Attention is a concept that is scientifically studied across multiple disciplines, including psychology, neuroscience, and, more recently, machine learning. While all disciplines may have produced their own definitions for attention, one core quality they can all agree on is that attention is a mechanism for making both biological and artificial neural systems more flexible. In […]
There are different ways of debugging code in Python, one of which is to introduce breakpoints into the code at points where one would like to invoke a Python debugger. The statements used to enter a debugging session at different call sites depend on the version of the Python interpreter that one is working with, […]
Running your Python scripts is an important step in the development process because it is in this manner that you’ll get to find out if your code works as you intended it to. Also, it is often the case that we would need to pass information to the Python script for it to function. In […]
Classes are one of the fundamental building blocks of the Python language, which may be applied in the development of machine learning applications. As we shall see, the Python syntax for developing classes is simple and can be applied to implement callbacks in Keras. In this tutorial, you will discover the Python classes and their […]
An artificial neural network is a computational model that approximates a mapping between inputs and outputs. It is inspired by the structure of the human brain, in that it is similarly composed of a network of interconnected neurons that propagate information upon receiving sets of stimuli from neighbouring neurons. Training a neural network involves a […]
The chain rule is an important derivative rule that allows us to work with composite functions. It is essential in understanding the workings of the backpropagation algorithm, which applies the chain rule extensively in order to calculate the error gradient of the loss function with respect to each weight of a neural network. We will […]
The chain rule allows us to find the derivative of composite functions. It is computed extensively by the backpropagation algorithm, in order to train feedforward neural networks. By applying the chain rule in an efficient manner while following a specific order of operations, the backpropagation algorithm calculates the error gradient of the loss function with […]
The Laplace operator was first applied to the study of celestial mechanics, or the motion of objects in outer space, by Pierre-Simon de Laplace, and as such has been named after him. The Laplace operator has since been used to describe many different phenomena, from electric potentials, to the diffusion equation for heat and fluid […]
In the literature, the term Jacobian is often interchangeably used to refer to both the Jacobian matrix or its determinant. Both the matrix and the determinant have useful and important applications: in machine learning, the Jacobian matrix aggregates the partial derivatives that are necessary for backpropagation; the determinant is useful in the process of changing […]
Higher-order derivatives can capture information about a function that first-order derivatives on their own cannot capture. First-order derivatives can capture important information, such as the rate of change, but on their own they cannot distinguish between local minima or maxima, where the rate of change is zero for both. Several optimization algorithms address this limitation […]
