Tensor trains speed up option pricing for multi-asset options.
problem Speeding up option pricing for multi-asset options.
method Tensor train learning algorithms to compress functions with parameter dependence.
result The proposed method outperforms Monte Carlo-based pricing in computational complexity.
New model for density estimation using tensor trains.
problem Estimation of high-dimensional probability density functions.
method Tensor train-based density estimation (TTDE) with Riemannian optimization.
result TTDE outperforms competitors in training speed and performance.
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.
Gradient optimization improves functional tensor-train regression performance.
problem Low-rank functional regression from scattered data.
method Gradient-based optimization of functional tensor-train parameters.
result Gradient methods outperform standard ALS in low-sample number scenarios.
Proposes a new method for high-dimensional density estimation.
problem Estimating high-dimensional probability density functions efficiently.
method Tensorizing flow method combining tensor-train and flow-based generative modeling.
result Efficiently constructs an approximate density in tensor-train form and trains a flow model to match empirical distribution.
KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.
problem Multi-way data imputation for high-dimensional functional MRI and dynamic graph recovery.
method Reformulates imputation as RKHS regression with TT-constrained coefficients and Hadamard overparameterization. Optimizes TT coefficients and kernel matrices on Riemannian manifolds.
result Consistently outperforms state-of-the-art methods in modeling accuracy.
KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.
problem Multi-way data imputation in high-dimensional spaces.
method Reformulates imputation as RKHS regression with TT-constrained coefficients, optimized on manifold frameworks.
result Consistently outperforms state-of-the-art methods in accuracy.
Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
problem Scalability limitations of Gaussian process regression.
method Bayesian tensor train kernel machine with Laplace approximation and variational inference.
result VI replaces cross-validation and offers up to 65x faster training.
A new method estimates rare events using tensor trains.
problem Estimating rare event probabilities in high-dimensional problems.
method Approximating optimal importance distribution via tensor-train decompositions and compositions.
result Better variance reduction and efficient computation of rare event probabilities.
Stochastic trace estimation with tensor train random vectors
problem Stochastic trace estimation for large-scale matrices
method Gaussian random tensor train vectors
result Median-of-means variant achieves dimension-independent guarantees
Efficiently samples complex distributions using tensor train format.
problem Sampling from high-dimensional complex probability densities efficiently.
method Integrates tensor train format with backward stochastic differential equations (BSDEs) for fast, robust, and accurate sampling.
result Improved efficiency in sampling from challenging target distributions.
Proposes a new kernel technique for tensor data in SVM.
problem Handling tensorial data in machine learning.
method Kernelized support tensor train machine for image classification.
result Tensorizes the standard SVM on its input structure and kernel mapping scheme.
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.
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.
TTPUDR uses tensor-train decomposition for high-dimensional data analysis.
problem High-dimensional data analysis challenges.
method Tensor-train decomposition and manifold optimization.
result TTPUDR significantly outperforms past methods and state-of-the-art methods.
New method uses tensor trains for efficient PDE approximation.
problem High-dimensional PDEs and the curse of dimensionality.
method Tensor trains and backward stochastic differential equations for parabolic PDEs.
result Achieves a favorable trade-off between accuracy and computational efficiency.
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.
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.
problem Efficient computation of Greeks for multi-asset options with high accuracy and low sample complexity.
method Tensor train (TT) representations of Fourier-based pricing functions, combined with numerical differentiation or analytical approaches.
result Significant speed-ups of up to 105imes over Monte Carlo simulations while maintaining comparable accuracy. TTRP method preserves distances in high-dimensional data with reduced storage and speed.
problem Preserving distances in high-dimensional datasets efficiently and accurately.
method Tensor train random projection (TTRP) using TT-ranks of one.
result TTRP is an expected isometric projection with bounded variance.
Introduces STTM to improve STM's performance.
problem Overfitting and curse of dimensionality in SVM.
method Replaces rank-one tensor in STM with tensor train.
result STTM outperforms SVM and STM.
Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.
problem Theoretical development of property inheritance for subtensors in tensor train decompositions.
method Theoretical analysis of incoherence and condition number preservation, and tensor train rank preservation through fiber-wise sampling.
result Key tensor properties (incoherence and condition number) can be well preserved to subtensors formed via fiber-wise sampling.
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.
Combines Koopman theory and tensor trains for high-dimensional dynamical systems.
problem Analyzing complex, high-dimensional dynamical systems.
method Tensor train (TT) format for low-rank approximation, Koopman operator theory for dynamics.
result Efficient algorithms for low-rank representation of evolution operators.
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
problem Limited expressivity and generalization of standard LoRA.
method TensorGuide uses a unified tensor-train structure with controlled Gaussian noise to generate correlated low-rank matrices.
result TensorGuide achieves superior accuracy and scalability with fewer parameters compared to standard LoRA and TT-LoRA.
Tensor trains simplify solving complex PDEs efficiently.
problem Solving high-dimensional parabolic PDEs using traditional methods is computationally infeasible.
method Reformulate PDEs as backward stochastic differential equations and use tensor train format for compression and efficient computation.
result Tensor train methods achieve a good balance between accuracy and computational efficiency.
Proposes TTNPE for tensor data embedding with improved trade-offs.
problem Embedding multi-dimensional tensor data into low dimensions.
method Tensor Train Neighborhood Preserving Embedding (TTNPE) with novel optimization approaches.
result Improves classification, computation, and dimensionality reduction trade-offs.
Paper proposes a new LSTM model for spatio-temporal learning.
problem Challenging video tasks require learning long-term spatio-temporal correlations.
method Introduces a higher-order convolutional LSTM model with tensor train decomposition.
result Model achieves state-of-the-art performance with significantly fewer parameters.
Paper develops a new model for forecasting ocean currents.
problem Forecasting the Loop Current and its eddies for the Gulf of Mexico.
method Physics-informed Tensor-train ConvLSTM, incorporating prior physical knowledge.
result PITT-ConvLSTM outperforms state-of-the-art methods in volumetric velocity forecasting.
Tensor Train layer improves BLEU scores in NMT models.
problem Improving Neural Machine Translation (NMT) models' performance.
method Implemented Tensor Train layer in TensorFlow for NMT training.
result Higher learning rates and more 'rectangular' core dimensions improve BLEU scores.
Efficiently trains GPs with billions of inducing inputs using Tensor Train decomposition.
problem Training GPs with large numbers of inducing inputs.
method Tensor Train decomposition for variational parameters in stochastic variational inference.
result Achieves state-of-the-art results on several benchmarks.
Develops a new tensor classification method for high-dimensional data.
problem Efficient learning algorithms exploiting tensorial structure in high-dimensional multi-way arrays.
method Tensor Train Multi-way Multi-level Kernel (TT-MMK) combining Canonical Polyadic decomposition, Dual Structure-preserving Support Vector Machine, and Tensor Train approximation.
result The TT-MMK method provides higher prediction accuracy and is more reliable computationally compared to other techniques.
New method uses TT approximations to solve HJB equations for efficient sampling.
problem Efficiently sampling from complex probability densities.
method Direct time integration of HJB equations using Tensor Train compression.
result Sample-free, dimensionality-avoiding integration method.
Study compares WTT and DWT for FTIR data feature extraction of medicinal plants.
problem Improving machine learning efficiency with FTIR spectra of medicinal plants.
method Comparison of WTT and DWT for feature extraction, varying preprocessing steps.
result WTT and DWT yield similar results, improving clustering and classification accuracy.
Introduces TT-NF for more compact neural field representations.
problem Finding more compact and easy-to-fit neural field representations.
method Tensor Train parameterization trained with backpropagation.
result Low-rank compression improves downstream task quality metrics.
TensorHyper-VQC improves VQC scalability and robustness.
problem Scalability and noise sensitivity in VQC.
method Tensor-train-guided hypernetwork framework.
result TensorHyper-VQC achieves superior performance and robust noise tolerance.
Efficiently learns and transports posterior densities for real-time inference.
problem High computational cost of Bayesian inference for complex posterior densities.
method Tensor-train (TT) format for offline learning, conditional transport for online inference.
result Significant improvement in inference performance for high-dimensional problems.
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.
Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential Machines (ExM), a predictor that models all interactions of every order. The key idea is to represent an exponentially l…
A new model SMPS alleviates the exponential decay of correlations in MPS.
problem Exponential decay of correlations in Matrix Product States (MPS) limits their power in capturing long-range dependences.
method Introducing long-range interactions (shortcuts) to MPS to decrease correlation length while preserving computational efficiency.
result SMPS can decrease significantly the correlation length of MPS, improving its ability to capture long-range dependences.
E2M optimizes tensor density estimation by relaxing α-divergence to KL-divergence.
problem Analytical challenges in traditional α-divergence optimization for tensor-based density estimation. method E2M algorithm: relaxes optimization to KL-divergence, then applies tensor many-body approximation. result Flexible modeling of various low-rank structures and their mixtures.
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.
Quantum state preparation framework speeds up basket option pricing.
problem Limited practical benefit of quantum amplitude estimation due to state-preparation depth.
method Structure-aware tensor-train rank-based variational state preparation.
result State-preparation depth scaling replaced with linear scaling, maintaining low basket-pricing errors.
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.
A new RNN architecture reduces model size and improves performance.
problem Overparameterization and resource limitations in RNNs.
method Jointly encodes weight matrices using tensor-train factorization.
result Reduces model size by several orders of magnitude without sacrificing performance.
Tensor networks constrain kernel machines to Gaussian processes.
problem Speeding up kernel machines with reduced model complexity.
method Proving CPD and TT-constrained models recover Gaussian processes with i.i.d. priors.
result TT-constrained models exhibit more Gaussian process behavior than CPD for the same parameters.
New method for tensor completion from specific mode observations.
problem Recovering multiway data tensors from partial observations.
method Tensor train decomposition for fiber-wise observations.
result Deterministic recovery guarantees for specific observation patterns.
New framework finds more efficient linear layers over structured matrices.
problem Efficient alternatives for dense linear layers in neural networks.
method Unified framework searching over all linear operators, developing a taxonomy based on computational and algebraic properties.
result BTT-MoE provides substantial compute-efficiency gains over dense layers and standard MoE.