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.
New analysis explains pathology of deep Gaussian processes.
Enhances RSCNs with hybrid regularization for nonlinear dynamics.
Lipschitz RNNs improve stability and performance in various tasks.
Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting substantially of a vertical contraction factor function and nonlinear transform…
DeepRSCN models nonlinear systems using stochastic configurations.
This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, exist…
DeepBayes uses neural networks to efficiently estimate parameters in complex dynamical models.
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingl…
SORSCNs improve nonstationary data modeling by self-organizing and adjusting network parameters.
This study uses high-frequency data to identify early warning signals for bank crises.
DynNet models dynamic responses of linear and nonlinear systems with fewer variables and higher accuracy.
Improves LSTM performance by initializing states via manifold learning.
Framework for reconstructing nonlinear systems from multi-modal time series data.
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dy…
Generalizes memory and forecasting capacities for nonlinear recurrent networks with dependent inputs.
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections and estimate system parameters of a recurrent network, given a sequence of node …
A common difficulty in applications of machine learning is the lack of any general principle for guiding the choices of key parameters of the underlying neural network. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear…
This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…
In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This feature is inspired by the communication principles in the nervous system of small …
A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. …
New neural networks with variable time constants for better time-series prediction.
This article demonstrates the possibility of constructing indicators of critical and crisis phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems such as recurrent analysis of dynamic systems and the calculation of permutation entropy are used. It is shown th…
Paper addresses LSTM stability for thermal systems using infinity-norm.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
We propose an autoencoding sequence-based transceiver for communication over dispersive channels with intensity modulation and direct detection (IM/DD), designed as a bidirectional deep recurrent neural network (BRNN). The receiver uses a sliding window technique to allow for efficient data stream estimation. We find t…
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide a sample complexity for this estimator in the case of stable dynamics, where th…
Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple ta…
The paper develops a convex parameterization for robust RNNs ensuring stability and robustness.
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is mo…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis testing and investigates potential differences in discriminant statistics between the…
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…
A new RNN model based on coupled oscillators mitigates gradient issues.
Neural networks predict traffic flow in smart cities.
Lyapunov analysis improves RNN performance prediction.
Nowadays, when crashes and crises are rather frequent events, an effective monitoring system for the international financial market is needed. Modern nonlinear methods, such as Recurrence Quantification Analysis (RQA), demonstrate the ability to reveal the regularities of the system behavior. Thus, they can be useful f…
Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures …
We extend Neural Processes (NPs) to sequential data through Recurrent NPs or RNPs, a family of conditional state space models. RNPs model the state space with Neural Processes. Given time series observed on fast real-world time scales but containing slow long-term variabilities, RNPs may derive appropriate slow latent …
This work addresses identifiability in sequential data with switching dynamics, introducing a new estimator.
VSE estimates complex processes from noisy measurements without a model.
We present a deep recurrent neural network architecture to solve a class of stochastic optimal control problems described by fully nonlinear Hamilton Jacobi Bellmanpartial differential equations. Such PDEs arise when one considers stochastic dynamics characterized by uncertainties that are additive and control multipli…
Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult…
We propose a method to infer stochastic low-rank RNNs from neural data.
Financial markets are systems with the complex behavior, that can be hardly analyzed by means of linear methods. Recurrence Quantification Analysis (RQA) is a nonlinear methodology, which is able to work with the nonstationary and short data series. Thus, we apply RQA for the studying of the critical events on financia…
Markovian RNN adapts to nonstationary data using HMM for better time series prediction.
Scalable verifier for recurrent neural networks using polyhedral abstractions.
Proposes a new model for better speech segmentation.