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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.
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 ...
So, we want to regard the conjugate gradient method as an iterative method. This also allows us to approximately solve systems where n is so large that the direct method would take too much time. We denote the initial guess for x ∗ by x 0 (we can assume without loss of generality that x 0 = 0, otherwise consider the system Az = b − Ax 0 ...
Next we rewrite in the last term as the sum over all weights of each weight times its corresponding input : = ′ [] Because we are only concerned with the i {\\displaystyle i} th weight, the only term of the summation that is relevant is x i w j i {\\displaystyle x_{i}w_{ji}} .
Universal approximation theorems are existence theorems: They simply state that there exists such a sequence ,,, and do not provide any way to actually find such a sequence. They also do not guarantee any method, such as backpropagation, might actually find such a sequence. Any method for searching the space of neural networks, including ...
Backpropagation through structure (BPTS) is a gradient-based technique for training recursive neural networks, proposed in a 1996 paper written by Christoph Goller and Andreas Küchler. [ 1 ] References
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 the worst case, this may completely stop the neural network from further learning. [1] As one example of this problem, traditional activation functions such as the hyperbolic tangent function have gradients in the range [-1,1], and backpropagation computes gradients using the chain rule.