NN2Poly: A Polynomial Representation for Deep Feed-Forward Artificial Neural Networks.

Interpretability of neural networks (NNs) and their underlying theoretical behavior remain an open field of study even after the great success of their practical applications, particularly with the emergence of deep learning. In this work, NN2Poly is proposed: a theoretical approach to obtain an explicit polynomial model that provides an accurate representation of an already trained fully connected feed-forward artificial NN a multilayer perceptron (MLP). This approach extends a previous idea proposed in the literature, which was limited to single hidden layer networks, to work with arbitrarily deep MLPs in both regression and classification tasks. NN2Poly uses a Taylor expansion on the activation function, at each layer, and then applies several combinatorial properties to calculate the coefficients of the desired polynomials. Discussion is presented on the main computational challenges of this method, and the way to overcome them by imposing certain constraints during the training phase. Finally, simulation experiments as well as applications to real tabular datasets are presented to demonstrate the effectiveness of the proposed method.

Mind the gender gap: COVID-19 lockdown effects on gender differences in preprint submissions.

The gender gap is a well-known problem in academia and, despite its gradual narrowing, recent estimations indicate that it will persist for decades. Short-term descriptive studies suggest that this gap may have actually worsened during the months of confinement following the start of the COVID-19 pandemic in 2020. In this work, we evaluate the impact of the COVID-19 lockdown on female and male academics' research productivity using preprint drop-off data. We examine a total of 307,902 unique research articles deposited in 5 major preprint repositories during the period between January and May each year from 2017 to 2020. We find that the proportion of female authors in online repositories steadily increased over time; however, the trend reversed during the confinement and gender parity worsened in two respects. First, the proportion of male authors in preprints increased significantly during lockdown. Second, the proportion of male authors in COVID-19-related articles was significantly higher than that of women. Overall, our results imply that the gender gap in academia suffered an approximately 1-year setback during the strict lockdown months of 2020, and COVID-related research areas suffered an additional 1.5-year setback.

News or social media? Socio-economic divide of mobile service consumption.

Reliable and timely information on socio-economic status and divides is critical to social and economic research and policing. Novel data sources from mobile communication platforms have enabled new cost-effective approaches and models to investigate social disparity, but their lack of interpretability, accuracy or scale has limited their relevance to date. We investigate the divide in digital mobile service usage with a large dataset of 3.7 billion time-stamped and geo-referenced mobile traffic records in a major European country, and find profound geographical unevenness in mobile service usage-especially on news, e-mail, social media consumption and audio/video streaming. We relate such diversity with income, educational attainment and inequality, and reveal how low-income or low-education areas are more likely to engage in video streaming or social media and less in news consumption, information searching, e-mail or audio streaming. The digital usage gap is so large that we can accurately infer the socio-economic status of a small area or even its Gini coefficient only from aggregated data traffic. Our results make the case for an inexpensive, privacy-preserving, real-time and scalable way to understand the digital usage divide and, in turn, poverty, unemployment or economic growth in our societies through mobile phone data.

Towards a mathematical framework to inform neural network modelling via polynomial regression.

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing interest in the overlapping area between neural networks and more traditional statistical methods, which can help overcome those problems. In this article, a mathematical framework relating neural networks and polynomial regression is explored by building an explicit expression for the coefficients of a polynomial regression from the weights of a given neural network, using a Taylor expansion approach. This is achieved for single hidden layer neural networks in regression problems. The validity of the proposed method depends on different factors like the distribution of the synaptic potentials or the chosen activation function. The performance of this method is empirically tested via simulation of synthetic data generated from polynomials to train neural networks with different structures and hyperparameters, showing that almost identical predictions can be obtained when certain conditions are met. Lastly, when learning from polynomial generated data, the proposed method produces polynomials that approximate correctly the data locally.

Conductors' tempo choices shed light over Beethoven's metronome.

During most part of Western classical music history, tempo, the speed of music, was not specified, for it was considered obvious from musical context. Only in 1815, Maelzel patented the metronome. Beethoven immediately embraced it, so much as to add tempo marks to his already published eight symphonies. However, these marks are still under dispute, as many musicians consider them too quick to be played and even unmusical, whereas others claim them as Bethoven's supposedly written will. In this work, we develop a methodology to extract and analyze the performed tempi from 36 complete symphonic recordings by different conductors. Our results show that conductor tempo choices reveal a systematic deviation from Beethoven's marks, which highlights the salience of "correct tempo" as a perceptive phenomenon shaped by cultural context. The hasty nature of these marks could be explained by the metronome's ambiguous scale reading point, which Beethoven probably misinterpreted.