Related papers: Deep Hamiltonian networks based on symplectic inte…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

Spatiotemporal time series forecasting plays a key role in a wide range of real-world applications. While significant progress has been made in this area, fully capturing and leveraging spatiotemporal heterogeneity remains a fundamental…

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with…

Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed…

We focus on semiparametric regression that has played a central role in statistics, and exploit the powerful learning ability of deep neural networks (DNNs) while enabling statistical inference on parameters of interest that offers…

Neural networks trained on biased datasets tend to inadvertently learn spurious correlations, hindering generalization. We formally prove that (1) samples that exhibit spurious correlations lie on a lower rank manifold relative to the ones…

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according to the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…

Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…

We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…

The variety and complexity of relations in multimedia data lead to Heterogeneous Information Networks (HINs). Capturing the semantics from such networks requires approaches capable of utilizing the full richness of the HINs. Existing…

Current robotic manipulators require fast and efficient motion-planning algorithms to operate in cluttered environments. State-of-the-art sampling-based motion planners struggle to scale to high-dimensional configuration spaces and are…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being…

Real-world datasets are often highly class-imbalanced, which can adversely impact the performance of deep learning models. The majority of research on training neural networks under class imbalance has focused on specialized loss functions,…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…

Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this…

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a new technique based on the…