Chiara Cammarota

Spectral properties and phase diagrams of sparse antagonistic random matrices with diagonal disorder and Jacobian-like structure

Luca Giammanco, Pietro Valigi, Chiara Cammarota

Complex interacting systems are often modelled by random matrices whose spectral properties dictate stability. In sparse antagonistic matrices without diagonal disorder, low connectivity gives rise to a characteristic reentrance effect in the spectral boundary near the real axis, which disappears via a …

Discontinuous BBP transitions

Dario Bocchi, Giulio Biroli, Chiara Cammarota, Federico Ricci‐Tersenghi

The Baik-Ben Arous-Peche (BBP) transition sets fundamental limits for detecting low-rank structure in noisy high-dimensional data and underlies a wide range of spectral methods in many fields from physics to statistics and data sciences. In standard settings, this transition is continuous, implying …

Escape dynamics and implicit bias of one-pass SGD in overparameterized quadratic networks

Dario Bocchi, Theotime Regimbeau, Carlo Lucibello, Luca Saglietti et autres

We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher--student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples $M$ diverge at fixed ratio $α= M/N$, and …

Eigenvalue spectral tails and localisation properties of asymmetric networks

Pietro Valigi, Joseph W. Baron, Izaak Neri, Giulio Biroli et autres

Abstract In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis, called Lifshitz tails. In the case of asymmetric matrices, concise mathematical results have proved …

it, gb, fr (code pays fourni par la source)

Overparametrization bends the landscape: BBP transitions at initialization in simple Neural Networks

Brandon Livio Annesi, Dario Bocchi, Chiara Cammarota

High-dimensional non-convex loss landscapes play a central role in the theory of Machine Learning. Gaining insight into how these landscapes interact with gradient-based optimization methods, even in relatively simple models, can shed light on this enigmatic feature of neural networks. In this …

Optimal sequencing depth for measuring the concentrations of molecular barcodes

Tommaso Ocari, Emilia A. Zin, Muge Tekinsoy, Timothé Van Meter et autres

In combinatorial genetic engineering experiments, next-generation sequencing (NGS) allows for measuring the concentrations of barcoded or mutated genes within highly diverse libraries. When designing and interpreting these experiments, sequencing depths are thus important parameters to take into account. Service providers follow established …

fr, it, jp (code pays fourni par la source)

The role of the time-dependent Hessian in high-dimensional optimization

Tony Bonnaire, Giulio Biroli, Chiara Cammarota

Abstract Gradient descent is commonly used to find minima in rough landscapes, particularly in recent machine learning applications. However, a theoretical understanding of why good solutions are found remains elusive, especially in strongly non-convex and high-dimensional settings. Here, we focus on the …

fr, it (code pays fourni par la source)

Daydreaming Hopfield Networks and their surprising effectiveness on correlated data

Ludovica Serricchio, Dario Bocchi, Claudio Chilin, Raffaele Marino et autres

To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms). For this reason, …

it, es (code pays fourni par la source)

Optimal sequencing depth for measuring the concentrations of molecular barcodes

Tommaso Ocari, Emilia A. Zin, Muge Tekinsoy, Timothé Van Meter et autres

Abstract In combinatorial genetic engineering experiments, next-generation sequencing (NGS) allows for measuring the concentrations of barcoded or mutated genes within highly diverse libraries. When designing and interpreting these experiments, sequencing depths are thus important parameters to take into account. Service providers follow …

fr, it, jp (code pays fourni par la source)

Daydreaming Hopfield Networks and their surprising effectiveness on correlated data

Ludovica Serricchio, Dario Bocchi, Claudio Chilin, Raffaele Marino et autres

To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms). For this reason, …

The Role of the Time-Dependent Hessian in High-Dimensional Optimization

Tony Bonnaire, Giulio Biroli, Chiara Cammarota

Gradient descent is commonly used to find minima in rough landscapes, particularly in recent machine learning applications. However, a theoretical understanding of why good solutions are found remains elusive, especially in strongly non-convex and high-dimensional settings. Here, we focus on the phase …

Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems

Pietro Valigi, Izaak Neri, Chiara Cammarota

Abstract We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in …

it, gb (code pays fourni par la source)