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Recent work suggests goal-driven training of neural networks can be used to model neural activity in the brain. While response properties of neurons in artificial neural networks bear similarities to those in the brain, the network…
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…
Neuroplasticity, the ability of the nervous system to adapt throughout an organism's lifespan, offers potential as both a biomarker and treatment target for neuropsychiatric conditions. Psychedelics, a burgeoning category of drugs, are…
Major depressive disorder (MDD) is a prevalent mental disorder associated with complex neurobiological changes that cannot be fully captured using a single imaging modality. The use of multimodal magnetic resonance imaging (MRI) provides a…
Event-based models (EBM) are a class of disease progression models that can be used to estimate temporal ordering of neuropathological changes from cross-sectional data. Current EBMs only handle scalar biomarkers, such as regional volumes,…
Computational models of neurodegeneration aim to emulate the evolving pattern of pathology in the brain during neurodegenerative disease, such as Alzheimer's disease. Previous studies have made specific choices on the mechanisms of…
Deep neural networks (DNNs) and, in particular, convolutional neural networks (CNNs) have brought significant advances in a wide range of modern computer application problems. However, the increasing availability of large amounts of…
Deep learning (DL) is rapidly advancing neuroimaging by achieving state-of-the-art performance with reduced computation times. Yet the numerical stability of DL models -- particularly during training -- remains underexplored. While…
Neural networks of the brain form one of the most complex systems we know. Many qualitative features of the emerging collective phenomena, such as correlated activity, stability, response to inputs, chaotic and regular behavior, can,…
Developmental Dyslexia (DD) is a learning disability related to the acquisition of reading skills that affects about 5% of the population. DD can have an enormous impact on the intellectual and personal development of affected children, so…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…
Continual Learning seeks to develop a model capable of incrementally assimilating new information while retaining prior knowledge. However, current research predominantly addresses a straightforward learning context, wherein all data…
Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
Neural field models are nonlinear integro-differential equations for the evolution of neuronal activity, and they are a prototypical large-scale, coarse-grained neuronal model in continuum cortices. Neural fields are often simulated…
Major depressive disorder (MDD) is a heterogeneous condition; multiple underlying neurobiological substrates could be associated with treatment response variability. Understanding the sources of this variability and predicting outcomes has…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…