Introduction
The backpropagation algorithm not only marked the 1980s but redefined the landscape of Artificial Intelligence (AI). Its popularization in 1986 was the turning point that allowed neural networks to evolve from a limited theoretical concept into powerful, practical tools. This technical breakthrough not only solved previous problems but also opened the door to deep learning, which underpins much of modern AI today.
The 1986 Milestone: Rebirth of Neural Networks
The publication of the paper “Learning representations by back-propagating errors” by David E. Rumelhart, Geoffrey Hinton, and Ronald J. Williams in 1986 is considered a crucial moment in AI history. Although the algorithm already existed in a rudimentary form, this work formalized it, explained it clearly, and demonstrated it on multilayer networks. By presenting a precise and applicable mathematical derivation, it transformed neural networks into trainable and functional systems, laying the groundwork for deep learning.
What is Backpropagation?
Backpropagation is an algorithm for training artificial neural networks by calculating the gradient of the loss function with respect to each weight in the model. In simple terms, it allows the network to learn from its errors by adjusting its internal parameters. This iterative process is the cornerstone of modern supervised learning, and its efficiency has been key to scaling models to previously unthinkable levels of complexity.
The Training Cycle: Forward Pass and Error Calculation
The training of a neural network is divided into two phases. In the Forward Pass, data is fed into the network and processed layer by layer to generate a prediction. This prediction is compared with the actual label using a loss function, which quantifies the error. This value is essential for the next phase, as it indicates how far the model is from the correct answer.
Backward Propagation: The Heart of Learning
In the Backward Pass, the calculated error is propagated backward from the output layer to the previous layers. Using differential calculus, the algorithm determines how each weight contributed to the total error. This allows the weights to be adjusted precisely, minimizing the loss in future iterations. It is here that backpropagation demonstrates its power: it allows each neuron to learn its role in the overall performance of the model.
The Chain Rule: Mathematical Foundation
Backpropagation is based on the chain rule, a principle of calculus that allows for the differentiation of composite functions. Since a neural network is a sequence of nested functions, this rule allows for the calculation of how a small change in a weight affects the final result. Thanks to this property, the algorithm can update all network parameters efficiently and coherently.
Overcoming the First AI Winter
Before 1986, neural networks were practically abandoned. The book Perceptrons (1969) by Minsky and Papert had shown that single-layer models could not solve non-linear problems. Without a practical way to train deeper networks, the scientific community moved away from this line of research. Backpropagation solved that obstacle, allowing hidden layers to actively participate in learning.
Backpropagation is Not Optimization
It is important to distinguish between backpropagation and optimization. Backpropagation calculates the gradients, that is, it indicates the direction in which the weights should be adjusted. But the actual adjustment is performed by an optimizer, such as Stochastic Gradient Descent (SGD) or Adam. In other words, backpropagation provides the information, and the optimizer executes the change. This conceptual separation is key to understanding modern network training.
Connectionism and Distributed Processing
The 1986 paper was published in parallel with the volume Parallel Distributed Processing, which introduced the connectionist paradigm. This theory holds that knowledge does not reside in isolated units but in distributed patterns of activation in interconnected networks. Backpropagation fit perfectly into this vision, by allowing internal representations to be adjusted dynamically based on error.
The Foundation of Deep Learning
Backpropagation enabled the training of networks with multiple layers, which gave rise to Deep Learning. These networks can learn hierarchical representations of data, from simple patterns to complex abstractions. Although hardware was limited in 1986, the algorithm proved the approach was viable. With the advent of GPUs and big data, deep learning became a scalable reality.
Current Applications: From Vision to Language
Today, backpropagation is indispensable in models for computer vision, natural language processing, and content generation. Models like YOLO for object detection and Transformers like GPT and BERT for language are trained using backpropagation. This technique allows the models to adjust their millions (or billions) of parameters to capture nuances, contexts, and complex relationships in the data.
Relevance and Future Challenges
Despite its effectiveness, backpropagation faces challenges such as the vanishing gradient in very deep networks and the sequentiality of training. These problems have motivated the development of new architectures and techniques, such as batch normalization and the use of activation functions like ReLU. However, backpropagation remains the core of modern machine learning, and its legacy continues to drive the evolution of artificial intelligence.