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Attractor Geometry Determines the Identifiability Limits of System Discovery
Matteo Gallo, Fabio Anselmi, Paolo Lazzari
Symbolic discovery of governing equations from data is limited not only by algorithm design and data volume, but by the geometry of the attractor: what the long-run dynamics allow…
PAC--Bayes Bounds on Quotient Parameter Spaces: Geometry-induced Implicit-Bias Priors
Nicola Aladrah, Fabio Anselmi
Overparameterized models often have continuous parameter symmetries, so different parameters define the same predictor. We show that PAC--Bayesian analysis should be performed on t…
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…
Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations
Lorenzo Basile, Santiago Acevedo, Luca Bortolussi +2
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations o…
Frequency maps reveal the correlation between Adversarial Attacks and Implicit Bias
Lorenzo Basile, Nikos Karantzas, Alberto d'Onofrio +4
Despite their impressive performance in classification tasks, neural networks are known to be vulnerable to adversarial attacks, subtle perturbations of the input data designed to…