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A basic block is the simplest building block studied in the original ResNet. [1] This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. Block diagram of ResNet (2015). It shows a ResNet block with and without the 1x1 convolution.
As an example, a single 5×5 convolution can be factored into 3×3 stacked on top of another 3×3. Both has a receptive field of size 5×5. The 5×5 convolution kernel has 25 parameters, compared to just 18 in the factorized version. Thus, the 5×5 convolution is strictly more powerful than the factorized version.
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.
Gated recurrent units (GRUs) are a gating mechanism in recurrent neural networks, introduced in 2014 by Kyunghyun Cho et al. [1] The GRU is like a long short-term memory (LSTM) with a gating mechanism to input or forget certain features, [2] but lacks a context vector or output gate, resulting in fewer parameters than LSTM. [3]
For example, the step function works. In particular, this shows that a perceptron network with a single infinitely wide hidden layer can approximate arbitrary functions. Such an f {\displaystyle f} can also be approximated by a network of greater depth by using the same construction for the first layer and approximating the identity function ...
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 ...
For example, the finite element method may be recast as a multigrid method. [3] In these cases, multigrid methods are among the fastest solution techniques known today. In contrast to other methods, multigrid methods are general in that they can treat arbitrary regions and boundary conditions .
A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).