What is perplexity in LLM evaluation?

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1. Definition

Perplexity is defined as the exponential of the average negative log-likelihood of a sequence of tokens. In simpler terms:

• A lower perplexity means the model is less "confused" about what comes next.

• A higher perplexity means the model finds the sequence more unpredictable.

Mathematically, for a sequence of tokens $x_1, x_2, ..., x_N$ and a model that estimates $P(x_i | x_1, ..., x_{i-1})$:

$$\text{Perplexity} = \exp \left( -\frac{1}{N} \sum_{i=1}^{N} \log P(x_i | x_1, ..., x_{i-1}) \right)$$

2. Intuition

Think of perplexity as a measure of surprise:

• If a model predicts the next word with high probability, it’s less surprised, so perplexity is low.

• If a model is unsure (assigns low probability), it’s more surprised, so perplexity is high.

Example:

• A perfect model that always predicts the correct next word will have perplexity = 1.

• A random uniform model over $V$ words will have perplexity = V.

3. Usage in LLM Evaluation

• Perplexity is often used during training and validation to monitor how well the model is learning.

• It’s most meaningful when comparing models of the same size or trained on the same data.

• While a lower perplexity generally indicates better predictive performance, it does not always correlate perfectly with human-perceived quality for tasks like summarization or dialogue.

4. Key Takeaways

• Lower perplexity = better model prediction.

• Sensitive to tokenization (subword vs word-level tokens can affect values).

• Useful for quantitative comparison, but not a complete measure of LLM quality.

Read more :

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