Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing.Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually performed in single-precision floating-point number format.The convergence of single-precision SGD is normally aligned with the theoretical results of real numbers since they exhibit negligible error.However, the numerical error increases when the computations are performed in low-precision number formats.This provides compelling reasons to study the SGD convergence adapted for low-precision computations.We present both deterministic and stochastic analysis of the SGD algorithm, obtaining bounds that show the effect of number format.Such bounds can provide guidelines as to how SGD convergence is affected when constraints render the possibility of performing high-precision computations remote.

In this paper, we speculate that abstract art can become an useful paradigm for both studying the relationship between neuroscience and art, and as a benchmark problem for the researches on Autonomous Machine Learning (AML) in brain-like computation. In particular, we are considering the case of some Kandinskij's oeuvres. There, it seems to see a deliberate willingness of introducing some effects today's hugely studied in the neuroscience, namely, for the retrieval of mental visual images or the neural correlates underlying visual tasks. The genial use of colours, geometry and vague forms generates very complex pictures that, we claim, excite preferentially mid-hierarchic levels of the bottom-up/top-down architecture of the brain, widely recognized as a possible framework for implementing AML. We introduce a quantitative metric for confirming the intuitive and psychological ranking of complexity given to paintings and pictures, the Artistic Complexity. The paintings of the artist are analysed, by selecting appropriately the oeuvres in order to point out different aspects of the topic. The concept of non-extensive Tsallis entropy is also introduced in an information-theoretic perspective, to cope with long-range interactions, as is done in spectral analysis of the human brain EEG. fMRI experimentations are sought to justify our speculations.

Despite their high specific stiffness and strength, carbon fiber reinforced polymers, stacked at different fiber orientations, are susceptible to interlaminar damages. They may occur in the form of micro-cracks and voids, and leads to a loss of performance. Within this framework, ultrasonic tests can be exploited in order to detect and classify the kind of defect. The main object of this work is to develop the evolution of a previous heuristic approach, based on the use of Support Vector Machines, proposed in order to recognize and classify the defect starting from the measured ultrasonic echoes. In this context, a real-time approach could be exploited to solve real industrial problems with enough accuracy and realistic computational efforts. Particularly, we discuss the cross wavelet transform and wavelet coherence for examining relationships in time-frequency domains between. For our aim, a software package has been developed, allowing users to perform the cross wavelet transform, the wavelet coherence and the Fuzzy Inference System. Since the ill-posedness of the inverse problem, Fuzzy Inference has been used to regularize the system, implementing a data-independent classifier. Obtained results assure good performances of the implemented classifier, with very interesting applications.