Perplexity is a metric used to evaluate the performance of language models. It measures how well a language model is able to predict a sequence of words based on the probability distribution of the next word in the sequence.

In general, the lower the perplexity, the better the language model is at predicting the next word in a given sequence of words. Perplexity is calculated using the probability distribution of the next word given the preceding words in the sequence, according to the language model. The formula for perplexity is:

perplexity = 2^H, where H is the cross-entropy loss of the language model on a given test set.

A lower perplexity indicates that the language model is more confident in its predictions and assigns higher probabilities to the correct next word in the sequence. A higher perplexity, on the other hand, indicates that the language model is less certain and assigns lower probabilities to the correct next word.

Perplexity is commonly used to compare the performance of different language models on the same task or dataset. It is also used to tune hyperparameters of a language model during training, such as the learning rate or the number of layers in the model, to optimize its performance on a given task.