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Despite their promise to facilitate new scientific discoveries, the opaqueness of neural networks presents a challenge in interpreting the logic behind their findings. Here, we use a eXplainable-AI (XAI) technique called $inception$ or…

Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the…

Over the past few years, an extensively studied phenomenon in training deep networks is the implicit bias of gradient descent towards parsimonious solutions. In this work, we investigate this phenomenon by narrowing our focus to deep linear…

Two major uncertainties, dataset bias and adversarial examples, prevail in state-of-the-art AI algorithms with deep neural networks. In this paper, we present an intuitive explanation for these issues as well as an interpretation of the…

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…

Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain…

Gradients play a pivotal role in neural networks explanation. The inherent high dimensionality and structural complexity of neural networks result in the original gradients containing a significant amount of noise. While several approaches…

Computing pseudospectra of non-normal matrices is essential for understanding the stability and transient behavior of dynamical systems. Such analysis is critical in applications including fluid dynamics, control systems, and differential…

Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not…

Schizophrenia is a chronic neuropsychiatric disorder that causes distinct structural alterations within the brain. We hypothesize that deep learning applied to a structural neuroimaging dataset could detect disease-related alteration and…

The ability of deep neural networks to generalise well even when they interpolate their training data has been explained using various "simplicity biases". These theories postulate that neural networks avoid overfitting by first learning…

The regularization and output consistency behavior of dropout and layer-wise pretraining for learning deep networks have been fairly well studied. However, our understanding of how the asymptotic convergence of backpropagation in deep…

Functional near-infrared spectroscopy (fNIRS) is a non-invasive technique for monitoring brain activity. To better understand the brain, researchers often use deep learning to address the classification challenges of fNIRS data. Our study…

Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…

Deep learning involves navigating a high-dimensional loss landscape over the neural network parameter space. Over the course of training, complex computational structures form and re-form inside the neural network, leading to shifts in…

Deep learning computer vision techniques have achieved many successes in recent years across numerous imaging domains. However, the application of deep learning to spectral data remains a complex task due to the need for augmentation…

In the field of medical image analysis, achieving high accuracy is not enough; ensuring well-calibrated predictions is also crucial. Confidence scores of a deep neural network play a pivotal role in explainability by providing insights into…

Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…