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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]
For many years, sequence modelling and generation was done by using plain recurrent neural networks (RNNs). A well-cited early example was the Elman network (1990). In theory, the information from one token can propagate arbitrarily far down the sequence, but in practice the vanishing-gradient problem leaves the model's state at the end of a long sentence without precise, extractable ...
In theory, classic RNNs can keep track of arbitrary long-term dependencies in the input sequences. The problem with classic RNNs is computational (or practical) in nature: when training a classic RNN using back-propagation, the long-term gradients which are back-propagated can "vanish", meaning they can tend to zero due to very small numbers creeping into the computations, causing the model to ...
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 ...
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 ...
Convolutional neural networks that have proven particularly successful in processing visual and other two-dimensional data; [154] [155] where long short-term memory avoids the vanishing gradient problem [156] and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition, [157] [158] text ...
In such case, the generator cannot learn, a case of the vanishing gradient problem. [ 13 ] Intuitively speaking, the discriminator is too good, and since the generator cannot take any small step (only small steps are considered in gradient descent) to improve its payoff, it does not even try.