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The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low-dimensional manifolds embedded in a high-dimensional Euclidean space. In this…
Deep learning has taken part in the competition since not long ago to learn and identify phase transitions in physical systems such as many body quantum systems, whose underlying lattice structures are generally regular as they're in…
Deep learning has led to significant advances in artificial intelligence, in part, by adopting strategies motivated by neurophysiology. However, it is unclear whether deep learning could occur in the real brain. Here, we show that a deep…
Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly…
This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…
Expressivity plays a fundamental role in evaluating deep neural networks, and it is closely related to understanding the limit of performance improvement. In this paper, we propose a three-pipeline training framework based on critical…
For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit…
Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…
Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing…
Deep neural networks can be effective means to automatically classify aerial images but is easy to overfit to the training data. It is critical for trained neural networks to be robust to variations that exist between training and test…
Deep learning models like Transformers and Convolutional Neural Networks (CNNs) have revolutionized various domains, but their parameter-intensive nature hampers deployment in resource-constrained settings. In this paper, we introduce a…
Deep Neural Networks (DNNs) rely on inherent fluctuations in their internal parameters (weights and biases) to effectively navigate the complex optimization landscape and achieve robust performance. While these fluctuations are recognized…
Artificial neural networks used for reinforcement learning are structurally rigid, meaning that each optimized parameter of the network is tied to its specific placement in the network structure. It also means that a network only works with…
Neural Networks are function approximators that have achieved state-of-the-art accuracy in numerous machine learning tasks. In spite of their great success in terms of accuracy, their large training time makes it difficult to use them for…
This paper proposes a technique for training a neural network by minimizing a surrogate loss that approximates the target evaluation metric, which may be non-differentiable. The surrogate is learned via a deep embedding where the Euclidean…
In this paper, we propose embedding sparsity into the structure of deep neural networks, where model parameters can be exactly zero during training with the stochastic gradient descent. Thus, it can learn the sparsified structure and the…
Artificial neural networks have gone through a recent rise in popularity, achieving state-of-the-art results in various fields, including image classification, speech recognition, and automated control. Both the performance and…
We propose a deep learning-based approach that integrates MRI sequence parameters to improve the accuracy and generalizability of quantitative image synthesis from clinical weighted MRI. Our physics-driven neural network embeds MRI sequence…