A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends geometrical description of tensor manifolds in tree-based formats.
The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the d…
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density …
Tensorized random projections reduce high-dimensional tensor size efficiently.
Low-bit training framework reduces energy consumption in CNNs.
Bayesian tensor train method recovers streaming data with high accuracy.
EM optimizes tensor density estimation by relaxing -divergence to KL-divergence.
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
Efficiently price high-dimensional Bermudan options using tensor compression.
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…
MEI model improves knowledge graph completion by efficiently modeling interactions between embeddings.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
Tensor trains simplify solving complex PDEs efficiently.
An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the trace-free Ricci tensor is contr…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT) format -- have become a valuable tool for the solution of large-scale problems …
Guaranteed convergence for tensor factorization using Riemannian gradient descent.
Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neura…
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 allows us to develop an efficient initialization scheme based on Gaussian Proce…
This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language modeling, generative networks and industrial recommendation systems. BFLOAT16 is attrac…
Optimizes neural network training by dynamically updating Tucker decomposition ranks.
The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classi…
Efficiently samples complex distributions using tensor train format.
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of rank-structured functions that can be seen as deep neural networks with a sparse arc…
A substantial progress in development of new and efficient tensor factorization techniques has led to an extensive research of their applicability in recommender systems field. Tensor-based recommender models push the boundaries of traditional collaborative filtering techniques by taking into account a multifaceted nat…
TTRP method preserves distances in high-dimensional data with reduced storage and speed.
The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint connected components. Then we show that each of these connected components, composed …
GrateTile optimizes CNN feature map storage for efficient data access.
SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application based on MATALB. It provides a wide range of facilities for generating tensor data w…
Causal deep learning tackles causal inference using tensor factor analysis.
By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there i…
ENTED efficiently decomposes binary and count tensors using nonparametric Gaussian processes.
Visual objects are composed of a recursive hierarchy of perceptual wholes and parts, whose properties, such as shape, reflectance, and color, constitute a hierarchy of intrinsic causal factors of object appearance. However, object appearance is the compositional consequence of both an object's intrinsic and extrinsic c…
Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this study, we show that tensor networks can systematically partition structured dat…
A new method estimates rare events using tensor trains.
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. Among the growing literature addressing this problem, Gass et al…
This paper finds a new way to compress CNN weights, improving on pruning and quantization.
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means that for higher order data like matrices or more generally tensors, data should be…
Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction of every order comes at an exponential computational and memory cost (Curse of D…
Tree tensor networks balance model complexity and empirical risk for high-dimensional function approximation.
New method uses TT approximations to solve HJB equations for efficient sampling.
This paper develops a method to train compact neural networks with reduced memory and computational costs.
New method shows fully-connected networks can learn convolutional structures from data.
Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further extensions of such algorithms. One of the new approaches to the probabilistic D…
Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in…
The paper models network formation using mixed logit models.
SoccerCPD detects tactical changes in soccer matches using spatiotemporal tracking data.
New method accelerates CNNs for mobile devices by approximating tensors and quantizing weights.
Unified multilinear model for causal factor disentanglement.