This document discusses using computational graphs to calculate gradients for neural networks and other deep learning models. It explains that directly calculating gradients on paper for complex models is difficult and inefficient. Instead, computational graphs can be used as a data structure to represent the calculation process within a model. Nodes in the graph correspond to mathematical operations like matrix multiplications and activation functions. This allows gradients to be efficiently calculated by backpropagating through the graph. Examples of linear models, convolutional networks, and neural Turing machines are given to show how computational graphs can handle both simple and complex models.
- The document discusses how a neural network with one hidden layer can approximate any function from RN to RM to arbitrary precision using universal approximation.
- It provides an example of using a neural network with ReLU activations to approximate a function from R to R. The output is a linear combination of shifted and scaled ReLU units.
- With 4 hidden units, this network architecture can represent a bump function by combining 4 different weighted hidden units.
This document discusses using computational graphs to calculate gradients for neural networks and other deep learning models. It explains that directly calculating gradients on paper for complex models is difficult and inefficient. Instead, computational graphs can be used as a data structure to represent the calculation process within a model. Nodes in the graph correspond to mathematical operations like matrix multiplications and activation functions. This allows gradients to be efficiently calculated by backpropagating through the graph. Examples of linear models, convolutional networks, and neural Turing machines are given to show how computational graphs can handle both simple and complex models.
- The document discusses how a neural network with one hidden layer can approximate any function from RN to RM to arbitrary precision using universal approximation.
- It provides an example of using a neural network with ReLU activations to approximate a function from R to R. The output is a linear combination of shifted and scaled ReLU units.
- With 4 hidden units, this network architecture can represent a bump function by combining 4 different weighted hidden units.