Neural networks have been shown to have astounding performance on a variety of different machine learning tasks and data sets, both for synthetic and real-world data.However, in spite of their widespread usage and implementation, the convergence and the training dynamics of neural networks are neither trivial, nor completely understood. This project regards investigating what some researchers refer to as the Spectral Bias of neural networks. Neural networks have been seen during training to initially fit to data of lower complexity rather than high. That is, the network learns features of the target that in the Fourier domain corresponds to lower frequencies first, before it learns features that correspond to high frequencies. In this thesis, a quantitative way of measuring this bias is proposed, and empirical experiments are able to show the prevalence of the spectral bias with respect to this measure. The experiments compare how different network parameters, architectures, and optimizers affect the network's ability to find high frequency content during training. Both tailored experiments with synthetic target functions, and real-world data are considered. The machine learning problems investigated in this report are low dimensional regression problems. The real-world problem is natural image regression, and is performed on the DIV2K data set used in the NTIRE challenge on Single Image Super Resolution (SISR). The proposed measure shows that there exists a spectral bias in this task as well, indicating that it does not only occur in simulated data and controlled experiments, but also in data from real-world applications. / Neurala nätverk har påvisats prestera utomordentligt på flertalet olika sorters maskininlärningsproblem och dataset. Trots dess utbredda användning och implementation är likväl inte dess konvergens och träningsbeteende varken triviala, eller fullt förstådda. Den här uppsatsen undersöker vad vissa forskare benämner spectral bias hos neurala nätverk. Neurala nätverk har observerats att först anpassa sig till data med låg komplexitet, före hög. Med andra ord, nätverken lär sig de egenskaper hos målfunktionen som motsvarar låga frekvenser i Fourierdomänen först, innan de anpassar sig till de som motsvarar höga frekvenser. I den här rapporten föreslås ett kvantitativt sätt att mäta spectral bias, och empiriska experiment visar förekomsten av fenomenet med avseende på måttet. Experimenten jämför hur olika nätverksarkitekturer och träningsalgoritmer påverkar nätverkets förmåga att lära sig högfrekventa komponenter under träning. Både syntetiska experiment med konstgjorda målfunktioner, och problem med data från verkliga tillämpningar undersöks. Problemuppställningen som behandlas är lågdimensionell regression, och det verkliga problemet är bildregression applicerat data från datasetet DIV2K som används i NTIREs tävling för Single Image Super Resolution.Det föreslagna måttet påvisar spectral bias även för detta dataset, vilket indikerar att det inte bara uppkommer i konstruerade problem, utan även är något som bör tas hänsyn till i tillämpade problem.

De nombreux tests de dépistage des troubles cognitifs légers ont été élaborés ces dernières années afin d'identifier des personnes plus à risque de développer une maladie neurodégénérative telle que la maladie d'Alzheimer. Plusieurs indices (sensibilité, spécificité, valeurs de prédiction et rapports de vraisemblance) permettent d'évaluer la performance et l'utilité d'un test en pratique. L'objectif de cette thèse était d'évaluer le degré de variation de la performance d'un outil de dépistage des troubles cognitifs légers et ses conséquences sur la prise de décision clinique. Nos résultats montrent une variation importante de la performance de l'outil étudié en fonction des caractéristiques démographiques des individus, de la nature et la sévérité du trouble cognitif La performance globale d'un test ne serait donc pas constante et exposerait à un risque de sous-estimer ou de surestimer la présence de troubles cognitifs dans certains sous-groupes de l'échantillon d'étude. La mesure de ce phénomène de variation (ou effet de spectre) devrait faire partie des étapes obligatoires de la validation d'un test de dépistage des troubles cognitifs. Elle implique l'analyse de grands échantillons permettant de rendre compte de la complexité de l'interprétation d'un test et son application au niveau pratique. L'utilisation de valeurs seuils ajustées selon l'âge et le niveau scolaire, est proposée afin d'améliorer la prise de décision clinique. Nous discutons également de l'intérêt d'utiliser le concept épidémiologique de dépistage dans la recherche et l'identification de troubles cognitifs et proposons le terme plus approprié de repérage qui ne préjuge pas de leur étiologie. / In recent years, numerous tests have been proposed to screen Mild Cognitive Impairment (MCI) in order to identify individuals who are at risk for developing a neurodegenerative pathology such as Alzheimer's disease. Severa! indices (sensitivity, specificity, predictive values and likelihood ratios) enable to assess the performance and the utility of a test in clinical practice. The main objective of this thesis was to determine the degree of variation of an MCI screening test performance and its impact on clinical decision. Our results showed that performance indices of the study test may vary depending on the demographic characteristics of the individuals, the type and the degree of cognitive impairment. They also highlight that the overall performance of a screening test is not fixed and may result in failure to identify cognitive impairment in true cases and misclassified non cases as cognitively impaired in some subgroups of the study sample. These findings support the perspective that this subgroup variation ( or spectrum effect) should routinely be taken into account to assess the quality of a cognitive screening test. One way to minimize the impact of this phenomena would be to focus the assessment on broad and well defined subgroups of patients. The use of adjusted eut-offs values could help clinicians to increase their level of certainty regarding whether a cognitive impairment is present. We also discuss the interest of using the epidemiological concept of screening in the identification of cognitive impairments and propose a more appropriate term of cognitive impairment detection without prejudging its aetiology