Related papers: Connection and Dispersion of Computation
A grand challenge in representation learning is to learn the different explanatory factors of variation behind the high dimen- sional data. Encoder models are often determined to optimize performance on training data when the real objective…
Graph neural networks (GNNs) have achieved remarkable advances in graph-oriented tasks. However, real-world graphs invariably contain a certain proportion of heterophilous nodes, challenging the homophily assumption of traditional GNNs and…
Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed…
In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…
The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…
The eigenvalue distribution of the Hessian matrix plays a crucial role in understanding the optimization landscape of deep neural networks. Prior work has attributed the well-documented ``bulk-and-spike'' spectral structure, where a few…
A comparison between neural network clustering (NNC), hierarchical clustering (HC) and K-means clustering (KMC) is performed to evaluate the computational superiority of these three machine learning (ML) techniques for organizing large…
We consider the problem of PAC-learning from distributed data and analyze fundamental communication complexity questions involved. We provide general upper and lower bounds on the amount of communication needed to learn well, showing that…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…
This paper proposes a fundamental answer to a frequently asked question in multimedia computing and machine learning: Do artifacts from perceptual compression contribute to error in the machine learning process and if so, how much? Our…
Let $\mathbf{Y}$ be the solution space of an $n$-layer cellular neural network, and let $\mathbf{Y}^{(i)}$ and $\mathbf{Y}^{(j)}$ be the hidden spaces, where $1 \leq i, j \leq n$. ($\mathbf{Y}^{(n)}$ is called the output space.) The…
A sum-product network (SPN) is a graphical model that allows several types of inferences to be drawn efficiently. There are two types of learning for SPNs: Learning the architecture of the model, and learning the parameters. In this paper,…
The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However,…
The physical scalar product between spin-networks has been shown to be a fundamental tool in the theory of topological quantum neural networks (TQNN), which are quantum neural networks previously introduced by the authors in the context of…
In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the…
Nowadays most research in visual recognition using Convolutional Neural Networks (CNNs) follows the "deeper model with deeper confidence" belief to gain a higher recognition accuracy. At the same time, deeper model brings heavier…
One challenging property lurking in medical datasets is the imbalanced data distribution, where the frequency of the samples between the different classes is not balanced. Training a model on an imbalanced dataset can introduce unique…
As Deep Neural Networks (DNNs) have demonstrated superhuman performance in a variety of fields, there is an increasing interest in understanding the complex internal mechanisms of DNNs. In this paper, we propose Relative Attributing…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…