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Deep Neural Networks (DNN) and especially Convolutional Neural Networks (CNN) are a de-facto standard for the analysis of large volumes of signals and images. Yet, their development and underlying principles have been largely performed in…
The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key…
Deep neural networks (DNNs) may outperform human brains in complex tasks, but the lack of transparency in their decision-making processes makes us question whether we could fully trust DNNs with high stakes problems. As DNNs' operations…
Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural…
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over…
In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies…
Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…
Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…
This paper explores the intricate behavior of deep neural networks (DNNs) through the lens of neuron activation dynamics. We propose a probabilistic framework that can analyze models' neuron activation patterns as a stochastic process,…
Deep neural networks (DNNs) are typically optimized using various forms of mini-batch gradient descent algorithm. A major motivation for mini-batch gradient descent is that with a suitably chosen batch size, available computing resources…
The application of Deep Neural Networks (DNNs) to a broad variety of tasks demands methods for coping with the complex and opaque nature of these architectures. When a gold standard is available, performance assessment treats the DNN as a…
While deep neural networks (DNNs) have been increasingly applied to choice analysis showing high predictive power, it is unclear to what extent researchers can interpret economic information from DNNs. This paper demonstrates that DNNs can…
Deep neural networks (DNNs) have achieved unprecedented performance on a wide range of complex tasks, rapidly outpacing our understanding of the nature of their solutions. This has caused a recent surge of interest in methods for rendering…
In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the…
We scrutinize the structural and operational aspects of deep learning models, particularly focusing on the nuances of learnable parameters (weight) statistics, distribution, node interaction, and visualization. By establishing correlations…
Despite their unprecedented success, DNNs are notoriously fragile to small shifts in data distribution, demanding effective testing techniques that can assess their dependability. Despite recent advances in DNN testing, there is a lack of…
Understanding why deep neural networks (DNNs) fail to generalize to unseen samples remains a long-standing challenge. Existing studies mainly examine changes in externally observable factors such as data, representations, or outputs, yet…
Deep neural networks and brains both learn and share superficial similarities: processing nodes are likened to neurons and adjustable weights are likened to modifiable synapses. But can a unified theoretical framework be found to underlie…
Deep neural networks (DNNs) have recently achieved impressive success across a wide range of real-world vision and language processing tasks, spanning from image classification to many other downstream vision tasks, such as object…
This work investigates the generalization behavior of deep neural networks (DNNs), focusing on the phenomenon of "fooling examples," where DNNs confidently classify inputs that appear random or unstructured to humans. To explore this…