5 papers
TopoFisher: Learning Topological Summary Statistics by Maximizing Fisher Information
Matteo Biagetti, Mathieu Carrière, Francesco Conti +3
Persistence diagrams provide stable, interpretable summaries of geometric and topological structure and are useful for simulation-based inference when low-order statistics miss key…
Understanding and inverse design of implicit bias in stochastic learning: a geometric perspective
Nicola Aladrah, Emanuele Ballarin, Matteo Biagetti +3
A key challenge in machine learning is to explain how learning dynamics select among the many solutions that achieve identical loss values in overparameterized models - a phenomeno…
Zigzag Persistence of Neural Responses to Time-Varying Stimuli
Yuri Gardinazzi, Alessio Ansuini, Eugenio Piasini +2
We use topological data analysis to study neural population activity in the Sensorium 2023 dataset, which records responses from thousands of mouse visual cortex neurons to diverse…
Persistent Topological Features in Large Language Models
Yuri Gardinazzi, Karthik Viswanathan, Giada Panerai +3
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 frame…
The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models
Karthik Viswanathan, Yuri Gardinazzi, Giada Panerai +2
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 sys…