Related papers: Learning Paths from Signature Tensors

Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…

The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…

In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…

The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to…

We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…

Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…

In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…

In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…

Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and…

Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…