Backpropagation

Backpropagation, short for backward propagation of errors, is the core algorithm that makes neural networkNeural NetworkA Neural Network is a computing system inspired by the structure of biological neural networks in the brain. It forms... training possible. It computes the gradient of the loss functionLoss FunctionA Loss Function quantifies the difference between a model's predictions and the true values, guiding the training pro... with respect to every weight in the network by applying the chain rule of calculus, propagating error signals from the output layer back through each hidden layer to the input. These gradients indicate the direction and magnitude of weight adjustments needed to reduce prediction errors. Combined with an optimizerOptimizerAn Optimizer is an algorithm that adjusts a neural network's weights during training to minimize the loss function. S... like SGD or Adam, backpropagation enables iterative training that progressively improves model performance. The Mechanics of Gradient ComputationDuring a forward pass, input data flows through the network, producing predictions at the output. The loss function computes the error between predictions and true values. Backpropagation then works backward: it computes the gradient of the loss with respect to the output layer weights, then uses these gradients and the chain rule to compute gradients for each preceding layer. Each layer's gradient depends on the gradients of the layers above it and the layer's own learned weights and activation functions. Modern deep learning frameworks like PyTorch and TensorFlow implement automatic differentiation, computing backpropagation gradients automatically for arbitrary network architectures. Relevance to Geospatial Deep LearningEvery deep learning model used in geospatial AI, from CNNs processing satellite imagerySatellite ImagerySatellite imagery consists of photographs and data captured by Earth observation satellites orbiting the planet. Thes... to Transformers analyzing temporal sequences, relies on backpropagation for training. Understanding backpropagation illuminates challenges in training deep networks, including vanishing gradients in very deep architectures (addressed by ResNetResNetResNet (Residual Network) is a deep neural network architecture that uses skip connections to enable training of very... skip connections), exploding gradients (mitigated by gradient clipping), and the computational cost of gradient computation for large models. The efficiency of backpropagation for specific architectures directly impacts the practical feasibility of training geospatial models on high-resolution, multi-band satellite imagery.