Related papers: Approximation Theory of Convolutional Architecture…
We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
Time series forecasting is essential for a wide range of real-world applications. Recent studies have shown the superiority of Transformer in dealing with such problems, especially long sequence time series input(LSTI) and long sequence…
In this paper, we use convolutional neural networks to address the problem of model identification for autoregressive moving average time series models. We compare the performance of several neural network architectures, trained on…
Deep Neural networks are efficient and flexible models that perform well for a variety of tasks such as image, speech recognition and natural language understanding. In particular, convolutional neural networks (CNN) generate a keen…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
Understanding the evolutionary patterns of real-world evolving complex systems such as human interactions, transport networks, biological interactions, and computer networks has important implications in our daily lives. Predicting future…
Over the last decade of machine learning, convolutional neural networks have been the most striking successes for feature extraction of rich sensory and high-dimensional data. While learning data representations via convolutions is already…
The investigation reported in this document focuses on identifying systems with symmetries using equivariant autoregressive reservoir computers. General results in structured matrix approximation theory are presented, exploring a two-fold…
Inspired by the tremendous success of deep Convolutional Neural Networks as generic feature extractors for images, we propose TimeNet: a deep recurrent neural network (RNN) trained on diverse time series in an unsupervised manner using…
Applying machine learning models to meteorological data brings many opportunities to the Geosciences field, such as predicting future weather conditions more accurately. In recent years, modeling meteorological data with deep neural…
Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional…
Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…
Major winning Convolutional Neural Networks (CNNs), such as AlexNet, VGGNet, ResNet, GoogleNet, include tens to hundreds of millions of parameters, which impose considerable computation and memory overhead. This limits their practical use…
We present a monocular object parsing framework for consistent keypoint localization by capturing temporal correlation on sequential data. In this paper, we propose a novel recurrent network based architecture to model long-range…
With the recent development and advancement of Transformer and MLP architectures, significant strides have been made in time series analysis. Conversely, the performance of Convolutional Neural Networks (CNNs) in time series analysis has…
Accurately estimating the remaining useful life (RUL) of industrial machinery is beneficial in many real-world applications. Estimation techniques have mainly utilized linear models or neural network based approaches with a focus on short…