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In machine learning, backpropagation [1] is a gradient estimation 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.
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Backpropagation allowed researchers to train supervised deep artificial neural networks from scratch, initially with little success. Hochreiter's diplom thesis of 1991 formally identified the reason for this failure in the "vanishing gradient problem", [2] [3] which not only affects many-layered feedforward networks, [4] but also recurrent ...
Back_Propagation_Through_Time(a, y) // a[t] is the input at time t. y[t] is the output Unfold the network to contain k instances of f do until stopping criterion is met: x := the zero-magnitude vector // x is the current context for t from 0 to n − k do // t is time. n is the length of the training sequence Set the network inputs to x, a[t ...
This can perform significantly better than "true" stochastic gradient descent described, because the code can make use of vectorization libraries rather than computing each step separately as was first shown in [6] where it was called "the bunch-mode back-propagation algorithm". It may also result in smoother convergence, as the gradient ...
Rprop, short for resilient backpropagation, is a learning heuristic for supervised learning in feedforward artificial neural networks. This is a first-order optimization algorithm. This algorithm was created by Martin Riedmiller and Heinrich Braun in 1992. [1]
In 1970, Seppo Linnainmaa published the modern form of backpropagation in his master thesis (1970). [23] [24] [13] G.M. Ostrovski et al. republished it in 1971. [25] [26] Paul Werbos applied backpropagation to neural networks in 1982 [7] [27] (his 1974 PhD thesis, reprinted in a 1994 book, [28] did not yet describe the algorithm [26]).
SciPy (pronounced / ˈ s aɪ p aɪ / "sigh pie" [2]) is a free and open-source Python library used for scientific computing and technical computing. [3]SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering.