Common method: measuring the perplexity of a new language model

There are many ways to evaluate new language models, some of which are based on evaluation by human experts, while others are based on automated evaluation. Each of these methods has advantages and disadvantages. This article will focus on perplexity methods based on automated evaluation.

Perplexity is an indicator used to evaluate the quality of language models. It measures the predictive power of a language model given a set of data. The smaller the value of confusion, the better the prediction ability of the model. This metric is often used to evaluate natural language processing models to measure the model's ability to predict the next word in a given text. Lower perplexity indicates better model performance.

In natural language processing, the purpose of a language model is to predict the probability of the next word in a sequence. Given a sequence of words w_1,w_2,…,w_n, the goal of the language model is to calculate the joint probability P(w_1,w_2,…,w_n) of the sequence. Using the chain rule, the joint probability can be decomposed into the product of conditional probabilities: P(w_1,w_2,…,w_n)=P(w_1)P(w_2|w_1)P(w_3|w_1,w_2)…P(w_n| w_1,w_2,…,w_{n-1})

Perplexity is an indicator used to calculate conditional probability. It measures the entropy of the probability distribution predicted using the model. The perplexity is calculated as follows: given the test data set D, the perplexity can be defined as perplexity(D)=\sqrt[N]{\prod_{i=1}^{N}\frac{1}{P(w_i |w_1,w_2,…,w_{i-1})}}. Among them, N represents the number of words in the test data set D, and P(w_i|w_1,w_2,...,w_{i-1}) represents the prediction of the i-th word when the first i-1 words are known. Probability. The lower the confusion, the better the model predicts the test data.

Among them, N represents the total number of words in data set D. P(w_i|w_1,w_2,…,w_{i-1}) is the conditional probability of the model predicting the i-th word given the first i-1 words. The smaller the value of confusion, the stronger the prediction ability of the model.

The principle of perplexity

The principle of perplexity is based on the concept of information entropy. Information entropy is a measure of the uncertainty of a random variable. It means that for a discrete random variable X, the entropy is defined as: H(X)=-\sum_{x}P(x)\log P(x)

Among them, P(x) is the probability that the random variable X takes the value x. The greater the entropy, the higher the uncertainty of the random variable.

In language models, the calculation of perplexity can be transformed into the average of the entropy sum of the conditional probabilities of each word in a given test data set D. The smaller the value of the confusion, the closer the probability distribution predicted by the model is to the true probability distribution, and the better the performance of the model.

How to implement perplexity

When calculating perplexity, you need to use a trained language model to compare each character in the test data set. Predict the conditional probability of a word. Specifically, the following steps can be used to calculate the perplexity:

For each word in the test data set, use the trained language model to calculate its conditional probability P(w_i|w_1, w_2,…,w_{i-1}).

Take the logarithm of the conditional probability of each word to avoid underflow or error after the product of probabilities becomes the sum of probabilities. The calculation formula is:\log P(w_i|w_1,w_2,…,w_{i-1})

Add the negative logarithm of the conditional probability of each word to get Test the perplexity of the data set. The calculation formula is: perplexity(D)=\exp\left{-\frac{1}{N}\sum_{i=1}^{N}\log P(w_i|w_1,w_2,…,w_{i- 1})\right}

The calculation of perplexity requires the use of a trained language model, so the language model needs to be trained first during implementation. There are many methods for training language models, such as n-gram models, neural network language models, etc. During training, a large-scale text corpus needs to be used so that the model can learn the relationships and probability distributions between words.

In general, perplexity is a commonly used indicator to evaluate the quality of a language model. The predictive power of a language model can be assessed by averaging the sum of the entropy values of the conditional probabilities for each word in the test data set. The smaller the confusion, the closer the probability distribution predicted by the model is to the true probability distribution, and the better the performance of the model.

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