Chain of Density (CoD) is a prompting technique that produces high-quality summaries by starting with a sparse draft and iteratively making it denser — adding missing important information in each pass while keeping the summary the same length. The result is a summary that captures more of the source material than a single-pass summary of the same length.
Where the Technique Comes From
Chain of Density was introduced in Adams et al., 2023, "From Sparse to Dense: GPT-4 Summarization with Chain of Density Prompting." The paper found that human evaluators consistently preferred CoD summaries over single-pass summaries for factual density and overall quality. The core insight: asking for a summary directly produces a summary biased toward the most obvious, prominent information. The iterative densification process forces the model to find and include less prominent but still important information.
The Technique Step by Step
Each iteration follows the same structure:
- Re-read the source material
- Identify the most important entity, concept, or fact not currently in the summary
- Incorporate it into the summary by rephrasing — not by appending sentences
- The summary stays the same length
"Same length" is the critical constraint. If the model can simply add sentences, it will. Constraining the length forces it to rewrite and compress, which produces a denser information structure rather than a longer list.
A Practical Prompt
You will summarize the following article using the Chain of Density technique.
Step 1 — Write an initial sparse summary of the article in exactly 4 sentences. This summary will be vague and miss details — that is expected.
Step 2 — Review the summary. Identify the single most important entity, concept, or finding from the article that is NOT mentioned in the current summary. Rewrite the summary to include it. The rewritten summary must still be exactly 4 sentences. Do not add sentences — rewrite existing ones to fit more information in.
Step 3 — Repeat Step 2 two more times.
After 3 densification rounds, output only the final summary.
Article:
[article text here]
The number of rounds (3) and the fixed length (4 sentences) are parameters you can adjust. For longer articles, 5-7 sentences and 4-5 rounds produces better coverage.
Why This Beats Asking for One Summary Directly
When you ask for a summary in one shot, the model picks the most salient information — typically the headline claim, the main conclusion, and one or two supporting details. It optimizes for the most obvious reading of the source.
The iterative densification process has a different dynamic. After the first round, the model must identify what is missing rather than what is most prominent. This forces it to read more carefully and include secondary findings, methodological details, and important caveats that single-pass summaries consistently omit.
For meeting summaries, this is especially useful. A single-pass meeting summary captures the main decisions. A CoD meeting summary captures the main decisions plus the key concerns raised, the owners assigned, and the open questions — the things a single-pass summary typically misses because they are less narratively prominent.
Adjusting the Parameters
Number of rounds: 3 rounds is the sweet spot for most articles (500-3,000 words). For longer sources (academic papers, full reports), 4-5 rounds improves coverage. Diminishing returns set in after the 5th round for most sources — additional densification rarely surfaces meaningful new information.
Summary length: Match to the source length and use case. 4 sentences works for news articles and blog posts. 8-10 sentences for academic papers. 2-3 sentences for quick executive summaries where brevity is the priority.
What to target in densification: The default instruction ("most important entity or concept not mentioned") works for general summaries. For specific use cases, you can target specific elements: "Identify the most important quantitative result not mentioned" for research summaries, or "Identify the most important action item not mentioned" for meeting summaries.
Practical Applications
Meeting summaries. Run CoD on meeting transcripts. The first pass captures the decisions. Subsequent passes surface the open questions, the raised concerns, and the specific owners — the details that determine whether a meeting was actionable.
Article summaries. CoD outperforms single-pass summaries for articles with multiple claims and supporting evidence. The iterative process forces coverage of secondary evidence that single-pass summaries miss.
Document distillation. For long documents (product specs, research reports, legal agreements), CoD produces a summary that accurately represents the full document rather than just the introduction and conclusion — which is what single-pass summaries of long documents typically reflect.
Research paper summaries. Academic papers have a hypothesis, a methodology, findings, limitations, and implications. Single-pass summaries rarely cover all of these. CoD rounds can be directed to ensure each element is represented.
Implementing CoD in Code
For automated summarization pipelines, implement CoD as multiple sequential API calls:
from openai import OpenAI
client = OpenAI()
def chain_of_density_summarize(text: str, rounds: int = 3, sentences: int = 4) -> str:
summary = None
for round_num in range(rounds):
if round_num == 0:
prompt = f"""Write an initial sparse summary of the following text in exactly {sentences} sentences.
It is okay to be vague — we will improve it in subsequent rounds.
Text: {text}"""
else:
prompt = f"""Here is the current summary of a text:
{summary}
Identify the single most important entity, concept, or finding from the original text that is NOT mentioned in the current summary.
Rewrite the summary to include it.
The rewritten summary must be exactly {sentences} sentences.
Do not add sentences — rewrite to fit more information in the same space.
Original text for reference:
{text}
Return only the rewritten summary, no explanation."""
response = client.chat.completions.create(
model="gpt-4o",
messages=[{"role": "user", "content": prompt}]
)
summary = response.choices[0].message.content.strip()
return summary
This implementation runs each round as a separate API call, which is slightly more expensive than a single call but produces better results because each round can focus on the densification task without the cognitive load of tracking the full format at once.
When CoD Is Worth the Cost
CoD costs 3-5x more in tokens than a single-pass summary because of the multiple rounds. It is worth the cost when:
- The summary will be read by many people (meeting notes sent to a team)
- The source contains important secondary information (research findings, detailed documents)
- The summary will be used to make decisions (executive briefings, status reports)
- Missing information has consequences (project handoffs, compliance summaries)
It is not worth the cost for quick internal summaries, informal notes, or cases where the main point is all that matters and secondary details are not needed.
Summary
Chain of Density prompting produces information-denser summaries by iteratively finding and incorporating missing important information while keeping the summary length fixed. The technique consistently outperforms single-pass summarization for sources with multiple important elements. The key constraint — same length — forces compression and rewriting rather than simple appending. Use it when summary quality matters more than API cost.
Keep Reading
- Chain of Thought Prompting with Examples — the broader reasoning technique that underlies iterative prompting approaches
- Prompt Engineering Complete Guide 2026 — where CoD fits in the full landscape of prompting techniques
- Prompt Engineering for Research — applying advanced summarization to research workflows
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