Talks

In this talk, I will argue and practically illustrate that insights in quantum information, concretely coming from the tensor network representations of quantum many-body states, can help in devising better privacy-preserving machine learning algorithms. In the first part, I will show that standard neural networks are vulnerable to a type of privacy leak that involves global properties of the data used for training, thus being a priori resistant to standard protection mechanisms. In the second, I will show that tensor networks, when used as machine learning architectures, are invulnerable to this vulnerability. The proof of the resilience is based on the existence of canonical forms for such architectures. Given the growing expertise in training tensor networks and the recent interest in tensor-based reformulations of popular machine learning architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed when using machine learning on sensitive data.

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We explore the physical consequences of embedding Einstein gravity with negative cosmological constant in Conformal Gravity in four dimensions. In the bulk, the procedure is equivalent to Holographic Renormalization, as the Einstein-AdS action appears augmented by the correct boundary counterterms. In codimension-2, 4D Conformal Gravity induces a 2D conformal invariant, which leads to a renormalized area for minimal surfaces attached to the conformal boundary. For arbitrary surfaces, this proposal reproduces other energy functionals as Willmore Energy and Reduced Hawking Mass. In particular, this procedure provides a more geometric approach to the computation of Holographic Entanglement Entropy for CFTs dual to 4D Einstein gravity.

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Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using associative information: maximize expected utility. There is an ongoing debate around the origin of probabilities involved in such calculation. In this work, we will show how the probabilities for decision-making can be grounded in causal models by considering decision problems in which the available actions and consequences are causally connected. In this setting, actions are regarded as an intervention over a causal model. Then, we extend a previous causal decision-making result, which relies on a known causal model, to the case in which the causal mechanism that controls some environment is unknown to a rational decision-maker. In this way, action-outcome probabilities can be grounded in causal models in known and unknown cases. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which the players of a strategic game consider causal information.

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