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 […]
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The Chain Rule of Calculus for Univariate and Multivariate Functions
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 […]
A Gentle Introduction to Markov Chain Monte Carlo for Probability
Probabilistic inference involves estimating an expected value or density using a probabilistic model. Often, directly inferring values is not tractable with probabilistic models, and instead, approximation methods must be used. Markov Chain Monte Carlo sampling provides a class of algorithms for systematic random sampling from high-dimensional probability distributions. Unlike Monte Carlo sampling methods that are […]
Finding Value with Data: The Cohesive Force Behind Luxury Real Estate Decisions
The real estate industry is a vast network of stakeholders including agents, homeowners, investors, developers, municipal planners, and tech innovators, each bringing unique perspectives and objectives to the table. Within this intricate ecosystem, data emerges as the critical element that binds these diverse interests together, facilitating collaboration and innovation. PropTech, or Property Technology, illustrates this […]
Prompt Engineering for Effective Interaction with ChatGPT
With the explosion in popularity of generative AI in general and ChatGPT in particular, prompting has become an increasingly important skill for those in the world of AI. Crafting a prompt, the mechanism of interacting with a large language model (LLM) such as ChatGPT, is not the simple syntactic undertaking it would first appear to […]
ChatGPT as Your Expert Helper
ChatGPT can help us learn new programming languages, courses, techniques, and skills. It has become a go-to tool for many professionals seeking to improve their workflows or learn something new. ChatGPT expert helper prompts can reduce our dependence on Google and provide detailed plans for achieving goals. In this post, you will learn to leverage […]
A Gentle Introduction to Prompt Engineering
ChatGPT is a service provided by OpenAI that is a conversational large language model. It is widespread, and it is found to be very useful. Behind the scene, it is a large language model. Unlike the other LLMs that generate continuing text from the leading sentence you provided, ChatGPT enables you to ask questions or provide […]
Building Transformer Models with Attention Crash Course. Build a Neural Machine Translator in 12 Days
Transformer is a recent breakthrough in neural machine translation. Natural languages are complicated. A word in one language can be translated into multiple words in another, depending on the context. But what exactly a context is, and how you can teach the computer to understand the context was a big problem to solve. The invention […]
Calculus in Action: Neural Networks
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 […]
A Gentle Introduction to the Jacobian
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 […]