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We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…
Deep learning's immense capabilities are often constrained by the complexity of its models, leading to an increasing demand for effective sparsification techniques. Bayesian sparsification for deep learning emerges as a crucial approach,…
Neural networks have achieved remarkable performance in various application domains. Nevertheless, a large number of weights in pre-trained deep neural networks prohibit them from being deployed on smartphones and embedded systems. It is…
Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise)…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Deep neural networks (DNNs) have become increasingly popular and achieved outstanding performance in predictive tasks. However, the DNN framework itself cannot inform the user which features are more or less relevant for making the…
In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…
Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating…
Graph Neural Networks (GNNs) have become a standard approach for learning from graph-structured data. However, their reliance on parametric classifiers (most often linear softmax layers) limits interpretability and sometimes hinders…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…
The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…
Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are…
Graph neural networks (GNN) are a promising tool to predict magnetic properties of large multi-grain structures, which can speed up the search for rare-earth free permanent magnets. In this paper, we use our magnetic simulation data to…
Uncovering unknown or missing links in social networks is a difficult task because of their sparsity and because links may represent different types of relationships, characterized by different structural patterns. In this paper, we define…
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a…
In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…
Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric…