scholarly journals Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Fabian Laakmann ◽  
Philipp Petersen
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Initial Conditions ◽  
Activation Function ◽  
Transport Equations ◽  
High Dimensional ◽  
Linear Transport ◽  
Approximation Rates ◽  
Curse Of Dimension ◽  
Efficient Approximation

AbstractWe demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For non-smooth initial conditions, the solutions of these PDEs are high-dimensional and non-smooth. Therefore, approximation of these functions suffers from a curse of dimension. We demonstrate that through their inherent compositionality deep neural networks can resolve the characteristic flow underlying the transport equations and thereby allow approximation rates independent of the parameter dimension.

Analysis of Non-Linear Activation Functions for Classification Tasks Using Convolutional Neural Networks

2019 ◽  
Vol 12 (3) ◽  
pp. 156-161 ◽  
Author(s):  
Aman Dureja ◽  
Payal Pahwa
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Activation Function ◽  
Primary Objective ◽  
Experimental Comparison ◽  
Activation Functions ◽  
Practical Applications ◽  
Network Activation ◽  
Non Linear ◽  
Hidden Layer

Background: In making the deep neural network, activation functions play an important role. But the choice of activation functions also affects the network in term of optimization and to retrieve the better results. Several activation functions have been introduced in machine learning for many practical applications. But which activation function should use at hidden layer of deep neural networks was not identified. Objective: The primary objective of this analysis was to describe which activation function must be used at hidden layers for deep neural networks to solve complex non-linear problems. Methods: The configuration for this comparative model was used by using the datasets of 2 classes (Cat/Dog). The number of Convolutional layer used in this network was 3 and the pooling layer was also introduced after each layer of CNN layer. The total of the dataset was divided into the two parts. The first 8000 images were mainly used for training the network and the next 2000 images were used for testing the network. Results: The experimental comparison was done by analyzing the network by taking different activation functions on each layer of CNN network. The validation error and accuracy on Cat/Dog dataset were analyzed using activation functions (ReLU, Tanh, Selu, PRelu, Elu) at number of hidden layers. Overall the Relu gave best performance with the validation loss at 25th Epoch 0.3912 and validation accuracy at 25th Epoch 0.8320. Conclusion: It is found that a CNN model with ReLU hidden layers (3 hidden layers here) gives best results and improve overall performance better in term of accuracy and speed. These advantages of ReLU in CNN at number of hidden layers are helpful to effectively and fast retrieval of images from the databases.

scholarly journals Trigonometric Inference Providing Learning in Deep Neural Networks

2021 ◽  
Vol 11 (15) ◽  
pp. 6704
Author(s):  
Jingyong Cai ◽  
Masashi Takemoto ◽  
Yuming Qiu ◽  
Hironori Nakajo
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Deep Neural Networks ◽  
Activation Function ◽  
Trigonometric Approximation ◽  
Model Parameters ◽  
Training Algorithms ◽  
Activation Functions ◽  
Classical Training ◽  
Sum Formula

Despite being heavily used in the training of deep neural networks (DNNs), multipliers are resource-intensive and insufficient in many different scenarios. Previous discoveries have revealed the superiority when activation functions, such as the sigmoid, are calculated by shift-and-add operations, although they fail to remove multiplications in training altogether. In this paper, we propose an innovative approach that can convert all multiplications in the forward and backward inferences of DNNs into shift-and-add operations. Because the model parameters and backpropagated errors of a large DNN model are typically clustered around zero, these values can be approximated by their sine values. Multiplications between the weights and error signals are transferred to multiplications of their sine values, which are replaceable with simpler operations with the help of the product to sum formula. In addition, a rectified sine activation function is utilized for further converting layer inputs into sine values. In this way, the original multiplication-intensive operations can be computed through simple add-and-shift operations. This trigonometric approximation method provides an efficient training and inference alternative for devices with insufficient hardware multipliers. Experimental results demonstrate that this method is able to obtain a performance close to that of classical training algorithms. The approach we propose sheds new light on future hardware customization research for machine learning.

scholarly journals Intrinsic motivation and episodic memories for robot exploration of high-dimensional sensory spaces

2020 ◽  
pp. 105971232092291
Author(s):  
Guido Schillaci ◽  
Antonio Pico Villalpando ◽  
Verena V Hafner ◽  
Peter Hanappe ◽  
David Colliaux ◽  
...  
Keyword(s):  
Neural Networks ◽  
Episodic Memory ◽  
Intrinsic Motivation ◽  
Computational Models ◽  
Deep Neural Networks ◽  
Image Sensor ◽  
Forward Kinematics ◽  
High Dimensional ◽  
Episodic Memories ◽  
Low Dimensional

This work presents an architecture that generates curiosity-driven goal-directed exploration behaviours for an image sensor of a microfarming robot. A combination of deep neural networks for offline unsupervised learning of low-dimensional features from images and of online learning of shallow neural networks representing the inverse and forward kinematics of the system have been used. The artificial curiosity system assigns interest values to a set of pre-defined goals and drives the exploration towards those that are expected to maximise the learning progress. We propose the integration of an episodic memory in intrinsic motivation systems to face catastrophic forgetting issues, typically experienced when performing online updates of artificial neural networks. Our results show that adopting an episodic memory system not only prevents the computational models from quickly forgetting knowledge that has been previously acquired but also provides new avenues for modulating the balance between plasticity and stability of the models.

scholarly journals Deep Neural Networks for High Dimension, Low Sample Size Data

2017 ◽  
Author(s):  
Bo Liu ◽  
Ying Wei ◽  
Yu Zhang ◽  
Qiang Yang
Keyword(s):  
Neural Networks ◽  
Sample Size ◽  
High Dimension ◽  
Deep Neural Networks ◽  
Genetic Data ◽  
High Dimensional ◽  
Large Sample Size ◽  
Prediction Problem ◽  
The Stability ◽  
Size Data

Deep neural networks (DNN) have achieved breakthroughs in applications with large sample size. However, when facing high dimension, low sample size (HDLSS) data, such as the phenotype prediction problem using genetic data in bioinformatics, DNN suffers from overfitting and high-variance gradients. In this paper, we propose a DNN model tailored for the HDLSS data, named Deep Neural Pursuit (DNP). DNP selects a subset of high dimensional features for the alleviation of overfitting and takes the average over multiple dropouts to calculate gradients with low variance. As the first DNN method applied on the HDLSS data, DNP enjoys the advantages of the high nonlinearity, the robustness to high dimensionality, the capability of learning from a small number of samples, the stability in feature selection, and the end-to-end training. We demonstrate these advantages of DNP via empirical results on both synthetic and real-world biological datasets.

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