**Coupled U-Net (CU-Net)**

We design a new connectivity pattern for the U-Net architecture. Given several stacked U-Nets, we couple each U-Net pair through the connections of their semantic blocks, resulting in the coupled U-Nets (CU-Net). The coupling connections could make the information flow more efficiently across U-Nets. The feature reuse across U-Nets makes each U-Net very parameter efficient. We evaluate the coupled U-Nets on two benchmark datasets of human pose estimation. Both the accuracy and model parameter number are compared. The CU-Net obtains comparable accuracy as state-of-the-art methods. However, it only has at least 60% fewer parameters than other approaches. … **LYRICS**

In spite of the amazing results obtained by deep learning in many applications, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference. Therefore, there is a clear need for the definition of a general and tight integration between low-level tasks, processing sensorial data that can be effectively elaborated using deep learning techniques, and the logic reasoning that allows humans to take decisions in complex environments. This paper presents LYRICS, a generic interface layer for AI, which is implemented in TersorFlow (TF). LYRICS provides an input language that allows to define arbitrary First Order Logic (FOL) background knowledge. The predicates and functions of the FOL knowledge can be bound to any TF computational graph, and the formulas are converted into a set of real-valued constraints, which participate to the overall optimization problem. This allows to learn the weights of the learners, under the constraints imposed by the prior knowledge. The framework is extremely general as it imposes no restrictions in terms of which models or knowledge can be integrated. In this paper, we show the generality of the approach showing some use cases of the presented language, including generative models, logic reasoning, model checking and supervised learning. … **Semantics**

The investigation of interpretations of a logical calculus (a formal axiomatic theory), of the study of the sense and meaning of constructions in formal language theory, and of the methods of understanding its logical connectives and formulas. Semantics studies the precise description and definition of such concepts as ‘truth’ , ‘definability’ , ‘denotation’ , at least in the context of a formal language. In a slightly narrower sense, by the semantics of a formalized language one means a system of agreements that determine the understanding of the formulas of the language, and that define the conditions for these formulas to be true. The semantics of logical connectives in classical and intuitionistic logic has an extensional nature: that is, the truth of a complex statement is determined only by the truth character of the expressions that form it. In other classical logics – for example, relevance logics – the meaningful content of concepts can be taken into account (such logics are called intensional). E.g., in logics of this kind not all true expressions are necessarily equivalent. … **Sparse Tensor Additive Regression (STAR)**

Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising. …

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Feb 2022

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