Backpropagation in LLMs

Weights play a major role in deciding an LLM’s behaviour and performance. The weights represent the strength of connections between neurons. These weights are adjusted during training to improve the performance of the model.

Each connection between two neurons has a specific weight associated with it. It represents the importance or strength of the connection. A high positive weight will have big effect on the activation of the second neuron. On the other hand, a negative weight indicates that the output of the first neuron will decrease activation of the second neuron.

In essence, backpropagation is a training algorithm used to train neural networks. It is a supervised learning method. It involves calculating the gradient of loss function with respect to parameters of the model. This gradient is used to update model’s parameters in the opposite direction of the gradient. It got established in the 1980s.

First, an error in model’s output is calculated. This error is propagated backwards through the network –layer by layer. It allows us to know how much each layer contributed to the entire error.

This information is used to update weights in each layer of the network.

The formula for this update is weight _new= weight__old — learning rate* data_weight

where

• weight_ new is the updated weight
• weight_old is the current weight
• learning rate is a hyperparameter that controls the size of the update.
• Delta_weight is the rate of change of the error with respect to the weight.
• Delta weight is calculated using calculus chain rule. It takes into account the contributions of weight in all subsequent layers of the network.
• Adjustment of weights improves learning and performance of the model. Weight are updated iteratively based on training data. The LLM slowly learns to associate patterns and relationships of the data, and the model makes better predictions and generalizations on unseen data.
• Weight initialization and optimization play a vital role in effectiveness of backpropagation. One has to choose appropriate initial values for weights. Optimizing hyperparameters such as learning rate are carefully chosen. These affect training significantly and also the overall performance of the LLM.