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Boltzmann Machines are probabilistic models developed in 1985 by D.H. Ackley, G.E. Hinton and T.J. Sejnowski. In 2006, Restricted Boltzmann Machines (RBMs) were used in the pre-training step of several successful deep learning models, leading to a new renaissance of neural networks and artificial intelligence. In spite of their nice mathematical formulation, there are a number of issues that are hard to compute: - The computation of the partition function is NP-hard, involving an exponential sum of terms - The exact computation of the derivative of the log-likelihood is also NP-hard, since it contains the derivative of the partition function Therefore, in practice we have to approximate both the computation of the probabilities and several components of the learning process itself. These drawbacks have prevented RBMs to show their real potential as truly probabilistic models. Currently, we are working on trying to improve several of the unsolved issues related to RBMs: - Mechanisms to control the learning process www.lsi.upc.edu/%7Eeromero/Publications/Downloads/2018-tnnls-stopcritRBM.pdf - Better approximations of the derivative of the log-likelihood http://www.lsi.upc.edu/%7Eeromero/Publications/Downloads/2019-nn-weightedCD.pdf - Efficient approximation of the partition function (work in progress) These works have opened new lines of research, some of which can be the topic of a Master's Thesis. The scope and degree of depth of the work can be adapted to the estimated times to complete the Thesis. For further details, contact Enrique Romero ( ).

We propose to a student or multiple students to work on processing techniques using Deep Learning (Convolutional Neural networks, Generative Adversarial Networks, Semantic Segmentation Networks) to detect and classify marine mammals in photographs and satellite imagery. The computational capacity offered by these new tools will allow the scientific community to better study endangered species and to give an adequate and rapid response to face the current biodiversity crisis.

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