New hierarchical tensor decomposition model for complex data.
problem Lack of natural generalization of hierarchical NMF to tensors.
method Proposes a new hierarchical nonnegative tensor decomposition (HNTF) model.
result Model more naturally illuminates topic hierarchy.
Paper compresses RNNs using HT decomposition for better performance.
problem Large model sizes of RNNs in sequence analysis.
method Hierarchical Tucker (HT) tensor decomposition for model compression.
result HT-LSTM achieves better compression and accuracy than state-of-the-art methods.
Unified algorithm for tensor decomposition supports multiple loss functions and models.
problem Efficient tensor decomposition for various models and loss functions.
method Hierarchical combination of ADMM and MM for optimization.
result Wide-range applications can be solved by the proposed algorithm.
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.
Improved spectral methods of moments for robust latent variable model learning.
problem Limited robustness of spectral methods of moments to model misspecification.
method Hierarchical approach using approximate joint diagonalization instead of tensor decomposition.
result Our method outperforms previous tensor decomposition methods in speed and model quality.
Unified tensor model disentangles object appearance factors.
problem Representing hierarchical intrinsic and extrinsic causal factors of object appearance.
method Compositional hierarchical tensor factorization.
result Interpretable object representation robust to occlusion and reduced training data requirements.
A new method reduces Volterra kernel complexity and uncertainty quantification.
problem Challenges in modeling nonlinear systems with Volterra series due to high model order.
method Bayesian Tensor Network Volterra kernel machines (BTN-V) using canonical polyadic decomposition.
result Competitive accuracy, enhanced uncertainty quantification, and reduced computational cost.
PolyGAN uses high-order polynomials to generate data without activation functions.
problem Learning generative models for high-dimensional distributions.
method PolyGAN models the generator as a high-order polynomial represented by high-order tensors, using tensor decompositions to reduce parameters.
result PolyGAN can approximate data distributions without activation functions.
A new method uses CPD to efficiently model feature interactions in non-sequential data.
problem Efficiently modeling feature interactions in non-sequential data with high computational and memory costs.
method Implicitly represent model parameters as a tensor, factorize into a compact Tensor Train (TT) format, and use Canonical Polyadic (CP) Decomposition for invariance to feature ordering.
result The proposed CP-based predictor outperforms other TN-based predictors on sparse data and matches neural network performance on dense non-sequential tasks.
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast empirical evidence supporting this belief, theoretical justifications to date are li…
We propose a probabilistic modeling framework for learning the dynamic patterns in the collective behaviors of social agents and developing profiles for different behavioral groups, using data collected from multiple information sources. The proposed model is based on a hierarchical Bayesian process, in which each obse…
Tensorial Neural Networks improve neural network compression and performance.
problem Efficiently compressing neural networks while maintaining or improving performance.
method Introducing tensor operations on high-order operands to solve hierarchical nonlinear tensor decomposition using stochastic gradient descent.
result TNNs achieve up to 5% test accuracy improvement on CIFAR10 compared to state-of-the-art compression methods.
A new tensor decomposition method that minimizes KL divergence.
problem Tensor reconstruction accuracy.
method Legendre decomposition, based on information geometry.
result Minimizes KL divergence and improves tensor reconstruction accuracy.
Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…
NCPF model improves traffic data imputation with neural and tensor methods.
problem Pervasive missing data in traffic analysis due to sensor failures and gaps.
method Neural Canonical Polyadic Factorization (NCPF) integrating CP decomposition and deep learning.
result NCPF outperforms state-of-the-art baselines in urban traffic datasets.
Efficiently decomposes large tensors using stochastic gradients.
problem Efficiently decomposing large tensors for multiway data analysis.
method Stochastic gradients computed via MTTKRP kernel for efficient computation.
result Advantages and scalability demonstrated for large-scale problems.
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
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.
NA0CT2 improves tensor regression predictions with ℓ0 regularization.
problem Improving tensor regression predictions with structural information.
method Noise-Augmented ℓ0 regularization on Tucker decomposition. result Achieves exact ℓ0 regularization on core tensor in linear and generalized linear tensor regression. To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictiona…
Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.
problem Unclear mathematical property of tensor decomposition.
method Algebraic geometrical method for upper bound derivation.
result Upper bound of real log canonical threshold (RLCT) derived.
Tensor decomposition improves robot control by modeling inverse dynamics.
problem Accurate modeling of inverse dynamics for robot control.
method Tensor decomposition of sparse tensors to approximate non-linear functions.
result Superior performance compared to state-of-the-art methods.
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
problem Understanding the training dynamics of gradient flow on tensor decomposition.
method Empirical observation and mathematical proof of gradient flow dynamics for orthogonally decomposable tensors.
result Gradient flow dynamics for orthogonally decomposable tensors follows a tensor deflation process, recovering all tensor components.
Paper tackles anomaly detection in e-commerce using Bayesian semi-supervised tensor decomposition.
problem Detecting anomalies in seller-reviewer data in e-commerce.
method Bayesian semi-supervised tensor decomposition with Polya-Gamma data augmentation and partial natural gradient learning.
result Semi-supervised approach outperforms state-of-the-art unsupervised baselines.
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
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.
The paper explores tensor decompositions in deep learning models.
problem Compressing parameter space and creating richer representations.
method Tensor decompositions applied to deep learning models.
result Tensor methods can yield richer adaptive representations of complex data.
New algorithms solve tensor problems with random components using SDP.
problem Exact tensor nuclear norm, decomposition, and completion for random tensors.
method Degree-4 Sum of Squares (SOS) semidefinite programs.
result Exact solutions for tensor nuclear norm, decomposition, and completion with random asymmetric components.
VecHGrad solves complex tensor decomposition problems more accurately and efficiently.
problem Complex tensor decomposition with multiple matrices and diagonal tensors.
method VecHGrad algorithm using gradient, Hessian-vector product, and adaptive line search.
result VecHGrad converges faster and more accurately than existing methods.
SaMbaTen efficiently maintains tensor decompositions for growing datasets.
problem Maintaining tensor decompositions for dynamic, growing datasets.
method Sampling-based batch incremental tensor decomposition algorithm.
result SaMbaTen achieves comparable accuracy to state-of-the-art techniques but is significantly faster and scalable.
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
The report analyzes Legendre decomposition for tensor data.
problem Finding effective lower dimensional representations of tensors.
method Theoretical analysis of dual parameters and dually flat manifold properties, followed by experimental verification and clustering.
result Parameters on submanifold cannot be directly used as low-rank representations.
This paper introduces tensors and their applications in machine learning.
problem No specific problem stated; focuses on tensor concepts and applications.
method Overview of tensor concepts, decomposition algorithms, and applications.
result Introduction to tensor decompositions and their use in machine learning.
Develops a tensor decomposition method with side information.
problem Identifying the relationship between a high-dimensional tensor and side information.
method Supervised tensor decomposition incorporating multiple feature matrices.
result Captures effective dimension reduction of the data tensor in feature space.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
problem Handling large-scale tensor data with missing entries and outliers.
method Auto-weighted steepest descent method for missing entries and outliers identification, FGMC and RStS strategies.
result Outperforms existing TR decomposition methods in the presence of outliers and runs faster than robust tensor completion algorithms.
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.
Develops SymGCP for tensor decompositions with general symmetry.
problem Handling symmetry in tensor decompositions for better model accuracy.
method Introduces SymGCP, a generalized CP decomposition that accounts for any subset of tensor modes' symmetry.
result SymGCP enables efficient and scalable tensor decomposition with improved model robustness and accuracy.
Paper addresses statistical efficiency and scalability in tensor train decomposition.
problem Statistical inefficiency and scalability issues in tensor train decomposition.
method Introduces a convex relaxation and alternating optimization method with randomization.
result Derives error bounds and demonstrates method's performance on real data.
Proposes polynomial neural networks for improved function approximation in various tasks.
problem Improving function approximation in various tasks like image generation, face verification, and 3D mesh representation learning.
method Introduces polynomial neural networks (Π-Nets) and three tensor decompositions to reduce parameter count and enhance expressiveness. result Demonstrates that Π-Nets can produce state-of-the-art results in challenging tasks without non-linear activation functions. Two methods preserve tensor structure for reduced dimensionality in tensor regression.
problem Reducing dimensionality of tensor predictors for improved interpretation and accuracy.
method Developed two tensor dimension reduction methods using Tucker and CP decompositions.
result Substantial improvement in accuracy over existing methods in simulations and applications.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
A novel approach to improve knowledge base completion using tensor decomposition.
problem Knowledge Base Completion (KBC) as a tensor completion problem.
method Canonical Tensor Decomposition (CP) with novel regularizers and reformulation.
result Improved KBC results using CP decomposition and ComplEx model.
The paper formalizes incidence tensors and their decomposition for geometric deep learning.
problem Representing structured data like graphs and simplicial complexes.
method Formalizes incidence tensors, analyzes their structure, and presents equivariant networks.
result Incidence tensors decompose into invariant subsets, leading to efficient linear map implementations.
Paper detects and mitigates concept drift in streaming tensor decompositions.
problem Variability of latent concepts over time in dynamic data streams.
method SeekAndDestroy algorithm for detecting and mitigating concept drift.
result SeekAndDestroy effectively detects and mitigates concept drift in streaming tensor decompositions.
Graphical notation simplifies tensor operations and decompositions.
problem Complex tensor operations are difficult to understand and represent.
method Introduces graphical notation to represent tensor operations.
result Simplified representation of tensor operations and decompositions.
ALℓ0CORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with ℓ0-norm constraint. result ALℓ0CORE achieves similar results to full Tucker decomposition at a fraction of the cost. TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.
problem Predict missing entries in time-evolving tensors with temporal dependency and sparsity issues.
method TATD (Time-Aware Tensor Decomposition) integrates temporal dependency and time-varying sparsity through a smoothing regularization with Gaussian kernel and alternating optimization.
result TATD achieves state-of-the-art accuracy for decomposing temporal tensors.
This work improves tensor decomposition methods, especially for large datasets.
problem Lack of efficient methods for estimating Tucker decompositions.
method Applies Johnson-Lindenstrauss type guarantees to Tucker decompositions with random embeddings.
result Effective dimension reduction with minimal error for large tensors.