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pro vyhledávání: '"Lucibello A"'
Autor:
Achilli, Beatrice, Ventura, Enrico, Silvestri, Gianluigi, Pham, Bao, Raya, Gabriel, Krotov, Dmitry, Lucibello, Carlo, Ambrogioni, Luca
Generative diffusion processes are state-of-the-art machine learning models deeply connected with fundamental concepts in statistical physics. Depending on the dataset size and the capacity of the network, their behavior is known to transition from a
Externí odkaz:
http://arxiv.org/abs/2410.08727
In this paper, we investigate the latent geometry of generative diffusion models under the manifold hypothesis. To this purpose, we analyze the spectrum of eigenvalues (and singular values) of the Jacobian of the score function, whose discontinuities
Externí odkaz:
http://arxiv.org/abs/2410.05898
Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and robust to addre
Externí odkaz:
http://arxiv.org/abs/2408.08319
Autor:
Kalaj, Silvio, Lauditi, Clarissa, Perugini, Gabriele, Lucibello, Carlo, Malatesta, Enrico M., Negri, Matteo
It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we reveal that
Externí odkaz:
http://arxiv.org/abs/2407.05658
We present InvMSAFold, a method for generating a diverse set of protein sequences that fold into a single structure. For a given structure, InvMSAFold defines a probability distribution over the space of sequences, capturing the amino acid covariance
Externí odkaz:
http://arxiv.org/abs/2406.11975
Autor:
Annesi, Brandon Livio, Lauditi, Clarissa, Lucibello, Carlo, Malatesta, Enrico M., Perugini, Gabriele, Pittorino, Fabrizio, Saglietti, Luca
Empirical studies on the landscape of neural networks have shown that low-energy configurations are often found in complex connected structures, where zero-energy paths between pairs of distant solutions can be constructed. Here we consider the spher
Externí odkaz:
http://arxiv.org/abs/2305.10623
Autor:
Lucibello, Carlo, Mézard, Marc
Publikováno v:
Phys. Rev. Lett. 132 (2024)
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another interesting
Externí odkaz:
http://arxiv.org/abs/2304.14964
Publikováno v:
Proceedings of IEEE Information Theory Workshop (ITW), pp. 323-328. IEEE, 2023
Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently, the algorit
Externí odkaz:
http://arxiv.org/abs/2304.12127
Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming data is gener
Externí odkaz:
http://arxiv.org/abs/2304.06636
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we propose and
Externí odkaz:
http://arxiv.org/abs/2303.16880