Review D, 2019
5. Primordial non-gaussianity

   P Daniel Meerburg, Daniel Green, Muntazir Abidi, and 8 more authors

   arXiv preprint arXiv:1903.04409, 2019
6. Primordial Non-Gaussianity

   P Daniel Meerburg, D Green, M Abidi, and 8 more authors

   2019

2018

1. Abundance of peaks and dips in 3D mass and halo density fields: a test for cosmology

   Adi Nusser, Matteo Biagetti, and Vincent Desjacques

   Monthly Notices of the Royal Astronomical Society, 2018
2. Primordial black holes from inflation and quantum diffusion

   Matteo Biagetti, Gabriele Franciolini, Alex Kehagias, and 1 more author

   Journal of Cosmology and Astroparticle Physics, 2018

2017

1. Verifying the consistency relation for the scale-dependent bias from local primordial non-Gaussianity

   Matteo Biagetti, Titouan Lazeyras, Tobias Baldauf, and 2 more authors

   Monthly Notices of the Royal Astronomical Society, 2017
2. Possible signatures of the inflationary particle content: spin-2 fields

   Matteo Biagetti, Emanuela Dimastrogiovanni, and Matteo Fasiello

   Journal of Cosmology and Astroparticle Physics, 2017

2016

1. Squeezing the halo bispectrum: a test of bias models

   Azadeh Moradinezhad Dizgah, Kwan Chuen Chan, Jorge Norena, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2016
2. The halo Boltzmann equation

   Matteo Biagetti, Vincent Desjacques, Alex Kehagias, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2016
3. Theoretical aspects of large scale clustering of dark matter halos

   Matteo Biagetti

   éditeur non identifié, 2016

2015

1. Gravitational waves and scalar perturbations from spectator fields

   Matteo Biagetti, Emanuela Dimastrogiovanni, Matteo Fasiello, and 1 more author

   Journal of Cosmology and Astroparticle Physics, 2015
2. What we can learn from the running of the spectral index if no tensors are detected in the cosmic microwave background anisotropy

   Matteo Biagetti, Alex Kehagias, and Antonio Riotto

   Physical Review D, 2015
3. Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier

   Matteo Biagetti and Vincent Desjacques

   Monthly Notices of the Royal Astronomical Society, 2015

2014

1. Non-local halo bias with and without massive neutrinos

   Matteo Biagetti, Vincent Desjacques, Alex Kehagias, and 1 more author

   arXiv preprint arXiv:1405.1435, 2014
2. Measuring non-local Lagrangian peak bias

   Matteo Biagetti, Kwan Chuen Chan, Vincent Desjacques, and 1 more author

   Monthly Notices of the Royal Astronomical Society, 2014
3. On the halo velocity bias

   Matteo Biagetti, Vincent Desjacques, Alex Kehagias, and 1 more author

   arXiv preprint arXiv:1408.0293, 2014
4. Ultraviolet background fluctuations with clustered sources

   Vincent Desjacques, Azadeh Moradinezhad Dizgah, and Matteo Biagetti

   Monthly Notices of the Royal Astronomical Society, 2014

2013

1. Testing the running of non-Gaussianity through the CMB μ-distortion and the halo bias

   Matteo Biagetti, Hideki Perrier, Antonio Riotto, and 1 more author

   Physical Review D—Particles, Fields, Gravitation, and Cosmology, 2013
2. Enhancing inflationary tensor modes through spectator fields

   Matteo Biagetti, Matteo Fasiello, and Antonio Riotto

   arXiv preprint arXiv:1305.7241, 2013
3. Testing multifield inflation with halo bias

   Matteo Biagetti, Vincent Desjacques, and Antonio Riotto

   Monthly Notices of the Royal Astronomical Society, 2013
4. Symmetries of vector perturbations during the de Sitter epoch

   Matteo Biagetti, Alex Kehagias, Enrico Morgante, and 2 more authors

   Journal of Cosmology and Astroparticle Physics, 2013