arXiv research

The study examines entropy and pressure at infinity in negatively curved manifolds, linking them to strong positive recurrence.

The architecture of Transformer is based entirely on self-attention, and has been shown to outperform models that employ recurrence on sequence transduction tasks such as machine translation. The superior performance of Transformer has been attributed to propagating signals over shorter distances, between positions in …

Given for instance a finite volume negatively curved Riemannian manifold $M$, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of $M$ and their linear divergence rates under the geodesic flow. As…

Verifies a conjecture for the figure eight knot.

It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, th…

We investigate the probability distributions of the recurrence intervals $τ$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresho…

Linear recurrent networks explain reinforcement learning performance in partially observable settings.

Understanding customer sentiments is of paramount importance in marketing strategies today. Not only will it give companies an insight as to how customers perceive their products and/or services, but it will also give them an idea on how to improve their offers. This paper attempts to understand the correlation of diff…

Method generates joint posterior samples of source and foreground mass distributions for gravitational lensing.

In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this process "grounding"). The approach is particularly well-suited for extracting large nu…

This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key …

This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.

The paper explores criteria for positivity of forms and proves their strong positivity in specific cases.

Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.

Recurrent models can produce infinite sequences, causing bias; new methods prevent this.

We investigate the spatial and temporal structures of four financial markets in Greater China. In particular, we uncover different characteristics of the four markets by analyzing the sector and subsector structures which are detected through the random matrix theory. Meanwhile, we observe that the Taiwan and Hongkong …

We define Recurrent Gaussian Processes (RGP) models, a general family of Bayesian nonparametric models with recurrent GP priors which are able to learn dynamical patterns from sequential data. Similar to Recurrent Neural Networks (RNNs), RGPs can have different formulations for their internal states, distinct inference…

mGRN improves multivariate time series prediction by managing marginal and joint memories.

ManifoldFlow relaxes fixed-spectrum Stiefel layers to learn a positive spectrum.

This paper proposes recurrent neuron networks (RNNs) for a fingerprinting indoor localization using WiFi. Instead of locating user's position one at a time as in the cases of conventional algorithms, our RNN solution aims at trajectory positioning and takes into account the relation among the received signal strength i…

This paper presents a novel latent variable recurrent neural network architecture for jointly modeling sequences of words and (possibly latent) discourse relations between adjacent sentences. A recurrent neural network generates individual words, thus reaping the benefits of discriminatively-trained vector representati…

Let $Γ'<Γ$ be two discrete groups acting properly by isometries on a Gromov-hyperbolic space $X$. We prove that their critical exponents coincide if and only if $Γ'$ is co-amenable in $Γ$, under the assumption that the action of $Γ$ on $X$ is strongly positively recurrent, i.e. has a growth gap at infinity. This genera…

Paper forecasts financial trading durations using a new point process model.

This study uses neural networks to approximate Bayesian filtering problems.

Real-world clinical time series data sets exhibit a high prevalence of missing values. Hence, there is an increasing interest in missing data imputation. Traditional statistical approaches impose constraints on the data-generating process and decouple imputation from prediction. Recent works propose recurrent neural ne…

We propose a multi-label multi-task framework based on a convolutional recurrent neural network to unify detection of isolated and overlapping audio events. The framework leverages the power of convolutional recurrent neural network architectures; convolutional layers learn effective features over which higher recurren…

We discuss relations among various positivities of knots and links, such as strong quasipositivity and quasipositivity. We give several pieces of supporting evidence for conjectural statements concerning these positivities and the defect of Bennequin inequality. Finally, we determine strong quasipositivity and quasipos…

Gradient descent optimally trains RNNs without overparameterization.

Recurrent neural networks (RNNs) are powerful architectures to model sequential data, due to their capability to learn short and long-term dependencies between the basic elements of a sequence. Nonetheless, popular tasks such as speech or images recognition, involve multi-dimensional input features that are characteriz…

Acoustic scenes are rich and redundant in their content. In this work, we present a spatio-temporal attention pooling layer coupled with a convolutional recurrent neural network to learn from patterns that are discriminative while suppressing those that are irrelevant for acoustic scene classification. The convolutiona…

Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of problems but only recently have found their way into generative image…

This paper proposed a method for stock prediction. In terms of feature extraction, we extract the features of stock-related news besides stock prices. We first select some seed words based on experience which are the symbols of good news and bad news. Then we propose an optimization method and calculate the positive po…

This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.

We show that the strong asymptotic class of Weil-Petersson (WP) geodesics with narrow end invariant and bounded annular coefficients is determined by the forward ending lamination. This generalizes the Recurrent Ending Lamination Theorem of Brock-Masur-Minsky. As an application we provide a symbolic condition for diver…

Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We sugge…

Cascades of information-sharing are a primary mechanism by which content reaches its audience on social media, and an active line of research has studied how such cascades, which form as content is reshared from person to person, develop and subside. In this paper, we perform a large-scale analysis of cascades on Faceb…

We show that a properly immersed minimal hypersurface in M x R_+ equals some M x {c} when M is a complete, recurrent n-dimensional Riemannian manifold with bounded curvature. If on the other hand, M has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph…

A simple baseline outperforms deep learning methods in transportation forecasting.

Predicting smartphone users location with WiFi fingerprints has been a popular research topic recently. In this work, we propose two novel deep learning-based models, the convolutional mixture density recurrent neural network and the VAE-based semi-supervised learning model. The convolutional mixture density recurrent …

New method for Transformer models to encode position information without sequential bias.

Recurrent neural network grammars (RNNG) are generative models of language which jointly model syntax and surface structure by incrementally generating a syntax tree and sentence in a top-down, left-to-right order. Supervised RNNGs achieve strong language modeling and parsing performance, but require an annotated corpu…

In this paper we consider Riemannian manifolds $(M^n,g)$ of dimension $n \geq 5$, with semi-positive $Q$-curvature and non-negative scalar curvature. Under these assumptions we prove $(i)$ the Paneitz operator satisfies a strong maximum principle; $(ii)$ the Paneitz operator is a positive operator; and $(iii)$ its Gree…

Predicting smartphone users activity using WiFi fingerprints has been a popular approach for indoor positioning in recent years. However, such a high dimensional time-series prediction problem can be very tricky to solve. To address this issue, we propose a novel deep learning model, the convolutional mixture density r…

Study solves a mathematical problem related to elliptic Schroedinger-to-Neumann maps.

Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well known difficulty in using RNNs is the \textit{vanishing or exploding gradient} problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogo…

Extends NAS to learn both intra-cell and inter-cell architectures for language modeling.

Traditional sequential multi-object attention models rely on a recurrent mechanism to infer object relations. We propose a relational extension (R-SQAIR) of one such attention model (SQAIR) by endowing it with a module with strong relational inductive bias that computes in parallel pairwise interactions between inferre…

LSTM models struggle with volatility prediction due to financial complexities.