A Gentle Introduction to Tensors and Computational Graphs in Neural Networks
Beneath the surface of artificial intelligence lies a hidden structure, a blueprint for thought. Tensors, the data containers, and the computation graph, their guiding path, form the engine that drives AI decisions.
Let’s start by explaining what is a Tensor.
Tensors are a generalization of vectors and matrices. Computationally, we can think of tensors as a data container for storing multi-dimensional arrays.
There are different types of tensors, each with a different rank.
- A rank zero tensor is a scalar, which is simply a number.
- A rank one tensor is a vector, which is a list of numbers.
- A rank two tensor is a matrix, which is a list of lists of numbers.
- A rank three tensor can be thought of as a vector of matrices
You might wonder why bother using tensors instead of lists.
Tensors vs lists:
- Tensors excel at numerical computations. Their optimized structure and operations are significantly faster than manipulating nested lists, especially on GPUs, which are hardware accelerators often used in AI tasks. This speed boost translates to faster training and inference times for neural networks.
- Tensors also offer greater flexibility and expressiveness. They seamlessly represent multi-dimensional data, encompassing images, video sequences, and complex mathematical objects. Lists, primarily one-dimensional, struggle to handle such diverse data efficiently.
With the building blocks (tensors) identified, let’s explore the blueprints (computational graphs) that dictate how they’re assembled to make predictions.
Computational Graph:
Think of the computation graph as a map of your neural network’s decision-making process. It’s a web of nodes and arrows, with each node representing a calculation the network performs, and each arrow showing how the output of one calculation flows into the next.
The computational graph allows us to grasp how data is processed and transformed at each stage.
- Tracking Forward Pass Calculations: During inference (making predictions), we can follow the graph’s arrows to observe how input data is fed into the initial nodes, undergoes a series of operations (multiplications, additions, activation functions), and ultimately produces an output. This clarifies the decision-making process.
- Understanding Backpropagation for Learning: When the network makes mistakes, the graph becomes crucial for learning and improvement. Through a process called backpropagation, we traverse the graph in reverse, starting from the output and calculating gradients (how much each calculation needs to change to reduce errors). These gradients guide the adjustments of weights (connections between neurons), enabling the network to learn and refine its predictions.
Breakdown of the essential elements that come together to create the intricate blueprint of a neural network’s computational graph:
1. Nodes: The Brain Cells of the Network
- Represented as circles, nodes are the fundamental units of computation.
- Each node performs a specific mathematical operation, such as multiplication, addition, or applying an activation function.
- Collectively, nodes form the layers of the network, responsible for processing and transforming data.
2. Edges: The Pathways of Information Flow
- Depicted as arrows, edges connect nodes, indicating the flow of data between them.
- They carry the output of one node as the input to another, enabling communication and collaboration within the network.
3. Input Nodes: The Gateways to Data
- These nodes act as the starting points of the graph, receiving raw data from the outside world.
- They introduce the information that the network will analyze and learn from.
4. Output Nodes: The Final Decision-Makers
- Located at the end of the graph, output nodes produce the network’s final predictions or decisions.
- They represent the network’s understanding and interpretation of the input data.
5. Bias Nodes: The Subtle Influencers
- Bias nodes introduce a shift in the network’s calculations.
- They help the network learn more complex patterns and prevent overfitting to the training data.
6. Weights: The Strength of Connections
- Represented as numerical values associated with edges, weights determine the influence of one node’s output on another.
- These adjustable parameters are the heart of learning in neural networks, modified during training to improve performance.
Now that we’ve unpacked the essential components of the computational graph, we have a foundation for further exploration. Ahead, we’ll dissect the calculations within each node, backpropagation, and uncover how this blueprint guides the neural network’s journey from data to decision.
