16 citations · 17 across the 6 of their papers we have counts for
7 papers
A differentiability framework for zigzag persistent homology via linear interpolation
Enrico Maria Ferrari, Clemens Bannwart, Matteo Biagetti
Persistent homology can be differentiated and incorporated into learning pipelines, but no analogous framework exists for zigzag persistence, which is needed when the underlying to…
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…
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…
Understanding and inverse design of implicit bias in stochastic learning: a geometric perspective
Nicola Aladrah, Emanuele Ballarin, Matteo Biagetti +3
Can we design a model such that its stochastic training favours a desired class of solutions without enforcing an explicit penalty? Under suitable conditions, the interplay between…
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…
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…
Cosmology with Persistent Homology: a Fisher Forecast
Jacky H. T. Yip, Matteo Biagetti, Alex Cole +2
Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool…