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During the late 1980s, "skip-layer" connections were sometimes used in neural networks. Examples include: [17] [18] Lang and Witbrock (1988) [19] trained a fully connected feedforward network where each layer skip-connects to all subsequent layers, like the later DenseNet (2016). In this work, the residual connection was the form () + (), where ...
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.
The ResNet paper, [17] however, provided strong experimental evidence of the benefits of going deeper than 20 layers. It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in [17]).
However, at initialization, batch normalization in fact induces severe gradient explosion in deep networks, which is only alleviated by skip connections in residual networks. [3] Others maintain that batch normalization achieves length-direction decoupling, and thereby accelerates neural networks. [4]
In 2021, a very simple NN architecture combining two deep MLPs with skip connections and layer normalizations was designed and called MLP-Mixer; its realizations featuring 19 to 431 millions of parameters were shown to be comparable to vision transformers of similar size on ImageNet and similar image classification tasks. [25]
In the mathematical theory of artificial neural networks, universal approximation theorems are theorems [1] [2] of the following form: Given a family of neural networks, for each function from a certain function space, there exists a sequence of neural networks ,, … from the family, such that according to some criterion.
A skip graph is a distributed data structure based on skip lists designed to resemble a balanced search tree.They are one of several methods to implement a distributed hash table, which are used to locate resources stored in different locations across a network, given the name (or key) of the resource.
In one direction, subsequent works aimed to train increasingly deep CNNs that achieve increasingly higher performance on ImageNet. In this line of research are GoogLeNet (2014), VGGNet (2014), Highway network (2015), and ResNet (2015). Another direction aimed to reproduce the performance of AlexNet at a lower cost.