Deep tensor factorization benefits from implicit regularization with polynomial growth.
problem Tensor factorization's implicit regularization effect in deep networks is not well understood.
method Investigated the implicit regularization in deep tensor factorization, showing polynomial growth.
result Implicit regularization in deep tensor factorization grows polynomially with depth, improving estimation accuracy and convergence.
Hybrid tensor networks improve machine learning by combining quantum and classical methods.
problem Limitations of regular tensor networks in machine learning.
method Quantum-classical hybrid tensor networks (HTN) combining tensor networks and classical neural networks.
result HTN overcomes limitations of regular tensor networks and enables deep learning training.
A simple self-supervised model for tensor RPCA using deep unfolding.
problem Tensor robust principal component analysis (RPCA) challenges in practical applications.
method Deep unfolding with only four hyperparameters.
result Competitive or superior performance compared to supervised methods, even in data-starved scenarios.
Efficiently calibrates volatility models using Chebyshev Tensors.
problem Calibrating pricing models efficiently.
method Used Chebyshev Tensors to speed up calibration of the rough Bergomi volatility model.
result Chebyshev Tensors can calibrate the rough Bergomi volatility model 40,000 times more efficiently than brute-force methods.
Deep learning models predict option prices from 3D tensor data.
problem Predicting option prices for risk management and trading.
method 3D tensor representation of financial data, deep learning models (2D tensors in 3 channels).
result Proposed models outperform traditional methods like B-S model and vector-based LSTM.
The paper explains implicit regularization in hierarchical tensor factorization and deep CNNs.
problem Understanding implicit regularization in complex neural network architectures.
method Theoretical analysis using dynamical systems to overcome challenges in hierarchy.
result Established implicit regularization towards low hierarchical tensor rank, equivalent to locality in CNNs.
Proposes FATTNN for tensor-on-tensor regression with improved prediction and reduced computation.
problem Tensor-on-tensor regression with complex tensor structures and nonlinear relationships.
method Integrates tensor factor models into deep neural networks to handle nonlinearity and reduce data dimensionality.
result Significant improvements in prediction accuracy and computational efficiency over traditional methods.
SPIDER uses deep neural networks for streaming tensor factorization.
problem Lack of effective approach for deep tensor factorization of streaming data.
method Bayesian neural networks with spike-and-slab prior, Taylor expansions, moment matching, and EPI framework.
result Effective incremental updates for latent factors and NN weights.
The paper analyzes implicit regularization in tensor factorization using neural networks.
problem Understanding implicit regularization in tensor factorization.
method Dynamical systems perspective and gradient descent analysis.
result Gradient descent induces a form of greedy low tensor rank search.
Ansor generates high-performance tensor programs for deep learning.
problem Generating high-performance tensor programs for deep learning on various hardware platforms is challenging.
method Ansor uses a hierarchical representation of the search space, sampling programs, and evolutionary search with a learned cost model to find high-performance programs.
result Ansor improves deep neural network execution performance up to 3.8x on Intel CPU, 2.6x on ARM CPU, and 1.7x on NVIDIA GPU.
RBM and DBM are represented as 2D tensor networks, revealing their expressive power and efficiency.
problem Understanding and optimizing RBM and DBM models.
method Representing RBM and DBM as 2D tensor networks and developing an efficient tensor network contraction algorithm.
result The proposed algorithm for computing partition functions is more accurate than state-of-the-art methods.
We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
problem Efficiency and stability in deep learning models with weight matrix compression.
method Spectral Tensor Train Parameterization (STTP) of weight matrices.
result Improved compression and training stability in neural networks.
DeepTensor uses deep networks to efficiently decompose tensors with improved performance and robustness.
problem Efficiently decomposing tensors with deep learning to capture nonlinear structures.
method Low-rank tensor decomposition using deep generative networks trained to minimize approximation error.
result DeepTensor outperforms classical methods like SVD and PCA in various applications, including image denoising and 3D MRI.
Causal deep learning tackles causal inference using tensor factor analysis.
problem Addressing causal questions in data using neural networks.
method Tensor factor analysis and neural network architectures (causal capsules, tensor transformer, multilinear projection algorithm).
result Derives deep neural networks for causal inference with tensor factor analysis.
New method compresses deep learning layers using tensor decomposition.
problem Reduction of computation cost and interpretability for tensor data.
method CP-decomposition to compress convolutional layers in deep learning.
result Reduces model complexity and maintains prediction performance.
A new algorithm reduces memory usage for deep learning models.
problem Training deep learning models requires significant memory.
method Dynamic Tensor Rematerialization (DTR) is a greedy online algorithm that dynamically plans recomputations.
result DTR achieves comparable performance to optimal static checkpointing with only a small memory budget.
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way data analysis, we consider the use of tensor decompositions in compressing the para…
Tensor networks improve anomaly detection efficiency.
problem Anomaly detection in high-dimensional data.
method Tensor networks for learning a linear transformation over high-dimensional space, penalizing global tendency to normality.
result Tensor networks outperform deep and classical algorithms on various datasets.
Tensor regression networks achieve high compression rate of neural networks while having slight impact on performances. They do so by imposing low tensor rank structure on the weight matrices of fully connected layers. In recent years, tensor regression networks have been investigated from the perspective of their comp…
DTCCA learns nonlinear transformations of multi-view data for high-order correlation.
problem Learning complex nonlinear transformations of multiple data views.
method Maximizes high-order canonical correlation by jointly learning transformations of each view using a reformulated tensor decomposition.
result DTCCA efficiently handles high-dimensional and large number of views, overcoming scalability issues.
A new tensor-based layer reduces neural network dimensions without losing important features.
problem Reducing dimensionality in tensor-structured feature data for deep neural networks.
method TensorProjection layer that projects input tensors into output tensors with reduced dimensions through mode-wise projections.
result The TensorProjection layer outperforms traditional downsampling methods in tasks like medical image classification and segmentation.
The trace norm is widely used in multi-task learning as it can discover low-rank structures among tasks in terms of model parameters. Nowadays, with the emerging of big datasets and the popularity of deep learning techniques, tensor trace norms have been used for deep multi-task models. However, existing tensor trace n…
Paper generalizes tensor-train approximation for complex random variables.
problem Characterizing intractable high-dimensional random variables.
method Extends inverse Rosenblatt transform to general reference measures and integrates into deep variable transformation framework.
result Deep inverse Rosenblatt transport significantly expands tensor approximations for complex random variables.
OpEvo automates tensor operator optimization for better efficiency.
problem Manual optimization of tensor operators is inefficient and limited.
method OpEvo uses evolutionary computation with topology-aware mutation.
result OpEvo finds optimal configurations with less effort and variance.
Optimizes tensor rank selection for neural network compression.
problem Finding optimal tensor rank for regression models.
method Analyzes population expressions for training-testing discrepancy under Gaussian design.
result Optimal rank minimizes prediction error and aligns with cross-validation.
DCTN uses tensor networks for image classification, achieving state-of-the-art results.
problem Improving image classification accuracy with deep neural networks.
method Developed a novel deep convolutional tensor network (DCTN) based on Entangled plaquette states (EPS).
result DCTN achieves state-of-the-art results on MNIST and FashionMNIST but overfits on CIFAR10.
Estimates metric tensor on neuromanifolds using Fisher information and random methods.
problem Computing the metric tensor on high-dimensional neuromanifolds efficiently and accurately.
method Deterministic bounds and unbiased random estimators based on Hutchinson's trace method.
result An efficient random estimator with bounded standard deviation.
Gradient descent promotes low-rank solutions in tensor completion.
problem Implicit regularization in tensor factorization using gradient descent.
method Introduced deep Tucker and TensorTrain (TT) unconstrained factorization to address tensor completion.
result Gradient descent promotes solutions with low-rank.
Tensor networks improve medical image classification performance.
problem Improving medical image classification accuracy.
method Extending tensor networks to medical image analysis, focusing on 2D images.
result Tensor networks achieve comparable performance to deep learning methods with fewer hyperparameters and resources.
TF-Coder simplifies tensor manipulation programming in TensorFlow.
problem Difficulty in programming with TensorFlow due to steep learning curve.
method Bottom-up weighted enumerative search with value-based pruning and type/value filtering.
result Solves 63 out of 70 real-world tasks within 5 minutes.
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model …
This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language modeling, generative networks and industrial recommendation systems. BFLOAT16 is attrac…
Tensor decomposition, a collection of factorization techniques for multidimensional arrays, are among the most general and powerful tools for scientific analysis. However, because of their increasing size, today's data sets require more complex tensor decomposition involving factorization with multiple matrices and dia…
Improves group fairness in tensor completion by augmenting tensors with balanced entities.
problem Preventing discrimination in tensor decomposition based on social grounds.
method STAFF (Sparse Tensor Augmentation For Fairness) which augments tensors with balanced entities to mitigate imbalance and bias.
result Consistently shows the best trade-off between completion error and group fairness, reducing errors by 36% and 59% respectively.
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information retrieval using deep-learning classifiers, such encodings are learnt on the flattened la…
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 algebraic formulation to multiply tensors via circulant convolution. In this $t…
Deep neural networks are powerful learning models that achieve state-of-the-art performance on many computer vision, speech, and language processing tasks. In this paper, we study a fundamental question that arises when designing deep network architectures: Given a target network architecture can we design a smaller ne…
THS-GAN uses tensorizing and high-order pooling for AD diagnosis.
problem Early diagnosis of Alzheimer's Disease (AD) using MRI images.
method Tensorizing a three-player cooperative game framework with high-order pooling for MRI images.
result THS-GAN achieves superior performance in AD diagnosis compared to existing methods.
We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective deep learning systems. However, existing systems rely on manually optimized librar…
In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our app…
Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors,…
Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor networks, thus leading to a highly efficient representation that we call tensor SPN…
Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of parameters and over a thousand layers. The trade-off is that these large architectures r…
Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations su…
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …
We propose a completely unsupervised method to understand audio scenes observed with random microphone arrangements by decomposing the scene into its constituent sources and their relative presence in each microphone. To this end, we formulate a neural network architecture that can be interpreted as a nonnegative tenso…
This paper develops a method to train compact neural networks with reduced memory and computational costs.
problem Training large neural networks consumes excessive resources and energy.
method End-to-end training framework using Bayesian tensor decomposition with automatic rank determination.
result The method achieves significant parameter reduction and maintains or improves accuracy.
NePTuNe combines neural and tensor methods for efficient link prediction in knowledge graphs.
problem Incomplete knowledge graphs, especially in link prediction.
method Hybrid model combining neural and tensor factorization methods.
result NePTuNe achieves state-of-the-art performance on FB15K-237 and near state-of-the-art on WN18RR datasets.