Nowadays proper detection of cognitive impairment has become a challenge for the scientific community. Alzheimer's Disease (AD), the most common cause of dementia, has a high prevalence that is increasing at a fast pace towards epidemic level. In the not-so-distant future this fact could have a dramatic social and economic impact. In this scenario, an early and accurate diagnosis of AD could help to decrease its effects on patients, relatives and society. Over the last decades there have been useful advances not only in classic assessment techniques, but also in novel non-invasive screening methodologies. Among these methods, automatic analysis of speech -one of the first damaged skills in AD patients- is a natural and useful low cost tool for diagnosis. In this paper a non-linear multi-task approach based on automatic speech analysis is presented. Three tasks with different language complexity levels are analyzed, and promising results that encourage a deeper assessment are obtained. Automatic classification was carried out by using classic Multilayer Perceptron (MLP) and Deep Learning by means of Convolutional Neural Networks (CNN) (biologically-inspired variants of MLPs) over the tasks with classic linear features, perceptual features, Castiglioni fractal dimension and Multiscale Permutation Entropy. Finally, the most relevant features are selected by means of the non-parametric Mann-Whitney U-test.