Perplexity

---
name: perplexity
description: This protocol evaluates language model memorisation and training data contamination by measuring how well the model predicts benchmark text compared to out-of-distribution baselines. Lower perplexity on benchmark passages relative to a clean baseline indicates the model has likely seen the text during training. Use when the user has predictions and gold and needs to compute perplexity.
metadata:
  skill_kind: metric
  source_arxiv: 2309.10677
  bibtex_key: li2023estimatingcontamination
  confidence: high
---

# perplexity

> Estimating Contamination via Perplexity: Quantifying Memorisation in Language Model Evaluation — Li et al. (2023) (arXiv:2309.10677, 2023)

## What this evaluates

This protocol evaluates language model memorisation and training data contamination by measuring how well the model predicts benchmark text compared to out-of-distribution baselines. Lower perplexity on benchmark passages relative to a clean baseline indicates the model has likely seen the text during training.

## Datasets

- **QuAC** — total ?; splits: test (-1)
- **BoolQ** — total ?; splits: test (-1)
- **SQuAD_v2** — total ?; splits: test (-1)
- **XSum** — total ?; splits: test (-1)
- **MMLU** — total ?; splits: test (-1)

## Metrics

- `perplexity` **(primary)** — range: other
  - Perplexity is computed as the exponentiated average negative log-likelihood of the tokens in the input text. The protocol compares the perplexity on benchmark samples against two baselines: a 'clean baseline' (text from post-training dates) and a 'memorised baseline' (text from training dates).

## Input / output format

**Input**: Benchmark text samples (passages or documents), truncated to the average length of the respective benchmark.

**Output**: Perplexity score for the input text, compared against clean and memorised baseline perplexities.

## Scoring recipe

```python
def compute_contamination_metric(model, benchmark_text, clean_baseline_text, memorised_baseline_text):
    pplx_bench = compute_perplexity(model, benchmark_text)
    pplx_clean = compute_perplexity(model, clean_baseline_text)
    pplx_mem = compute_perplexity(model, memorised_baseline_text)
    # Lower perplexity on benchmark vs clean baseline indicates memorisation
    return pplx_clean - pplx_bench
```

## Common pitfalls

- Truncating benchmark texts to average length may discard context critical for accurate perplexity estimation.
- Using Wikipedia/BBC news as baselines assumes uniform distribution across the domain, which may not hold for specific benchmark subsets.
- Perplexity is sensitive to tokenization and model version; results are not directly comparable across different LLM architectures without normalization.

## Evidence (verbatim from paper)

> We found all four foundation model exhibit significant memorisation behaviour on the three benchmarks. For large foundation models, e.g., gpt-3 and llama-13b,30b, benchmarks are largely memorised which leads to lower perplexity than the clean baseline.

## Citation

```bibtex
@misc{li2023estimatingcontamination,
  title={Estimating Contamination via Perplexity: Quantifying Memorisation in Language Model Evaluation},
  author={Li et al. (2023)},
  year={2023},
  note={arXiv:2309.10677}
}
```

- arXiv: 2309.10677