So far in this series, we have worked with machine learning models that take inputs and produce predictions. A neural network does the same thing. The main difference is what happens between the input and the prediction. Instead of using a single equation, a neural network passes the information through a collection of small computational... Continue Reading →

Building Logistic Regression in NumPy In the previous two parts, we separated logistic regression into its main pieces. The model calculates a weighted score, passes it through the sigmoid function, measures the error with log loss, and updates its parameters using gradient descent. Now we can place those pieces inside a training loop and build... Continue Reading →

How Logistic Regression Learns In the previous part, we followed a logistic regression model from input features to a predicted probability. The model calculated a weighted score:z=w1x1+w2x2+⋯+bz = w_1x_1 + w_2x_2 + dots + b Then it passed that score through the sigmoid function:y^=σ(z)hat{y} = sigma(z) This gave us a probability between 0 and 1.... Continue Reading →

Before moving further into neural networks, it helps to spend some time with a much simpler model: logistic regression. Despite its name, logistic regression is mainly used for classification. It can help answer questions such as: Is this email spam or not? Does this image contain a cat or a dog? Is a medical finding... Continue Reading →

Not Every Deep Learning Model Solves the Same Problem After learning what a neural network is, it’s tempting to imagine that deep learning is built around one universal model. It isn’t. “Deep learning” is really a collection of architectures, each designed with different kinds of data and different kinds of problems in mind. They all... Continue Reading →

The Hardware Finally Caught Up With the Ideas By the mid-1980s, neural networks had already existed for decades. The problem wasn't a lack of ideas. It was figuring out how to train larger networks effectively. In 1986, David E. Rumelhart, together with Geoffrey Hinton and Ronald Williams, published the now-famous paper that popularized the backpropagation... Continue Reading →

Deep Learning Took Almost 70 Years to Become an Overnight Success Today, it feels like deep learning appeared almost out of nowhere. One day, it was mostly an academic topic, and a few years later, everyone was talking about ChatGPT, Claude, image generation, and AI assistants. The reality is much less dramatic. Most of the... Continue Reading →

Running Your First Deep Learning Model Is Simpler Than It Used to Be One of the biggest misconceptions I had before learning deep learning was that I would need an expensive computer to do anything meaningful. Training neural networks requires a significant amount of computation. For a long time, that meant having access to powerful... Continue Reading →

For a long time, “deep learning” sounded like one of those terms that mostly belonged to research labs, conference talks, or overly dramatic tech headlines. Then suddenly it became part of normal life. People started using systems powered by deep learning without necessarily thinking about the underlying models anymore. Recommendation systems, translation tools, image generation,... Continue Reading →

Most people write financial goals in the wrong order. They start with this year what they want to earn, save, buy. Then they extrapolate forward to five years, somewhat optimistically. Then they leave the fifteen-year horizon vague, because it feels too far away to think about concretely. Understanding the psychology of money can help explain... Continue Reading →