Donsker-Varadhan asymptotics for degenerate jump Markov processes

We consider a class of continuous time Markov chains on a compact metric space that admit an invariant measure strictly positive on open sets together with absorbing states. We prove the joint large deviation principle for the empirical measure and flow. Due to the lack of uniform ergodicity, the zero level set of the rate function is not a singleton. As corollaries, we obtain the Donsker-Varadhan rate function for the empirical measure and a variational expression of the rate function for the empirical flow

A gradient flow approach to linear Boltzmann equations

We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows

Large deviations for Kac-like walks

We introduce a Kac's type walk whose rate of binary collisions preserves the total momentum but not the kinetic energy. In the limit of large number of particles we describe the dynamics in terms of empirical measure and flow, proving the corresponding large deviation principle. The associated rate function has an explicit expression. As a byproduct of this analysis, we provide a gradient flow formulation of the Boltzmann-Kac equation

Composición florística y productividad primaria neta aérea de campos naturales sobre suelos profundos de basalto

Programa de Posgrad

Relating Implicit Bias and Adversarial Attacks through Intrinsic Dimension

Despite their impressive performance in classification, neural networks are known to be vulnerable to adversarial attacks. These attacks are small perturbations of the input data designed to fool the model. Naturally, a question arises regarding the potential connection between the architecture, settings, or properties of the model and the nature of the attack. In this work, we aim to shed light on this problem by focusing on the implicit bias of the neural network, which refers to its inherent inclination to favor specific patterns or outcomes. Specifically, we investigate one aspect of the implicit bias, which involves the essential Fourier frequencies required for accurate image classification. We conduct tests to assess the statistical relationship between these frequencies and those necessary for a successful attack. To delve into this relationship, we propose a new method that can uncover non-linear correlations between sets of coordinates, which, in our case, are the aforementioned frequencies. By exploiting the entanglement between intrinsic dimension and correlation, we provide empirical evidence that the network bias in Fourier space and the target frequencies of adversarial attacks are closely tied

Emergent representations in networks trained with the Forward-Forward algorithm

The Backpropagation algorithm, widely used to train neural networks, has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, and avoid to back-propagate gradients in favour of using local learning rules, the recently introduced Forward-Forward algorithm replaces the traditional forward and backward passes of Backpropagation with two forward passes. In this work, we show that internal representations obtained with the Forward-Forward algorithm organize into robust, category-specific ensembles, composed by an extremely low number of active units (high sparsity). This is remarkably similar to what is observed in cortical representations during sensory processing. While not found in models trained with standard Backpropagation, sparsity emerges also in networks optimized by Backpropagation, on the same training objective of Forward-Forward. These results suggest that the learning procedure proposed by Forward-Forward may be superior to Backpropagation in modelling learning in the cortex, even when a backward pass is used.Comment: 14 pages, 8 figure

Fostering academic interdisciplinarity : Italy's pioneering experiment on sustainability education in schools and universities

The world needs a systemic transformation from a social, economic and environmental point of view in order to deal with present and future challenges, which are crosscutting in nature. Education and research can become powerful drivers for this radical change, provided they can break free from narrow disciplinary approaches and cultivate the interconnectedness of knowledge. With a view to repurposing teaching and research toward an integrated approach, Italy has introduced a number of reforms, including a mandatory module for all schools and an interdisciplinary course for universities, largely modeled on the interdisciplinary concept of sustainability. Italy was the first country in the world to do so and the news had resonance throughout the globe, indicating a thirst for innovative methods in education and research. This article discusses the approach and the obstacles faced, with the aim of encouraging debate over its structure and contents and potentially replicating its implementation in other parts of the world.https://www.frontiersin.org/journals/sustainabilityam2022Political Science