The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss functions, their behaviour in generically non-convex, high dimensional landscapes is poorly understood.In this work, we use dynamical mean field theory techniques to describe analytically the average dynamics of these methods in a prototypical non-convex model: the (spiked) matrix-tensor model. We derive a closed set of equations that describe the behaviour of heavy-ball momentum and Nesterov acceleration in the infinite dimensional limit. By numerical integration of these equations, we observe that these methods speed up the dynamics but do not improve the algorithmic threshold with respect to gradient descent in the spiked model.

Multi-objective reinforcement learning (MORL) is an excellent framework for multi-objective sequential decision-making. MORL employs a utility function to aggregate multiple objectives into one that expresses a user's preferences. However, MORL still misses two crucial theoretical analyses of the properties of utility functions: (1) a characterisation of the utility functions for which an associated optimal policy exists, and (2) a characterisation of the types of preferences that can be expressed as utility functions. As a result, we formally characterise the families of preferences and utility functions that MORL should focus on: those for which an optimal policy is guaranteed to exist. We expect our theoretical results to promote the development of novel MORL algorithms that exploit our theoretical findings.

The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss functions, their behaviour in generically non-convex, high dimensional landscapes is poorly understood.In this work, we use dynamical mean field theory techniques to describe analytically the average dynamics of these methods in a prototypical non-convex model: the (spiked) matrix-tensor model. We derive a closed set of equations that describe the behaviour of heavy-ball momentum and Nesterov acceleration in the infinite dimensional limit. By numerical integration of these equations, we observe that these methods speed up the dynamics but do not improve the algorithmic threshold with respect to gradient descent in the spiked model.

In recent years, the field of Natural Language Generation (NLG) has been boosted by the recent advances in deep learning technologies. Nonetheless, these new data-intensive methods introduce language-dependent disparities in NLG as the main training data sets are in English. Also, most neural NLG systems use decoder-only (causal) transformer language models, which work well for English, but were not designed with other languages in mind. In this work we depart from the hypothesis that they may introduce generation bias in target languages with less rigid word ordering, subject omission, or different attachment preferences for relative clauses, so that for these target languages other language generation strategies may be more desirable. This paper first compares causal and non-causal language modeling for English and Spanish, two languages with different grammatical structures and over 1.5 billion and 0.5 billion speakers, respectively. For this purpose, we define a novel metric of average causal and non-causal context-conditioned entropy of the grammatical category distribution for both languages as an information-theoretic a priori approach. The evaluation of natural text sources (such as training data) in both languages reveals lower average non-causal conditional entropy in Spanish and lower causal conditional entropy in English. According to this experiment, Spanish is more predictable than English given a non-causal context. Then, by applying a conditional relative entropy metric to text generation experiments, we obtain as insights that the best performance is respectively achieved with causal NLG in English, and with non-causal NLG in Spanish. These insights support further research in NLG in Spanish using bidirectional transformer language models.

Corona VIrus Disease abbreviated as COVID-19 is a novel virus which is initially identified in Wuhan of China in December of 2019 and now this deadly disease has spread all over the world. According to World Health Organization (WHO), a total of 3,124,905 people died from 2019 to 2021, April. In this case, many methods, AI base techniques, and machine learning algorithms have been researched and are being used to save people from this pandemic. The SARS-CoV and the 2019-nCoV, SARS-CoV-2 virus invade our bodies, causing some differences in the structure of cell proteins. Protein-protein interaction (PPI) is an essential process in our cells and plays a very important role in the development of medicines and gives ideas about the disease. In this study, we performed clustering on PPI networks generated from 92 genes of the Covi-19 dataset. We have used three graph-based clustering algorithms to give intuition to the analysis of clusters.

We study model feed forward networks as time series predictors in the stationary limit. The focus is on complex, yet non-chaotic, behavior. The main question we address is whether the asymptotic behavior is governed by the architecture, regardless the details of the weights . We find hierarchies among classes of architectures with respect to the attract or dimension of the long term sequence they are capable of generating; larger number of hidden units can generate higher dimensional attractors. In the case of a perceptron, we develop the stationary solution for general weights, and show that the flow is typically one dimensional.