1,214 research outputs found
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 florÃstica 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
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