Related papers: Discrete Time Elastic Vector Spaces
Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical…
In this article, we first define the concept of ordered intervals, then introduce ordered fuzzy inner product and describe some of its properties.
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.…
For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…
This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…
Quantum mechanics requires a hermitian inner product <~,~> -- linear in one variable, antilinear in the other -- while the inner product (~,~) that comes most naturally from Euclidean path integrals is linear in each variable. Here we…
In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…
Most of existing embedding based recommendation models use embeddings (vectors) corresponding to a single fixed point in low-dimensional space, to represent users and items. Such embeddings fail to precisely represent the users/items with…
Embedding methods for product spaces are powerful techniques for low-distortion and low-dimensional representation of complex data structures. Here, we address the new problem of linear classification in product space forms -- products of…
In many scientific problems such as video surveillance, modern genomics, and finance, data are often collected from diverse measurements across time that exhibit time-dependent heterogeneous properties. Thus, it is important to not only…
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is…
We study the use of a time series encoder to learn representations that are useful on data set types with which it has not been trained on. The encoder is formed of a convolutional neural network whose temporal output is summarized by a…
In video analysis, understanding the temporal context is crucial for recognizing object interactions, event patterns, and contextual changes over time. The proposed model leverages adjacency and semantic similarities between objects from…
We explore self-supervised models that can be potentially deployed on mobile devices to learn general purpose audio representations. Specifically, we propose methods that exploit the temporal context in the spectrogram domain. One method…
Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the…
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…