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Sliding down the stairs: how correlated latent variables accelerate learning with neural networks

Neural networks extract features from data using stochastic gradient descent (SGD). In particular, higher-order input cumulants (HOCs) are crucial for their performance. However, extracting information from the p th cumulant of d -dimensional inputs is computationally hard: the number of samples required to recover a single direction from an order-p tensor (tensor PCA) using SGD grows as dp−1 , which is prohibitive for high-dimensional inputs. This result raises the question of how neura...

Emocy: Towards physiological signals-based stress detection

The prompt detection of stress can prevent long-term consequences on people's health, economy and society. In this work, we present EMoCy, a reproducible methodology and analysis pipeline for automatic and continuous stress detection based on physiological signals. By providing reproducible experiments and exploring more constrained settings with state-of-the-art accuracy, we set new benchmarks for future works on stress detection. Our study includes signal selection and preprocessing, featur...

Aspects of Toeplitz Determinants

We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego, Fisher-Hartwig asymptotics, and how a transition between them is related to the Painlevé V equation. Certain Toeplitz and Hankel determinants reduce, in certain double-scaling limits, to Fredholm determinants which appear in the theory of group representations, in random matrices, random permutations and ...

1ST-PRINCIPLES CALCULATION OF THE VIBRATIONAL PROPERTIES OF GAXAL1-XAS ALLOYS