Chain-of-Density Prompting for Summaries

TL;DR: Chain-of-density prompting rewrites a summary at a fixed length, again and again, each time packing in one to three entities the previous version left out. It comes from a real 2023 paper that found denser is preferred up to a point, then readability drops. It's a specific, tested procedure, not just a request to make a summary denser.

What Is Chain-of-Density Prompting?

Chain-of-density (CoD) is an iterative prompting method for summarization: you generate an initial summary, then repeatedly rewrite it at the exact same length, folding in a small number of previously-missing facts each time without dropping anything already there. The length is fixed from the first draft to the last; only the concentration of information changes.

That constraint is the entire point. Ask a model to make a summary better and it will usually get longer. Chain-of-density forces the opposite move: hold the word count still and make the model earn every word by cutting filler to make room for facts. The paper opens with exactly this framing: prompt engineering for summarization usually optimizes for length or topic, and, in the authors' own words, "Selecting the “right” amount of information to include in a summary is a difficult task."

Where Does Chain-of-Density Actually Come From?

A lot of prompting "frameworks" circulating online are community-coined mnemonics with no traceable author. Chain-of-density is not one of those. It's a named research paper: Griffin Adams, Alexander R. Fabbri, Faisal Ladhak, Eric Lehman, and Noémie Elhadad, "From Sparse to Dense: GPT-4 Summarization with Chain of Density Prompting" (arXiv:2309.04269, posted September 8, 2023). The authors are affiliated with Columbia University, Salesforce AI, and MIT. arXiv's own listing marks it a preprint, with no separate conference or journal record, so it hasn't (as far as this listing shows) gone through venue peer review beyond arXiv's own moderation. Read that as a specific, citable, reproducible study, not as an unverified idea passed around online.

It also shouldn't be confused with chain-of-thought prompting, which despite the similar name is a different technique for a different job: chain-of-thought asks a model to reason step by step before answering a question, while chain-of-density asks it to rewrite an existing summary, repeatedly, at a fixed length. Both happen to trace back to real papers with named authors; see our guide to chain-of-thought prompting if that's the technique you actually need.

The paper's core finding, in its own words: "Summaries generated by CoD are more abstractive, exhibit more fusion, and have less of a lead bias than GPT-4 summaries generated by a vanilla prompt." Translated: densified summaries stop just copying the first few sentences of the source (lead bias), start combining information from multiple places in the article (fusion), and stop being lightly-edited extracts (abstraction). The method changes how the model summarizes, not only how much it says.

How Does the Chain-of-Density Method Actually Work?

The procedure has two fixed steps, repeated a fixed number of times, against one fixed length:

1. Generate an initial summary that is deliberately vague. The paper specifies roughly 80 words, written to be verbose and non-specific on purpose, padded with throat-clearing filler phrases, and covering only one to three entities. This sounds backwards, but it's deliberate: starting sparse leaves room to add facts on every later pass instead of running out of space on step one.
2. Repeat, a fixed number of times: identify 1 to 3 missing entities, then rewrite the summary at the same length to include them. Each missing entity the paper asks for must be relevant to the main story, specific (five words or fewer), novel (not already in the summary), faithful to the source article, and can come from anywhere in the article, not just the opening. The rewrite has to make room for the new entities through compression and fusion, and it may never drop an entity that was already included. If there's truly no room, the instruction is to add fewer new entities rather than lose old ones.

The paper runs this cycle 5 times, producing 5 increasingly dense versions of the same summary at a constant length. Here's the method adapted for a copy-paste chat prompt:

Article:
[paste your source text]

You will generate increasingly concise, entity-dense summaries of the
above article, at a fixed length of about [N] words.

Repeat the following two steps 5 times:

Step 1: Identify 1-3 informative entities from the article that are
missing from the previous summary.
Step 2: Rewrite the summary at the same length so it covers every
entity and detail from the previous summary plus the missing ones.

A missing entity must be:
- Relevant to the main story
- Specific (five words or fewer)
- Novel (not already in the previous summary)
- Faithful (actually present in the article)
- From anywhere in the article, not just the opening

Never drop an entity that's already in the summary. If there's no
room, add fewer new entities rather than cut old ones.

The first summary should be long, vague, and padded with filler
("this article discusses...") — that's intentional, it leaves room
to densify. Make every later rewrite tighter through compression and
fusion, not by shortening sentences into fragments.

Output all 5 summaries, labeled by step.

Compare that to the paper's own worked example, run on a short news article about a Formula 1 collision. Step 1 opens with padded, throat-clearing filler and names only the two drivers involved and the outcome for one of them. By step 5, the same word count also names the lap number, both cars' teams, the exact penalty (a five-second penalty and two superlicence points), the driver who avoided the crash and advanced two places, and who lapped whom afterward. Nothing from step 1 was dropped; it was compressed to make room.

What Did the Paper's Own Evaluation Actually Find?

The authors ran this on 100 articles from the CNN/DailyMail summarization dataset and measured token count, unique entities, and entity density (entities per token) at each of the 5 steps, against a human-written reference summary and a plain, single-shot baseline prompt asking for a very short summary at roughly the same length:

(Source: Table 1, Adams et al. 2023, read directly from the paper PDF.)

Two things stand out. First, density rises steadily and roughly doubles from step 1 to step 5 (0.089 to 0.167), while token count barely moves, which is the constraint working as designed. Second, the plain "vanilla" GPT-4 prompt, the kind almost everyone actually writes, lands at 0.122, below the human reference's 0.151. Chain-of-density's step 3, at 0.148, is the closest single step to how dense a human writer's summary actually is.

Then there's the human preference data, and it complicates the simple story. The authors themselves rated all 500 summaries (5 steps × 100 articles) for overall quality. Individually, 3 of the 4 raters gave the most first-place votes to step 1, the least dense, most padded version (28%, 43%, and 31.4% of their votes respectively). But in aggregate across all four raters, 61% of first-place votes went to summaries from step 3 or later. "The median preferred CoD step is in the middle (3), and the expected step is 3.06." Individual raters disagreed with each other more than they agreed (the paper reports a low Fleiss' kappa of 0.112), but the center of gravity, once you pool everyone, sits in the middle of the range, not at either end.

Automatic GPT-4-as-judge scoring (1 to 5 scale) tells a matching story: informativeness climbs through step 4, but the paper's own "Quality" and "Coherence" scores start declining after step 2 and step 1 respectively. Averaged across all five dimensions, the first and last steps score lowest, and the middle three (steps 2, 3, and 4) cluster close together and highest.

Is Denser Always Better? The Real Trade-Off

No, and that's the finding to actually take away, rather than a one-line instruction to ask the model for a denser summary. The paper's conclusion states plainly that a degree of densification is preferred, but past a point, packing in more entities per token makes a summary harder to read and to follow coherently. There is a real cost to density, and it shows up before the process is finished, not only at the extreme end.

For a lot of everyday summarizing, plain summarization is the right call: a quick recap of a meeting, a one-line description of an email thread, a TL;DR for a Slack message. None of those need entity density optimized against a fixed word budget; they need to be fast and correct. Chain-of-density earns its extra rewrite passes when the summary itself is the deliverable and has to carry maximum information in a fixed space: an executive briefing, a reference abstract, a card in a dashboard where the space is genuinely fixed and every word has to work.

How Do You Adapt This for ChatGPT, Claude, or Gemini Today?

The mechanism doesn't depend on GPT-4 specifically; the source article's own text is transformed one rewrite at a time regardless of which model runs the loop, so any current chat model can run the same two-step cycle. What's worth adjusting for 2026:

• Don't over-trust exactly 5 steps as a magic number. The paper picked 5 to have enough data points to plot a trend; the preferred step, per their own evaluation, was closer to 3. If you're running this by hand, try stopping earlier and comparing against your fixed-length draft, rather than assuming the last rewrite is the best one.
• Ask for a structured format if you're running this in an API pipeline. The original prompt asks for JSON output listing each step's missing entities and summary. Since 2023, all three major vendors have shipped schema-enforced structured output that goes further than a plain instruction to answer in JSON: OpenAI's Structured Outputs "ensures the model will always generate responses that adhere to your supplied JSON Schema," rather than just formatting a best effort. If you're automating this rather than reading it in a chat window, enforce the schema instead of hoping for valid JSON back.
• Read the middle output before you ship the last one. Because the paper's own human raters preferred step 3 over step 5 on aggregate, the practical move is to actually look at 2 or 3 of the intermediate rewrites rather than defaulting to whichever one finishes last.

This is a genuinely different discipline from breaking a big task into stages and checking each stage's output before moving on, which is a more general workflow problem. If you're decomposing a larger job, not just densifying one summary, see our guide to task decomposition for AI.

Chain-of-Density vs. Other Ways to Ask for a Summary

The middle column matters because it's the thing chain-of-density gets mistaken for. Asking a model once to make a summary denser or pack in more detail is a different, untested prompt: nothing forces the length to stay fixed, nothing identifies specific missing entities against the source, and there's no equivalent study behind it showing where quality starts to fall. It might still produce a useful result, but it isn't the technique this paper describes, and you can't borrow its preference data to justify a one-shot request for something denser.

The Bottom Line

Chain-of-density prompting is a real, specific, published procedure: hold the length fixed, repeat a rewrite-and-densify cycle, and stop before you've traded away readability for information you didn't need. The paper's own data says the sweet spot is usually somewhere in the middle of the process, not at either end, and that a plain summary is still the right call whenever fast and readable beats maximally dense. Use it where a summary is the deliverable and every word has a job; skip it everywhere else.