Related papers: Stable Attractors for Neural networks classificati…

Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…

Artificial neural networks that can recover latent dynamics from recorded neural activity may provide a powerful avenue for identifying and interpreting the dynamical motifs underlying biological computation. Given that neural variance…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field.…

Training multi-layer neural networks (MLNNs), a challenging task, involves finding appropriate weights and biases. MLNN training is important since the performance of MLNNs is mainly dependent on these network parameters. However,…

Classification of posts in social media such as Twitter is difficult due to the noisy and short nature of texts. Sequence classification models based on recurrent neural networks (RNN) are popular for classifying posts that are sequential…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…

We propose self-adaptive training -- a unified training algorithm that dynamically calibrates and enhances training processes by model predictions without incurring an extra computational cost -- to advance both supervised and…

We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…

The Neural Autoregressive Distribution Estimator (NADE) and its real-valued version RNADE are competitive density models of multidimensional data across a variety of domains. These models use a fixed, arbitrary ordering of the data…

This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic…