Related papers: Dynamical systems' based neural networks
Sparse Neural Networks regained attention due to their potential for mathematical and computational advantages. We give motivation to study Artificial Neural Networks (ANNs) from a network science perspective, provide a technique to embed…
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks…
We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…
Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However,…
Optimizing a neural network's performance is a tedious and time taking process, this iterative process does not have any defined solution which can work for all the problems. Optimization can be roughly categorized into - Architecture and…
This work presents a neural network that consists of nodes with heterogeneous sensitivity. Each node in a network is assigned a variable that determines the sensitivity with which it learns to perform a given task. The network is trained by…
This paper introduces a new neural network model that aims to mimic the biological brain more closely by structuring the network as a complete directed graph that processes continuous data for each timestep. Current neural networks have…
This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th…
Two major uncertainties, dataset bias and adversarial examples, prevail in state-of-the-art AI algorithms with deep neural networks. In this paper, we present an intuitive explanation for these issues as well as an interpretation of the…
While deep feature learning has revolutionized techniques for static-image understanding, the same does not quite hold for video processing. Architectures and optimization techniques used for video are largely based off those for static…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…
Deep neural networks (DNNs) are vulnerable to small adversarial perturbations of the inputs, posing a significant challenge to their reliability and robustness. Empirical methods such as adversarial training can defend against particular…
Autonomous construction of deep neural network (DNNs) is desired for data streams because it potentially offers two advantages: proper model's capacity and quick reaction to drift and shift. While the self-organizing mechanism of DNNs…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
Many existing deep learning models are vulnerable to adversarial examples that are imperceptible to humans. To address this issue, various methods have been proposed to design network architectures that are robust to one particular type of…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…
We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…