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The gradient thus does not vanish in arbitrarily deep networks. Feedforward networks with residual connections can be regarded as an ensemble of relatively shallow nets. In this perspective, they resolve the vanishing gradient problem by being equivalent to ensembles of many shallow networks, for which there is no vanishing gradient problem. [17]
Sepp Hochreiter discovered the vanishing gradient problem in 1991 [20] and argued that it explained why the then-prevalent forms of recurrent neural networks did not work for long sequences. He and Schmidhuber later designed the LSTM architecture to solve this problem, [ 4 ] [ 21 ] which has a "cell state" c t {\displaystyle c_{t}} that can ...
Long short-term memory (LSTM) [1] is a type of recurrent neural network (RNN) aimed at mitigating the vanishing gradient problem [2] commonly encountered by traditional RNNs. Its relative insensitivity to gap length is its advantage over other RNNs, hidden Markov models , and other sequence learning methods.
This problem is also solved in the independently recurrent neural network (IndRNN) [87] by reducing the context of a neuron to its own past state and the cross-neuron information can then be explored in the following layers. Memories of different ranges including long-term memory can be learned without the gradient vanishing and exploding problem.
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 ...
Since Inception v1 is deep, it suffered from the vanishing gradient problem. The team solved it by using two "auxiliary classifiers", which are linear-softmax classifiers inserted at 1/3-deep and 2/3-deep within the network, and the loss function is a weighted sum of all three: L = 0.3 L a u x , 1 + 0.3 L a u x , 2 + L r e a l {\displaystyle L ...
For example, using a 5 × 5 tiling region, each with the same shared weights, requires only 25 neurons. Using regularized weights over fewer parameters avoids the vanishing gradients and exploding gradients problems seen during backpropagation in earlier neural networks. [2] [3]
Then, the backpropagation algorithm is used to find the gradient of the loss function with respect to all the network parameters. Consider an example of a neural network that contains a recurrent layer and a feedforward layer . There are different ways to define the training cost, but the aggregated cost is always the average of the costs of ...