Key papers in Computational Mathematics
Pofolia’s corpus holds 83 papers from the Computational Mathematics subfield (2012–2022). The list below starts with the most cited.
Most cited
Ranked by citation count. Because citations accumulate over time, this list naturally leans towards work published a few years ago; for where the field is now, see “recently added”.
Tensor Decomposition for Signal Processing and Machine Learning
IEEE Transactions on Signal Processing · 2017 · Q1 · SJR 1.00 · FWCI 58.10 · 1,611 citations
This overview article introduces tensor decomposition, a powerful mathematical tool for analyzing multi-dimensional data, to researchers and practitioners in signal processing and machine learning.
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis
IEEE Signal Processing Magazine · 2015 · Q1 · SJR 2.00 · FWCI 42.62 · 1,384 citations
Higher-order tensors (multiway arrays) offer a more versatile data analysis paradigm than traditional matrix models, enabling polynomial models with guaranteed uniqueness under mild conditions.
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging
SIAM Journal on Matrix Analysis and Applications · 2013 · Q1 · SJR 1.00 · FWCI 5.60 · 1,206 citations
This paper introduces a novel framework treating third-order tensors as operators on matrices, defining matrix lengths, angles, and orthogonality, and enabling new computational methods.
Most Tensor Problems Are NP-Hard
Journal of the ACM · 2013 · Q1 · SJR 1.00 · FWCI 21.80 · 1,146 citations
Many fundamental problems involving tensors, the multidimensional generalization of matrices, are proven to be NP-hard, meaning they are computationally intractable for large inputs.
Model Compression and Hardware Acceleration for Neural Networks: A Comprehensive Survey
Proceedings of the IEEE · 2020 · Q1 · SJR 5.00 · FWCI 61.79 · 931 citations
This survey comprehensively reviews recent advances in compressing and accelerating Deep Neural Networks (DNNs) for efficient deployment on embedded systems, addressing the trade-off between performance and accuracy.
Tensor decompositions for learning latent variable models
CaltechAUTHORS (California Institute of Technology) · 2014 · FWCI 32.58 · 818 citations
A new method uses tensor decompositions to efficiently estimate parameters in latent variable models like Gaussian mixture models and hidden Markov models.
Escaping From Saddle Points --- Online Stochastic Gradient for Tensor\n Decomposition
arXiv (Cornell University) · 2015 · 611 citations · Open access
This paper introduces a novel stochastic gradient descent method that guarantees convergence to a local minimum for non-convex functions, a significant improvement over existing methods prone to saddle points.
Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination
IEEE Transactions on Pattern Analysis and Machine Intelligence · 2015 · Q1 · SJR 4.00 · FWCI 12.53 · 606 citations
This paper introduces a novel Bayesian approach to CP tensor factorization that automatically determines the tensor rank, overcoming a major limitation of existing methods.
A literature survey of low‐rank tensor approximation techniques
GAMM-Mitteilungen · 2013 · Q3 · FWCI 17.82 · 584 citations
This survey provides an overview of low-rank tensor approximation, a technique that has emerged as a powerful tool for solving large-scale scientific computing problems previously considered intractable.
Tensor Regression with Applications in Neuroimaging Data Analysis
Journal of the American Statistical Association · 2013 · Q1 · SJR 3.00 · FWCI 6.82 · 569 citations
A new family of tensor regression models is proposed to efficiently analyze ultrahigh-dimensional neuroimaging data, reducing dimensionality and enabling efficient estimation and prediction.
Tensorizing Neural Networks
arXiv (Cornell University) · 2015 · 499 citations · Open access
Researchers have developed a method to convert dense weight matrices in neural networks to the Tensor Train format, significantly reducing the number of parameters while preserving the network's expressive power.
Discovering faster matrix multiplication algorithms with reinforcement learning
Nature · 2022 · Q1 · SJR 19.00 · FWCI 53.78 · 456 citations · Open access
A deep reinforcement learning agent, AlphaTensor, has discovered novel algorithms for matrix multiplication that outperform state-of-the-art complexity for many matrix sizes, including a breakthrough for 4x4 matrices.
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions
Foundations and Trends® in Machine Learning · 2016 · Q1 · SJR 5.00 · FWCI 10.15 · 437 citations
This paper introduces tensor networks as a novel approach to overcome the 'curse of dimensionality' in analyzing large, complex datasets by enabling efficient dimensionality reduction and optimization.
Tensor displays
ACM Transactions on Graphics · 2012 · Q1 · SJR 5.00 · FWCI 15.47 · 418 citations
Researchers introduce 'tensor displays,' a new class of light field displays that use stacked, time-multiplexed layers to emit light fields representable by mathematical tensors.
SimplE Embedding for Link Prediction in Knowledge Graphs
arXiv (Cornell University) · 2018 · 395 citations · Open access
A new method called SimplE enhances Canonical Polyadic (CP) decomposition for knowledge graph link prediction by learning dependent entity embeddings, significantly outperforming existing tensor factorization techniques.
Information Retrieval using a Singular Value Decomposition Model of Latent Semantic Structure
ACM SIGIR Forum · 2017 · FWCI 6.13 · 388 citations
This paper introduces a novel approach to information retrieval by modeling latent semantic structure using Singular Value Decomposition (SVD). The method aims to improve search accuracy by uncovering underlying relationships between terms and documents.
Model Reduction and Approximation
Society for Industrial and Applied Mathematics eBooks · 2017 · FWCI 4.04 · 386 citations · Open access
New complexity reduction methods based on low-rank tensor approximation are presented for solving high-dimensional problems in computational science.
Learning with Pseudo-Ensembles
arXiv (Cornell University) · 2014 · 361 citations · Open access
A new regularization technique formalizes 'pseudo-ensembles'—collections of models derived from a parent model via noise—achieving state-of-the-art results in semi-supervised learning.
Tensors for Data Mining and Data Fusion
ACM Transactions on Intelligent Systems and Technology · 2016 · Q1 · SJR 2.00 · FWCI 15.66 · 361 citations
This survey highlights tensors and tensor decompositions as powerful tools for modeling complex, multi-aspect data, enabling extraction of latent information for data mining applications.
The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
SIAM Journal on Scientific Computing · 2012 · Q1 · SJR 1.00 · FWCI 8.93 · 360 citations
A new stable, generic algorithm (ALS/MALS) is introduced for optimizing tensors in the Tensor Train (TT) format, generalizing the alternating least squares method.
Recently added
Discovering faster matrix multiplication algorithms with reinforcement learning
Nature · 2022 · Q1 · SJR 19.00 · FWCI 53.78 · 456 citations · Open access
A deep reinforcement learning agent, AlphaTensor, has discovered novel algorithms for matrix multiplication that outperform state-of-the-art complexity for many matrix sizes, including a breakthrough for 4x4 matrices.
Tensor Methods in Computer Vision and Deep Learning
Proceedings of the IEEE · 2021 · Q1 · SJR 5.00 · FWCI 15.39 · 174 citations
Tensors, or multidimensional arrays, are increasingly fundamental to deep learning, enabling efficient network architectures, improved robustness, and theoretical understanding in computer vision.
Low-Rank Tensor Graph Learning for Multi-View Subspace Clustering
IEEE Transactions on Circuits and Systems for Video Technology · 2021 · Q1 · SJR 2.00 · FWCI 19.04 · 201 citations
A novel multi-view clustering method, Low-Rank Tensor Graph (LRTG), simultaneously learns data representation and affinity matrices in a single step, outperforming 17 state-of-the-art methods.
A Refined Laser Method and Faster Matrix Multiplication
Society for Industrial and Applied Mathematics eBooks · 2021 · 277 citations · Open access
A refined laser method improves the bound on matrix multiplication complexity to ω < 2.37286, surpassing the previous best of ω < 2.37287.
Bayesian Temporal Factorization for Multidimensional Time Series Prediction
IEEE Transactions on Pattern Analysis and Machine Intelligence · 2021 · Q1 · SJR 4.00 · FWCI 25.92 · 255 citations
A new Bayesian temporal factorization (BTF) framework models multidimensional time series, like spatiotemporal data, by integrating low-rank factorization and vector autoregressive processes, enabling probabilistic predictions and uncertainty estimates without imputing missing values.
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