Adaptive algorithm learns tensor network structures from data.
problem Identifying optimal tensor network structure from data.
method Greedy approach starting from rank one tensor, small rank increments.
result Adaptive algorithm identifies efficient tensor network structures.
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. …
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
TRNN combines tensor geometry with neural network nonlinearity for HD data.
problem Modeling high-dimensional data with preserved tensor geometry and nonlinear interactions.
method Introduces TRNN that integrates tensor geometry and neural network nonlinearity.
result TRNN preserves tensor geometry while offering nonlinearity.
T-Basis represents neural network tensors with fewer parameters.
problem Efficiently representing neural network tensors with fewer parameters.
method T-Basis uses Tensor Rings to represent tensors in a neural network, parameterizing them with a small number of coefficients.
result T-Basis achieves high compression rates with minimal performance loss.
Improved machine learning with reduced tensor rank constraints and dropout.
problem Efficiently approximating large tensors in machine learning.
method Tree tensor networks with CP rank constraints and tensor dropout.
result Low-rank TTN classifier achieves 90.3% accuracy in Fashion-MNIST.
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…
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motiv…
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 new tensor completion method using tensor networks with Tucker wrapper.
problem Low-rank tensor completion in various applications.
method Solving LRTC as a system of nonlinear equations using a two-level alternative least squares method.
result The method converges to the exact solution at a linear rate with high probability.
A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.
problem How to provide principled uncertainty estimates for tensor network kernel machines.
method Employing a linearized Laplace approximation for Bayesian inference.
result Consistently matches or surpasses Gaussian Processes and BNNs across diverse UCI regression benchmarks.
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In o…
Improves tensor networks for classifying medical images.
problem Classifying 2D and 3D medical images efficiently.
method Develops LoTeNet, a tensor network that treats small image regions as orderless and aggregates local representations hierarchically.
result LoTeNet achieves comparable or superior performance to other methods with less computational resources.
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices bui…
The study analyzes XRP transaction networks to understand market dynamics.
problem Understanding market dynamics of XRP through transaction data.
method Weekly weighted directed networks are embedded into a vector space using network embedding techniques. A correlation tensor is calculated and analyzed using singular value decomposition.
result The correlation tensor provides insights into the system's behavior and dependence on model parameters.
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.
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.
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.
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.
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize models…
This paper shows how infinitely wide Tensor Networks converge to Gaussian Processes.
problem Understanding the relationship between Tensor Networks and Gaussian Processes.
method Analyzing the infinite-width limit of Tensor Networks and comparing them to Gaussian Processes.
result Infinitely wide Tensor Networks converge to Gaussian Processes, proving their equivalence.
Unified tensor network formalism for combining neural and symbolic AI.
problem Combining neural and symbolic AI approaches remains a challenge.
method Introduces a tensor network formalism capturing sparsity principles.
result Unified treatment identifies tensor network contractions as a fundamental inference class.
We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data to classical data, and thus preserve the interpretability of data under tensor tr…
Paper proposes a new method for density estimation using tree tensor-network states.
problem Density estimation for complex graphical models with loops.
method Determines tree topology with Chow-Liu algorithm and uses sketching techniques to define tensor-network components.
result Sample complexity guarantees and empirical validation provided.
Tensor networks reveal limitations for efficient text description but suggest potential for images.
problem Efficiently describing large text and image data sets using tensor networks.
method Investigation of mutual information scaling, introduction of mutual information estimators, and use of autoregressive and convolutional neural networks.
result Text data cannot be efficiently described by 1D tensor networks, while images may be better described by 2D tensor networks.
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.
Quantum neural network and tensor network models outperform classical models in Japanese stock market predictions.
problem Improving stock return predictions using quantum and quantum-inspired machine learning.
method Evaluation of quantum neural network and tensor network models against classical models like linear and neural networks.
result Tensor network model outperforms classical models in Japanese stock market, including linear and neural network models.
New method combines Monte Carlo and tensor networks for solving complex equations.
problem Solving high-dimensional partial differential equations efficiently.
method Uses Monte Carlo simulations and tensor train sketching for updates and re-estimations.
result Demonstrates versatility and efficacy in solving specific equations.
Tensor networks improve anomaly detection at LHC for new physics.
problem Identifying new phenomena in proton collision events at LHC.
method Tensor network-based anomaly detection using Matrix Product State with an isometric feature map.
result Tensor networks outperform established quantum methods in identifying new phenomena.
New method approximates high-dimensional probability densities efficiently.
problem Approximating high-dimensional probability densities accurately and efficiently.
method Hierarchical tensor-network approach using randomized SVD and linear equations.
result The method effectively approximates high-dimensional densities with linear complexity.
New method compresses LSTM networks using MPS tensor trains.
problem Challenges in maintaining performance of compressed RNNs.
method Use of MPS tensor trains for LSTM network compression.
result MPS tensor trains outperform MPOs in storage and inference time.
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.
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.
We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a q-state Potts model defined as a planar graph with weighted edges that corresponds to the knot. For any integer q, we cast…
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.
RWTNs improve NTN performance in SRL tasks.
problem Improving NTN performance in SRL tasks.
method Randomly weighted, untrained tensors in NTN encoder network.
result RWTNs outperform LTNs in SII tasks.
Dual-Channel Tensor Neural Network (DC-TNN) decomposes tensor data into low-rank and sparse components for better estimation and inference.
problem Tensor-valued data with multilinear dependencies are challenging to process due to loss of multiway geometry under vectorization.
method DC-TNN decomposes tensors into a low-rank core and a sparse refinement, processing them through coupled neural channels.
result Established non-asymptotic risk bounds and developed structure-aware conformal ROC and AUC confidence bands.
Extends geometrical description of tensor manifolds in tree-based formats.
problem Geometrical description of tensor manifolds in tree-based formats.
method Provided a new geometrical description of manifolds of tensors in tree-based format.
result Geometrical description compatible with Tucker format.
Tensor networks improve image classification but require more expressive states.
problem Understanding why tensor networks work in image classification.
method Investigated entanglement properties of tensor network models for supervised image classification.
result Tensor networks can learn states that are robustly entangled, suggesting long-range entanglement is not essential.
Quantum-inspired tensor network speeds up financial risk assessment.
problem Efficiently pricing multi-asset derivatives in finance.
method Tensor network algorithms for multi-asset options pricing.
result Tensor network approach yields several orders of magnitude speedup.
Tensor networks improve unsupervised learning performance.
problem Improving unsupervised machine learning models.
method Autoregressive Matrix Product States (AMPS) combining quantum and machine learning.
result AMPS significantly outperforms existing tensor network models and neural networks.
New neural networks respect symmetries in symmetric tensors, improving efficiency and generalization.
problem Learning from symmetric tensors efficiently and respecting their inherent symmetries.
method Developed two characterizations of linear permutation equivariant functions between symmetric power spaces of R^n.
result These functions are highly data efficient compared to standard MLPs and generalize well to different sizes of symmetric tensors.
Tensor neural network improves human pose classification from 3D skeleton data.
problem Efficiently processing spatiotemporal data for human pose classification.
method Proposes a tensor-based neural network with three components: spatiotemporal feature construction, tensor fusion, and tensor-based neural network processing.
result Achieves state-of-the-art performance in human pose classification.
No free lunch theorem formalized for tensor network models.
problem Understanding limitations of tensor network machine learning models.
method Formalized rigorous no-free-lunch theorem for specific tensor network models.
result Revealed intrinsic limitations of tensor network-based learning models.
New tensor formulation reveals gradient flow's bias in linear neural networks.
problem Understanding implicit bias in linear neural network training.
method Tensor formulation of neural networks, including fully-connected, diagonal, and convolutional networks.
result Gradient flow on linear tensor networks converges to solutions of specific optimization problems.
New model uses PEPS for image classification, outperforming tree-like networks.
problem Efficiently modeling and classifying 2D data like images.
method Feature map followed by PEPS contraction with trainable parameters.
result Significantly superior to tree-like networks on MNIST and Fashion-MNIST.
Introduces P-tensors for generalized higher-order message passing in graph neural networks.
problem Expanding the expressive power of graph neural networks through higher-order structures.
method Introduces P-tensors to define the most general form of permutation equivariant message passing.
result Achieves state-of-the-art performance on molecular datasets.
Tree tensor networks balance model complexity and empirical risk for high-dimensional function approximation.
problem Selecting optimal tree structure and ranks for high-dimensional function approximation.
method Proposes a complexity-based model selection method for tree tensor networks in empirical risk minimization.
result Demonstrates near-minimax adaptive performance across various smoothness classes.