The relation between vectors and neural networks
Imagine teaching a friend how to recognise different fruits, from apples to oranges to bananas. Now, imagine doing this with the power of mathematics and computers. This is where neural networks come in, a concept rooted in the basics of linear algebra, where “vectors” play a starring role. If this sounds complicated, don’t worry; we’ll break it down into simple, digestible parts.
In this blog, we’ll cover what vectors are, how they relate to data in neural networks, and how these networks, inspired by the human brain, make machines “learn” by recognizing patterns. By the end, you’ll have a clear understanding of how neural networks process information and how they use vectors as their building blocks.
What is a Vector?
To start, let’s talk about what a vector is. A vector is a mathematical object that has both magnitude (size) and direction. You can picture a vector as an arrow, where the length represents its magnitude, and the direction shows where it’s pointing.
Example: Imagine you’re at a grocery store and need to pick up three apples and two oranges. You could represent this as a vector like [3, 2] — where “3” is the number of apples and “2” is the number of oranges. In essence, you’ve created a “shopping list” vector with specific items in specific amounts.
In math, vectors usually look like this:
- [2, 5] — a 2D vector with two elements.
- [4, 7, 1] — a 3D vector with three elements.
Why Vectors Matter in Machine Learning?
In machine learning, vectors help represent data. For example, if you want a machine to recognize fruits, you might have to show it vectors with characteristics like size, color, and weight. So, an apple might be represented by a vector [size, color, weight] = [3, red, 150 grams], and a banana by [4, yellow, 120 grams]. Each fruit becomes a point in a multi-dimensional “fruit space” where machines can analyze and find patterns.
Neural Networks: Learning Like a Human Brain
Neural networks are inspired by the way the human brain works. Just as our brains use neurons to process information, a neural network has “artificial neurons” or “nodes” to do something similar. Think of these nodes as little mathematical decision-makers.
When we give the network data, it looks at each piece and tries to understand the patterns using multiple layers, such as:
- Input Layer — This layer takes in the data (e.g., the size and weight of a fruit).
- Hidden Layers — These layers process the data, making sense of it.
- Output Layer — This final layer makes the decision or prediction, like identifying a fruit as an apple or a banana.
Each connection between nodes has a “weight,” which determines how much influence one node has on the next. Think of this weight as a “preference.” Just like if you’re very hungry, your preference (or “weight”) for picking more apples goes up.
Training a Neural Network
Training is a process where we feed the neural network with a lot of data so it can “learn.” For instance, if we want a network to identify fruits, we show it images of fruits, and each image has a vector associated with it. The network looks at the vector, learns the differences, and adjusts the weights until it can correctly identify each fruit.
To visualize this, imagine teaching a kid to recognise an apple. At first, they might mistake a tomato for an apple. But with enough examples (apples and non-apples), the kid starts recognising the unique features of an apple. The neural network does something similar by adjusting its weights until it can recognise patterns and classify objects correctly.
Real-Life Example
A well-known example in machine learning is recognising handwritten digits. Imagine a postal service that wants to automatically read zip codes from envelopes. Each digit (0–9) is represented as a grid of pixels, and each pixel has a value depending on how dark it is. These pixel values form a vector.
The neural network “learns” by comparing the patterns in these pixel vectors to recognise each number. So, when it sees a new zip code, it can identify each digit accurately, just like you’d recognize handwriting differences from multiple people.
How Do Vectors and Neural Networks Work Together?
Vectors are the language of neural networks. Each vector tells the network something about the data — colors, shapes, weights, or even handwriting details. By converting real-world data into vectors, the network learns to process and make decisions about that data.
In technical terms:
- The input data is converted into vectors.
- Each vector passes through the network’s layers, where the nodes process it.
- The output vector gives the network’s “answer” — like recognising a digit or identifying a fruit.
Conclusion
Understanding vectors and neural networks is the first step toward seeing how machines make sense of the world. Vectors translate our data into a format that computers understand, while neural networks help computers “think” by recognizing and learning from patterns. Whether it’s identifying handwritten digits or recognizing fruits, these concepts help build the systems powering modern AI.
So, go ahead, dive deeper into the world of AI! And hey, if you liked this breakdown, make sure to follow The AI Guy. Why? Because who else is going to teach a neural network to recognize the difference between sarcasm and an actual reason to subscribe? 😉
