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Delta Rule
In machine learning, the delta rule is a gradient descent learning rule for updating the weights of the inputs to artificial neurons in a single-layer neural network. It can be derived as the backpropagation algorithm for a single-layer neural network with mean-square error loss function. For a neuron j with activation function g(x) , the delta rule for neuron j 's i -th weight w_ is given by \Delta w_ = \alpha(t_j-y_j) g'(h_j) x_i , where * \alpha is a small constant called ''learning rate'' * g(x) is the neuron's activation function * g' is the derivative of g * t_j is the target output * h_j is the weighted sum of the neuron's inputs * y_j is the actual output * x_i is the i -th input. It holds that h_j = \sum_i x_i w_ and y_j=g(h_j) . The delta rule is commonly stated in simplified form for a neuron with a linear activation function as \Delta w_ = \alpha \left(t_j-y_j\right) x_i While the delta rule is similar to the perceptron's update rule, the derivati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gradient Descent
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a trajectory that maximizes that function; the procedure is then known as ''gradient ascent''. It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Artificial Neurons
An artificial neuron is a mathematical function conceived as a model of a biological neuron in a neural network. The artificial neuron is the elementary unit of an ''artificial neural network''. The design of the artificial neuron was inspired by biological neural circuitry. Its inputs are analogous to excitatory postsynaptic potentials and inhibitory postsynaptic potentials at neural dendrites, or . Its weights are analogous to synaptic weights, and its output is analogous to a neuron's action potential which is transmitted along its axon. Usually, each input is separately weighted, and the sum is often added to a term known as a ''bias'' (loosely corresponding to the threshold potential), before being passed through a nonlinear function known as an activation function. Depending on the task, these functions could have a sigmoid shape (e.g. for binary classification), but they may also take the form of other nonlinear functions, piecewise linear functions, or step functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Feedforward Neural Network
Feedforward refers to recognition-inference architecture of neural networks. Artificial neural network architectures are based on inputs multiplied by weights to obtain outputs (inputs-to-output): feedforward. Recurrent neural networks, or neural networks with loops allow information from later processing stages to feed back to earlier stages for sequence processing. However, at every stage of inference a feedforward multiplication remains the core, essential for backpropagationRumelhart, David E., Geoffrey E. Hinton, and R. J. Williams.Learning Internal Representations by Error Propagation. David E. Rumelhart, James L. McClelland, and the PDP research group. (editors), Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundation. MIT Press, 1986. or backpropagation through time. Thus neural networks cannot contain feedback like negative feedback or positive feedback where the outputs feed back to the ''very same'' inputs and modify them, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Backpropagation
In machine learning, backpropagation is a gradient computation method commonly used for training a neural network to compute its parameter updates. It is an efficient application of the chain rule to neural networks. Backpropagation computes the gradient of a loss function with respect to the weights of the network for a single input–output example, and does so efficiently, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this can be derived through dynamic programming. Strictly speaking, the term ''backpropagation'' refers only to an algorithm for efficiently computing the gradient, not how the gradient is used; but the term is often used loosely to refer to the entire learning algorithm – including how the gradient is used, such as by stochastic gradient descent, or as an intermediate step in a more complicated optimizer, such as Adaptive Moment Estimation. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Activation Function
The activation function of a node in an artificial neural network is a function that calculates the output of the node based on its individual inputs and their weights. Nontrivial problems can be solved using only a few nodes if the activation function is ''nonlinear''. Modern activation functions include the logistic ( sigmoid) function used in the 2012 speech recognition model developed by Hinton et al; the ReLU used in the 2012 AlexNet computer vision model and in the 2015 ResNet model; and the smooth version of the ReLU, the GELU, which was used in the 2018 BERT model. Comparison of activation functions Aside from their empirical performance, activation functions also have different mathematical properties: ; Nonlinear: When the activation function is non-linear, then a two-layer neural network can be proven to be a universal function approximator. This is known as the Universal Approximation Theorem. The identity activation function does not satisfy this property. W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Learning Rate
In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. A too high learning rate will make the learning jump over minima but a too low learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Perceptron
In machine learning, the perceptron is an algorithm for supervised classification, supervised learning of binary classification, binary classifiers. A binary classifier is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of Weighting, weights with the feature vector. History The artificial neuron network was invented in 1943 by Warren McCulloch and Walter Pitts in ''A Logical Calculus of the Ideas Immanent in Nervous Activity, A logical calculus of the ideas immanent in nervous activity''. In 1957, Frank Rosenblatt was at the Cornell Aeronautical Laboratory. He simulated the perceptron on an IBM 704. Later, he obtained funding by the Information Systems Branch of the United States Office of Naval Research and the Rome Air Development Center, to build a custom- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Heaviside Step Function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value are in use. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one. The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely. Heaviside developed the operational calculus as a tool in the analysis of telegraphic communications and represented the function as . Formulation Taking the convention that , the Heaviside function may be defined as: * a piecewise function: H(x) := \begin 1, & x \geq 0 \\ 0, & x * an indicator function: H(x) := \mathbf_=\mathbf 1_(x) For the al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chain Rule
In calculus, the chain rule is a formula that expresses the derivative of the Function composition, composition of two differentiable functions and in terms of the derivatives of and . More precisely, if h=f\circ g is the function such that h(x)=f(g(x)) for every , then the chain rule is, in Lagrange's notation, h'(x) = f'(g(x)) g'(x). or, equivalently, h'=(f\circ g)'=(f'\circ g)\cdot g'. The chain rule may also be expressed in Leibniz's notation. If a variable depends on the variable , which itself depends on the variable (that is, and are dependent variables), then depends on as well, via the intermediate variable . In this case, the chain rule is expressed as \frac = \frac \cdot \frac, and \left.\frac\_ = \left.\frac\_ \cdot \left. \frac\_ , for indicating at which points the derivatives have to be evaluated. In integral, integration, the counterpart to the chain rule is the substitution rule. Intuitive explanation Intuitively, the chain rule states that knowing t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
