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.
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…
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.
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.
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 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…
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.
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.
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.
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.
The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
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.
New fusion blocks improve equivariant neural networks for molecular dynamics.
problem Designing equivariant neural networks for tasks with global symmetries.
method Using fusion diagrams from tensor networks to design novel equivariant components.
result Improved performance with fewer parameters on chemical problems.
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.
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.
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.
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.
Tensor Neural Networks improve pricing accuracy for interest rate derivatives.
problem Inaccurate pricing of Bermudan Swaptions using traditional methods.
method Leveraging Tensor Neural Networks to solve backward Stochastic Differential Equations.
result Tensor Neural Networks provide more accurate and robust prices than Dense Neural Networks.
Characterizes a specific type of neural network for alternating group equivariance.
problem Understanding and characterizing neural networks with alternating group equivariance.
method Characterization of all possible An-equivariant neural networks using tensor powers of Rn. result Found a basis of matrices for learnable, linear An-equivariant layer functions. 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.
MARS automatically selects tensor decomposition ranks, improving performance in neural network tasks.
problem Determining optimal decomposition ranks in tensor decompositions.
method MARS uses binary masks to learn optimal tensor structure during training via relaxed MAP estimation.
result MARS achieves better results than previous methods in various tasks.
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.
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.
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.
Study Gaussian-process limits of neural networks using tensor programs.
problem Understanding the behavior of neural networks as they approach infinite width.
method Quantitative analysis through tensor programs and Wasserstein distance.
result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.
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.
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…
Tensor programs prove neural network limits for any architecture.
problem Understanding the limits of neural networks of any architecture.
method Prove convergence of neural network's Tangent Kernel (NTK) to a deterministic limit as network widths increase.
result Identify conditions for correct NTK limit calculation based on gradient independence assumption.
Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in neural networks from perspectives of PAC-Bayes, robustness, overparametrization, co…
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.
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.
Proposes ANOVA-TPNN for stable interpretation of complex functions.
problem Stability issues in estimating components of functional ANOVA models.
method Introduces ANOVA-TPNN based on tensor product basis expansion.
result ANOVA-TPNN provides stable estimation of components.
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.
Tensor Neural Networks solve high-dimensional PDEs for financial pricing.
problem High-dimensional PDEs in financial pricing.
method Tensor Neural Networks (TNN) and Tensor Network Initializer (TNN Init).
result TNN provides significant parameter savings and faster training than DNN.
Gradient descent can find better tensor decompositions than lazy training in over-parameterized settings.
problem Finding better tensor decompositions in over-parameterized settings.
method Gradient descent on over-parameterized tensor decomposition problems.
result Gradient descent can find an approximate tensor decomposition with rank m=O∗(r2.5llogd), while lazy training requires m=Ω(dl−1). Tensor networks and RNNs are equivalent, improving wave function encoding.
problem Efficiently encoding quantum states in neural networks.
method Generalized RNN architecture for tensor networks, supporting polynomial time wave function evaluation.
result Tensorial RNNs can encode quantum states with lower bond dimensions and higher accuracy.
Tensor Neural Networks improve regression accuracy and efficiency.
problem Nonparametric regression problems with complex, high-dimensional functions.
method Integrates statistical regression and numerical integration within a tensor neural network framework.
result Superior performance in approximation accuracy and generalization capacity compared to FFNs and RBNs.
Characterizes group-equivariant neural networks for three groups.
problem Understanding equivariant neural networks for orthogonal, special orthogonal, and symplectic groups.
method Characterized all possible group-equivariant neural networks for three groups.
result Found spanning sets of matrices for learnable, linear equivariant layer functions.
Low-rank structure emerges in neural networks during learning.
problem Understanding the evolution of synaptic connectivity over learning.
method Investigated the rank of 3-tensor formed by weight matrices throughout learning.
result Inferred weights are low-tensor-rank and evolve in a fixed low-dimensional subspace.
Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information from inputs. For modeling long-term dependencies in a dataset, the gating mecha…
Develops a tensor network framework to reduce RNN complexity for high-dimensional sequence modeling.
problem Exponential parameter growth in RNNs for large multidimensional data.
method Embeds a multi-linear graph filter in a tensor network architecture to approximate RNN hidden states.
result Demonstrates superior performance and reduced complexity compared to traditional RNNs.
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.
DEMOTE uses neural diffusion-reaction processes to capture temporal dynamics in sparse tensor data.
problem Sparse and temporally associated tensor data with limited structural knowledge.
method Develops a neural diffusion-reaction process to estimate dynamic embeddings for tensor modes.
result Captures both commonalities and personalities in evolving tensor entries.
The digital revolution of the banking system with evolving European regulations have pushed the major banking actors to innovate by a newly use of their clients' digital information. Given highly sparse client activities, we propose CPOPT-Net, an algorithm that combines the CP canonical tensor decomposition, a multidim…
Machine learning models accurately predict molecular magnetic anisotropy tensors.
problem Accurately modeling molecular magnetic anisotropy tensors.
method Gaussian-moment neural-network approach for machine learning.
result Achieved accuracy of 0.3--0.4 cm−1 for magnetic anisotropy tensor predictions. 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.
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…
Neural networks learn faster with correlated latent variables.
problem Efficiently learning from higher-order correlations in neural networks.
method Analytical derivation and simulations of two-layer neural networks.
result Correlations between latent variables speed up learning from higher-order correlations.