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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.
The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network.It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [1] or it is specified in several implementations with different running times. [2]
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 ...
The admissible network G̃ f (V, Ẽ f ) is composed of the set of arcs e ∈ E f that are admissible. The admissible network is acyclic. For a fixed flow f, a vertex v ∉ {s, t} is called active if it has positive excess with respect to f, i.e., x f (u) > 0.
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Residual connections, or skip connections, refers to the architectural motif of +, where is an arbitrary neural network module. This gives the gradient of ∇ f + I {\displaystyle \nabla f+I} , where the identity matrix do not suffer from the vanishing or exploding gradient.
Physics-informed neural networks for solving Navier–Stokes equations. Physics-informed neural networks (PINNs), [1] also referred to as Theory-Trained Neural Networks (TTNs), [2] are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs).
Minimum cut displayed on the network (triangles VS circles). We now construct the network whose nodes are the pixel, plus a source and a sink, see Figure on the right. We connect the source to pixel i by an edge of weight a i. We connect the pixel i to the sink by an edge of weight b i. We connect pixel i to pixel j with weight p ij. Now, it ...