Activation function in neural network

Download a PDF of the paper titled Microdisk modulator-assisted optical nonlinear activation functions for photonic neural networks, by Bin Wang and 6 other authors Abstract: On-chip implementation of optical nonlinear activation functions (NAFs) is essential for realizing large-scale photonic neural chips. To implement different neural processing and machine learning tasks with optimal performances, different NAFs are explored with the use of different devices. From the perspective of on-chip integration and reconfigurability of photonic neural network (PNN), it is highly preferred that a single compact device can fulfill multiple NAFs. Here, we propose and experimentally demonstrate a compact high-speed microdisk modulator to realize multiple NAFs. The fabricated microdisk modulator has an add-drop configuration in which a lateral PN junction is incorporated for tuning. Based on high-speed nonlinear electrical-optical (E-O) effect, multiple NAFs are realized by electrically controlling free-carrier injection. Thanks to its strong optical confinement of the disk cavity, all-optical thermo-optic (TO) nonlinear effect can also be leveraged to realize other four different NAFs, which is difficult to be realized with the use of electrical-optical effect. With the use of the realized nonlinear activation function, a convolutional neural network (CNN) is studied to perform handwritten digit classification task, and an accuracy as large as 98% is demonstrated, which verifies the...

tf . keras . activations . relu ( x , alpha = 0.0 , max_value = None , threshold = 0.0 ) Applies the rectified linear unit activation function. With default values, this returns the standard ReLU activation: max(x, 0), the element-wise maximum of 0 and the input tensor. Modifying default parameters allows you to use non-zero thresholds, change the max value of the activation, and to use a non-zero multiple of the input for values below the threshold. For example: >>> foo = tf . constant ([ - 10 , - 5 , 0.0 , 5 , 10 ], dtype = tf . float32 ) >>> tf . keras . activations . relu ( foo ) . numpy () array ([ 0. , 0. , 0. , 5. , 10. ], dtype = float32 ) >>> tf . keras . activations . relu ( foo , alpha = 0.5 ) . numpy () array ([ - 5. , - 2.5 , 0. , 5. , 10. ], dtype = float32 ) >>> tf . keras . activations . relu ( foo , max_value = 5. ) . numpy () array ([ 0. , 0. , 0. , 5. , 5. ], dtype = float32 ) >>> tf . keras . activations . relu ( foo , threshold = 5. ) . numpy () array ([ - 0. , - 0. , 0. , 0. , 10. ], dtype = float32 ) Arguments • x: Input tensor or variable. • alpha: A float that governs the slope for values lower than the threshold. • max_value: A float that sets the saturation threshold (the largest value the function will return). • threshold: A float giving the threshold value of the activation function below which values will be damped or set to zero. Returns A Tensor representing the input tensor, transformed by the relu activation function. Tensor will be of th...

As expected, the sigmoid function is non-linear and bounds the value of a neuron in the small range of . When the output value is close to 1, the neuron is active and enables the flow of information, while a value close to 0 corresponds to an inactive neuron. Also, an important characteristic of the sigmoid function is the fact that it tends to push the input values to either end of the curve (0 or 1) due to its S-like shape. In the region close to zero, if we slightly change the input value, the respective changes in the output are very large and vice versa. For inputs less than -5, the output of the function is almost zero, while for inputs greater than 5, the output is almost one. Finally, the output of the sigmoid activation function can be interpreted as a probability since it lies in the range . That’s why it is also used in the output neurons of a prediction task. 4. Tanh We observe that the tanh function is a shifted and stretched version of the sigmoid. Below, we can see its plot when the input is in the range : The output range of the tanh function is and presents a similar behavior with the sigmoid function. The main difference is the fact that the tanh function pushes the input values to 1 and -1 instead of 1 and 0. 5. Comparison As we mentioned earlier, the tanh function is a stretched and shifted version of the sigmoid. Therefore, there are a lot of similarities. Both functions belong to the S-like functions that suppress the input value to a bounded range. T...

Elements of a Neural Network Input Layer: This layer accepts input features. It provides information from the outside world to the network, no computation is performed at this layer, nodes here just pass on the information(features) to the hidden layer. Hidden Layer : Nodes of this layer are not exposed to the outer world, they are part of the abstraction provided by any neural network. The hidden layer performs all sorts of computation on the features entered through the input layer and transfers the result to the output layer. Output Layer: This layer bring up the information learned by the network to the outer world. What is an activation function and why use them? The activation function decides whether a neuron should be activated or not by calculating the weighted sum and further adding bias to it. The purpose of the activation function is to introduce non-linearity into the output of a neuron. Explanation: We know, the neural network has neurons that work in correspondence with weight, bias, and their respective activation function. In a neural network, we would update the weights and biases of the neurons on the basis of the error at the output. This process is known as back-propagation. Activation functions make the back-propagation possible since the gradients are supplied along with the error to update the weights and biases. Why do we need Non-linear activation function? A neural network without an activation function is essentially just a linear regression mod...

393 share edit What is ReLu? ReLu is a non-linear where x = an input value According to equation 1, the output of ReLu is the maximum value between zero and the input value. An output is equal to zero when the input value is negative and the input value when the input is positive. Thus, we can rewrite equation 1 as follows: where x = an input value Examples of ReLu Given different inputs, the function generates different outputs. For example, when x is equal to -5, the output of f(-5) is 0. By contrast, the output of f(0) is 0 because the input is greater or equal to 0. Further, the result of f(5) is 5 because the input is greater than zero. The Purpose of ReLu Traditionally, some prevalent non-linear activation functions, like • Computation saving - the ReLu function is able to accelerate the training speed of deep neural networks compared to traditional activation functions since the derivative of ReLu is 1 for a positive input. Due to a constant, deep neural networks do not need to take additional time for computing error terms during training phase. Solving the - the ReLu function does not trigger the vanishing gradient problem when the number of layers grows. This is because this function does not have an asymptotic upper and lower bound. Thus, the earliest layer (the first hidden layer) is able to receive the errors coming from the last layers to adjust all weights between layers. By contrast, a traditional activation function like sigmoid is restricted between 0 and...

Download a PDF of the paper titled Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark, by Shiv Ram Dubey and 2 other authors Abstract: Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: \url{

Research and Development Scientist at International Institute of Information Technology, Bangalore Bharath Krishnamuthy is a research and development scientist for the International Institute of Information Technology, Bangalore, with an expertise in AI, deep learning and robotics. Krishnamurthy has worked as a researcher since 2021. A rectified linear unit (ReLU) is an activation function that introduces the property of non-linearity to a deep learning model and solves the vanishing gradients issue. "It interprets the positive part of its argument. It is one of the most popular activation functions in deep learning. In artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs. A standard integrated circuit can be seen as a digital network of activation functions that can be “ON” or “OFF,” depending on the input. An example of the sigmoid activation function. | Image: An example of a tanh linear graph. | Image: Sigmoid and tanh were monotonous, differentiable and previously more popular activation functions. However, these functions suffer saturation over time, and this leads to problems occurring with vanishing gradients . An alternative and the most popular activation function to overcome this issue is the Rectified Linear Unit (ReLU). What Is the ReLU Activation Function? The diagram below with the blue line is the representation of the Rectified Linear Unit (ReLU), whereas the green line is a variant o...

Consider a supervised learning problem where we have access to labeled training examples (x^ To train our neural network, we can now repeatedly take steps of gradient descent to reduce our cost function \textstyle J(W,b).