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A residual neural network (also referred to as a residual network or ResNet) [1] is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition , and won the ImageNet Large Scale Visual Recognition Challenge ( ILSVRC ) of that year.
In mathematics, the concept of a residuated mapping arises in the theory of partially ordered sets. It refines the concept of a monotone function . If A , B are posets , a function f : A → B is defined to be monotone if it is order-preserving: that is, if x ≤ y implies f ( x ) ≤ f ( y ).
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The residual capacity of an arc e with respect to a pseudo-flow f is denoted c f, and it is the difference between the arc's capacity and its flow. That is, c f (e) = c(e) - f(e). From this we can construct a residual network, denoted G f (V, E f), with a capacity function c f which models the amount of available capacity on the set of arcs in ...
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: neural network parameters. In words, it is a neural network that maps an input into an output , with the hidden vector playing the role of "memory", a partial record of all previous input-output pairs. At each step, it transforms input to an output, and modifies its "memory" to help it to better perform future processing.
An echo state network (ESN) [1] [2] is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer (with typically 1% connectivity). The connectivity and weights of hidden neurons are fixed and randomly assigned.
In the example, the h and e values denote the label ๐ and excess x f , respectively, of the node during the execution of the algorithm. Each residual graph in the example only contains the residual arcs with a capacity larger than zero. Each residual graph may contain multiple iterations of the perform operation loop.