The principle and application of rejection sampling in large model training

Rejection sampling is a common technique in the training of large language models. It samples based on the probability density function of the target distribution to generate samples that fit the target distribution. The purpose of rejection sampling is to increase the diversity of training data, thereby improving the generalization ability of the model. This method is particularly important in language model training because it can help the model learn richer and more accurate language expressions. By rejecting sampling, the model can generate text from different perspectives and styles, making it more adaptable and creative. In this way, the model can more accurately predict the next word or phrase when processing various types of text, thereby improving the overall generation quality. The application of rejection sampling can also alleviate the problem of training.

Rejection sampling is a basic idea that uses an auxiliary distribution to generate samples and accept or reject the samples according to a certain probability. Auxiliary distributions are usually simple distributions such as uniform distributions or Gaussian distributions. In rejection sampling, the probability of accepting a sample is proportional to the probability of the target distribution. If the generated sample conforms to the target distribution, the sample is accepted; otherwise, it is rejected and a new sample is regenerated. This method can be used to generate samples that satisfy a specific probability distribution, which is especially useful when the target distribution is complex or cannot be directly sampled. By rejecting sampling, you can effectively obtain a sample set that conforms to the target distribution.

For example, when training a text generation model, we can use rejection sampling to generate sentences that are grammatically correct but different from the training data to expand the diversity of the training data. Such an approach can improve the model's generative capabilities and creativity, enabling it to generate more creative and diverse text content.

In principle, we can use an auxiliary distribution, such as an n-gram model or language model, to generate samples. For example, suppose we adopt a 3-gram model. First, we randomly select a 3-gram sequence from the training data as the starting point. Next, according to the probability distribution in the 3-gram model, we randomly select a next word as the next word of the current sequence. If the generated sequence is reasonable under the grammar rules, we accept the sequence; otherwise, we reject the sequence and regenerate a new sequence. In this way, we can generate sample sequences that comply with grammatical rules.

For example, there are the following two sentences in the training data:

The cat sat on the mat.

The dog chased the cat.

In order to generate new samples, we can use the 3-gram model to generate new sentences. First, we randomly select a 3-gram sequence from the training data as the starting point, such as "The cat sat". Then, according to the probability distribution in the 3-gram model, we randomly select a next word as the next word of the current sequence, such as "on". Next, we update the current sequence to "cat sat on" and repeat the above steps until we generate a sentence that conforms to the grammatical rules. Eventually, we can get a new sentence, such as "The dog sat on the mat."

Combined with the above examples, it can be found that rejection sampling can be used to generate sentences that are different from the training data but are grammatically correct, so that the model has better understanding and generation capabilities for different types of sentences. . In addition, rejection sampling can also be used to generate sentences that are similar to the training data but have different meanings, allowing the model to better understand the semantics of the language.

In rejection sampling, it is very important to choose an appropriate auxiliary distribution. The auxiliary distribution should be simple enough to make it easy to generate samples, but close enough to the target distribution that the probability of accepting a sample is not too low. In practical applications, commonly used auxiliary distributions include n-gram models, language models, and context-based models.

However, there are still some problems and challenges in rejecting sampling. For example, if the probability density function of the target distribution is complex, then rejection sampling may be inefficient. Furthermore, if the rejection rate is too high, the diversity of the training data may be affected, resulting in reduced generalization ability of the model. Therefore, reasonable parameter adjustment and optimization need to be carried out in practical applications.

In short, rejection sampling is an important technique in large language model training. It can be used to increase the diversity of training data and improve the generalization ability of the model.

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