Related papers: Local tensor-train surrogates for quantum learning…
We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models, which are the sum of pairwise products instead of a…
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…
The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…
Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical…
In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…
In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that tensor is high-dimensional, and tensor values are generated by an unknown smooth function. The assumption…
One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…
Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider…
Quantum machine learning (QML) presents potential for early industrial adoption, yet limited access to quantum hardware remains a significant bottleneck for deployment of QML solutions. This work explores the use of classical surrogates to…
Estimating the total treatment effect (TTE) of a new feature in social platforms is crucial for understanding its impact on user behavior. However, the presence of network interference, which arises from user interactions, often complicates…
Variational quantum circuits are increasingly studied as continuous-function approximators, but quantum regression remains difficult to train when global losses, finite-shot stochasticity, and circuit-depth growth combine to produce weak or…
Recurrent neural networks (RNNs) with deep test-time memorization modules, such as Titans and TTT, represent a promising, linearly-scaling paradigm distinct from Transformers. While these expressive models do not yet match the peak…
This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov…
Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…
We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…
Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify…