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CoD

Chain of Density

The length is fixed. That constraint is the entire mechanism.

AI & Prompt Engineering Pro Framework

What is CoD?

Chain of Density is a summarisation technique with one unusual rule: the model writes a deliberately vague summary, then rewrites it several times, adding missing detail at each pass while the word count stays exactly the same. The fixed length is not a formatting preference. It is the thing that makes the technique work.

Ask for a summary and you get one that is readable and thin — general phrasing, "the study found", a few headline numbers, and a strong bias toward whatever appeared in the first few pages. Ask for more detail and you get a longer summary, which is not the same thing at all. CoD forces the trade. If the summary cannot grow but must absorb three new named entities, the only way to fit them is to compress the vague phrasing, fuse two sentences into one and delete the filler — which is exactly the work a good human summariser does and the work a model will otherwise skip. Density comes out of the constraint, not out of asking for it.

Best used for
Long document summarization research paper digests news briefings executive summaries content compression without losing key information

Where CoD Came From

Adams et al., 2023 — "From Sparse to Dense"

The technique comes from "From Sparse to Dense: GPT-4 Summarization with Chain of Density Prompting" (Griffin Adams, Alex Fabbri, Faisal Ladhak, Eric Lehman and Noémie Elhadad, 2023). The method: have the model produce an initial entity-sparse summary, then iteratively fold in missing salient entities without increasing the length. The resulting summaries were measurably more abstractive, showed more fusion, and had less lead bias than summaries from an ordinary prompt.

Humans preferred the denser ones — up to a point

In a preference study over 100 CNN/DailyMail articles, readers preferred the denser CoD summaries to the vanilla ones, and rated them nearly as dense as human-written summaries. The paper is careful about the ceiling: it identifies a genuine trade-off between informativeness and readability. Densify far enough and a summary stops being prose and becomes a list of nouns nobody can read.

Which is why you choose the round, not the maximum

The practical consequence, and the part most write-ups omit. CoD does not produce a summary — it produces a ladder of them, and the best one for your purpose is usually not the last. Ask for every round to be shown, then pick. A briefing for someone who will read it aloud wants round three; a reference note for someone who already knows the material wants round five.

The 5 Slots, One at a Time

Each slot is a decision. Leave it out and the model still makes it — just without you.

1
The sparse first pass
A deliberately vague summary, written to be improved.

Counterintuitive and important: the first round should be bad on purpose — general, indirect, full of "the study found" and "several segments". A first pass that is already dense leaves the later rounds nothing to do, and the whole ladder collapses into one summary repeated five times.

Weak Write a good summary of this report.
Strong Write a 90-word summary that is deliberately entity-sparse — general, high-level, using indirect phrases like "the study found" and "several segments".
2
The fixed length
The same word count at every round, stated as a hard number.

The mechanism. Do not soften it. "Roughly the same length" is not a constraint and the summary will drift twenty per cent longer each round, which turns the technique into ordinary expansion. Give a number and a tolerance — 90 words, within five — and say explicitly that new entities have to be paid for by compressing what is already there.

Weak Keep it fairly concise as you add detail.
Strong Each round rewrites the previous summary at the SAME 90 words. The length must not grow: to fit new entities you have to compress the vague phrasing, fuse sentences and drop filler.
3
The entities to add
What counts as a missing entity, and how many per round.

Say what kind of thing you want folded in — named segments, dated findings, specific percentages, named competitors — or the model will add adjectives and call them detail. Two or three per round is the working range; more and the compression becomes violent.

Weak Add more detail each time.
Strong Each round adds two or three salient entities that were missing — named segments, specific percentages, dated findings, named competitors.
4
The two prohibitions
Never drop an earlier entity, never invent a new one.

Both are needed and they fail differently. Without the first, round four quietly deletes what round two added and the ladder stops accumulating. Without the second, compression pressure makes the model manufacture a plausible statistic to fill a gap — which is the one failure that survives into the finished summary looking like a fact.

Weak (nothing)
Strong Never drop an entity a previous round added, and never add an entity that is not in the source report.
5
Show every round
All the summaries, labelled, plus what each round added.

The output is a ladder and you want to see it. Requiring one line per round naming the entities added makes the progression auditable and makes it obvious which round is the right one to actually use — which is a decision you should be making rather than defaulting to the densest.

Weak Give me the final summary.
Strong Output five numbered sections, one per round, each followed by one line naming the entities that round added.

One Task, Before and After

The task: A 90-word summary of a 30-page market research report, densified over five rounds. Both prompts below are scored by our free prompt checker — paste either in and you will get the same number, because the scoring is deterministic.

26 Without CoD · weak
Summarise this long report.

Five words. You get a readable, forgettable paragraph drawn mostly from the first four pages, with two headline numbers and none of the segment detail the report exists to convey.

91 With CoD · strong
Summarise the market research report below using chain of density: an initial sparse summary, then four rounds of densification at a fixed length.

Round 1: write a 90-word summary that is deliberately entity-sparse - general, high-level, and using indirect phrases like "the study found" and "several segments".

Rounds 2 to 5: each round rewrites the previous summary at the SAME 90 words, adding two or three salient entities that were missing - named segments, specific percentages, dated findings, named competitors. The length must not grow. This is the constraint that does the work: to fit new entities you have to compress the vague phrasing, fuse sentences and drop filler, which is what makes the final summary dense rather than merely longer.

Never drop an entity that a previous round added, and never add an entity that is not in the source report.

Write for a product director who has not read the report and will use this to decide whether to commission a second phase. Output five numbered sections, one per round, each followed by one line naming the entities that round added. Work out the missing entities before each rewrite, rather than discovering them mid-sentence. For example:
```
Round 3 (90 words): [the rewritten summary]
Added: 34% repeat-purchase rate; the 25-34 segment; Q2 2026 fieldwork window.
```
Ensure every round is within five words of 90, and prioritise entities that would change the director's decision over ones that are merely interesting. Do not invent figures, segment names or dates that are not in the source, do not let readability collapse into a list of nouns, and do not add commentary outside the labelled rounds.

Ninety-one. The single most load-bearing phrase is "the SAME 90 words" — weaken it to "roughly the same length" and the technique degrades into writing a longer summary five times.

Ninety-one, and nothing checks whether the length actually held

One check is structurally out of reach, and the two failures specific to this technique are both invisible to scoring:

Role0 / 8

No persona slot — CoD is a procedure, not a brief. Eight points are available for adding one, and on our scorer a generic persona earns as many as a considered one, so the number tells you nothing.

Whether the rounds held lengthunscored

The entire mechanism, and no rubric sees it. Five rounds at 90, 108, 131, 160 and 195 words score exactly as well as five at 90 — and only the second is chain of density. Count the words on round five; it is a ten-second check that tells you whether the technique ran.

Whether readability survivedunscored

The paper names the trade-off explicitly. A final round that has become a comma-separated list of proper nouns scores fine and is unreadable — which is why you pick the round rather than taking the last.

So the two checks worth doing yourself take under a minute: count the words on the last round, and read it aloud. If it grew, the constraint did not hold. If you stumble reading it, you have gone one round past useful — and the one before it is probably the summary you wanted.

Copy-Paste Prompt Template

Replace the bracketed placeholders with your specific details.

[The source document, and the reader who will use the summary]

Round 1: [a deliberately SPARSE summary at N words — vague on purpose, so later rounds have work to do]

Rounds 2-5: [rewrite the previous summary at the SAME N words, adding 2-3 missing entities each time. Name what counts as an entity: people, dates, percentages, named segments]
[The length must not grow — new entities are paid for by compressing what is there]

[Never drop an entity an earlier round added. Never add one not in the source]

[Show every round, numbered, each with one line naming what it added — then pick the round that suits your reader rather than taking the last]

When CoD Fits — and When It Does Not

Reach for it
  • Long documents where the detail matters — research reports, contracts, post-mortems.
  • Executive summaries that must survive being the only thing anybody reads.
  • Compressing a transcript, where the vague first pass is otherwise the whole output.
  • Abstracts and briefing notes with a hard word budget.
  • Anywhere an ordinary summary keeps coming back correct but useless.
Use something else
  • Short source material. There is nothing to densify and the rounds repeat themselves.
  • Creative or narrative summarising, where fusion destroys the voice.
  • Anything needing an opinion or a recommendation — CoD compresses, it does not judge.
  • Cases where readability matters more than completeness. Stop at round two or three.
  • Sources you cannot verify. Compression pressure is exactly when a model invents a statistic.

10 Ready-Made CoD Prompts

Every prompt below was produced by the Frompting generator with CoD selected — not written by hand for this page. Each is scored by our prompt checker; the median is 83/100. Click one to open it, then copy.

A 30-page market research report 95
You are an expert market‑research analyst tasked with creating a concise, information‑dense executive summary of a 30‑page market research report.

**Task**
1. Produce an initial brief, sparse summary that captures the core findings, key metrics, and primary conclusions of the report.
2. Using the same word count as the first draft, rewrite the summary to increase information density, prioritizing the most critical insights while preserving the overall length.
3. Incorporate relevant market‑research concepts (e.g., Jobs‑to‑Be‑Done, research design choices, segmentation approaches, preference measurement, customer‑journey mapping, market‑sizing methods) where they naturally support the summarized content.

**Audience**: [AUDIENCE: specify who will read the executive summary – e.g., senior leadership, product team, investors]
**Purpose**: [PURPOSE: state the intended use of the summary – e.g., strategic decision‑making, investment pitch, product roadmap]
**Key Focus Areas** (if any): [FOCUS: list any particular sections or topics that must be emphasized – e.g., competitive landscape, consumer preferences, growth forecasts]

**Output**
- A single paragraph of approximately **200 words** (the same length for both drafts).
- The first paragraph is the sparse version; the second paragraph is the densified version.
- Present the two versions consecutively, clearly labeled “Initial Summary 1” and “Summary 2”.

**Quality Criteria**
1. Accuracy: all facts must reflect the source report; indicate any approximations.
2. Relevance: only include insights that directly support the stated purpose and audience.
3. Clarity: use plain language while correctly applying technical terms, defining them on first use.

**Boundary**
Do not add new data or speculative conclusions beyond what the original report contains.

If any of the placeholders above are unknown, state your assumptions and ask up to three clarifying questions before proceeding.

Before writing the final answer, work through the problem step by step and weigh the main trade-offs; present only the reasoned conclusion, not your working notes.
298 words · scores 95/100 strong
A long technical RFC 78
You are an expert technical summarizer.
Your task is to transform a lengthy technical RFC into a concise brief that retains all essential information.

1. Read the provided RFC text.
2. Produce an initial sparse summary that captures the core purpose, key specifications, and major implications in roughly the same length as the final brief.
3. Rewrite this summary to increase information density while keeping the word count unchanged, prioritizing the most critical details.
4. Perform a second rewrite following the same constraints, further tightening the language without sacrificing meaning.

The final output must be a single paragraph of exactly **[TARGET WORD COUNT]** words, written for **[AUDIENCE]**.

**Quality criteria**:
- Accuracy: all major technical points from the RFC are present and correctly represented.
- Brevity: no superfluous wording; each sentence contributes essential information.
- Clarity: terminology is precise yet understandable to the specified audience.

If any required details (e.g., the RFC content, audience characteristics, or desired word count) are missing, state your assumptions and ask up to three clarifying questions before proceeding.
169 words · scores 78/100 solid
A two-hour meeting transcript 88
You are an expert summarizer tasked with condensing a two‑hour meeting transcript into a concise, information‑dense summary.

The summary must be produced in three iterative passes, each pass rewriting the previous version to increase density while keeping the overall length constant. The final output should retain all critical points, decisions, and action items from the meeting.

**Audience:** [AUDIENCE: specify who will read the summary, e.g., senior leadership, project team, external stakeholder]
**Desired length:** [WORD COUNT: indicate the target word count for the final summary, e.g., 250 words]
**Format:** plain text paragraph(s) without headings; include a brief bullet list of action items at the end (no more than 5 items).

**Process:**
1. Produce an initial sparse summary that captures the main topics and speaker contributions, adhering to the target word count.
2. Rewrite the summary to be more information‑dense, preserving the same word count, by prioritizing the most important details and eliminating redundancies.
3. Perform a final rewrite that further compresses the content while still meeting the word‑count target, ensuring that key decisions and next steps are unmistakably clear.

**Quality criteria:**
- Accuracy: all factual statements must reflect the transcript.
- Completeness: every major decision and assigned action must be included.
- Clarity: the final summary should be easy to read and understand without additional context.

**Boundary:** Do not add any speculative content or information not present in the transcript. If any required detail is missing, note it briefly in brackets.
242 words · scores 88/100 strong
A research paper for non-specialists 83
You are a research‑communication specialist tasked with transforming a scholarly article into a concise, non‑technical abstract.

Your work proceeds in three iterative passes, each maintaining the same overall length while increasing information density:

1. **Initial condensation** – read the full paper and produce a brief, sparse summary that captures the core purpose, methods, primary results, and overall significance in plain language.
2. **Focused enrichment** – rewrite the summary, adding essential details that a non‑specialist needs to understand the study’s contribution, while keeping the word count unchanged.
3. **Final densification** – refine the text to maximize clarity and impact, prioritizing the most critical information and eliminating any remaining redundancies, still within the same length.

**Deliverable:** a single abstract of exactly **[TARGET_ABSTRACT_LENGTH] words** that a lay audience can read and grasp without specialist background.

**Quality criteria:**
- Uses clear, jargon‑free language while briefly defining any unavoidable technical terms.
- Accurately reflects the study’s objectives, methodology, key findings, and implications.
- Maintains logical flow and readability for non‑experts.

**Boundary:** Do not include detailed methodological tables, statistical formulas, or citations; focus solely on narrative explanation.

If any aspect of the request is unclear—such as the paper’s title, research field, or desired abstract length—state your assumptions and ask up to three clarifying questions before proceeding.

Before writing the final answer, work through the problem step by step and weigh the main trade-offs; present only the reasoned conclusion, not your working notes.
242 words · scores 83/100 solid
A year of customer feedback 79
You are an expert summarizer tasked with distilling a full year of customer feedback into a concise, information‑dense summary.

Your work will proceed in three passes, each producing a summary of the same length but increasingly dense with the most critical insights.

**Audience:** [AUDIENCE: who will read the summary, e.g., senior leadership, product team, marketing]
**Desired length:** [WORD COUNT: target number of words for each pass, e.g., 250]
**Key focus areas (if any):** [FOCUS AREAS: specific topics or metrics the user wants highlighted, e.g., satisfaction trends, recurring complaints]

**Process:**
1. Create an initial “sparse” version that captures all major themes and notable quotes, staying within the target word count.
2. Rewrite the same‑length summary, removing redundancies and emphasizing the most impactful points.
3. Produce a final, highly dense version that retains the essential insights while maximizing information per word, again respecting the same word count.

**Output format:**
- Pass 1: Sparse summary – plain paragraph.
- Pass 2: Refined summary – plain paragraph.
- Pass 3: Dense summary – plain paragraph.

**Quality criteria:**
- Accurately reflects the full range of feedback.
- Prioritizes insights that affect decision‑making.
- Uses clear, professional language without jargon unless necessary, defining any technical terms on first use.

If any of the placeholders above are unknown, state your assumptions explicitly and ask up to three clarifying questions before proceeding.
220 words · scores 79/100 solid
A commercial contract's key terms 83
You are a legal summarization specialist.
Your task is to transform a lengthy commercial contract into a concise list of its essential terms, preserving all critical obligations, rights, and conditions while keeping the overall length unchanged.

1. Produce an initial brief summary that captures the main parties, purpose, and scope of the agreement.
2. Refine this summary by iteratively rewriting it to increase information density, each pass retaining the same word count but prioritizing the most important clauses (payment, deliverables, term, termination, liability, confidentiality, governing law, dispute resolution, etc.).

Deliver the final output as a plain‑text bullet list, each bullet no longer than **[MAX_BULLET_LENGTH]: specify the maximum characters per bullet**. The entire list should not exceed **[TOTAL_WORD_LIMIT]: specify total word count**.

Quality criteria:
- **Accuracy**: all key contractual provisions must be correctly represented.
- **Completeness**: no major obligation or right is omitted.
- **Conciseness**: language is tight, avoiding unnecessary filler.

Exclude any full legal clauses or boilerplate text; focus only on the distilled terms.

If any essential details are missing, state your first assumption and then ask up to three clarifying questions before proceeding.

Write this for [AUDIENCE: who will read the output, and how much they already know]. Match the depth, vocabulary and examples to that reader.
211 words · scores 83/100 solid
A competitor's annual report 72
You are a business analyst specializing in concise executive summaries.
Your task is to create a two‑stage summary of the annual report for **[COMPETITOR NAME]**.

1. Produce an initial brief that captures the report’s main sections (financial performance, strategic initiatives, market outlook, risks) in a sparse style, using only the most essential points.
2. Rewrite that brief to be more information‑dense while keeping the total length exactly **[WORD COUNT]** words, prioritizing the facts that matter most to **[TARGET AUDIENCE]**.

Deliver the final dense summary as a single paragraph of the specified word count.
Quality criteria:
- Accuracy: all stated figures and statements must reflect the source report.
- Relevance: include only information that a senior decision‑maker would need.
- Clarity: language should be precise, avoiding unnecessary filler.

Exclude any speculative commentary, marketing language, or unrelated company details.

If any of the placeholders above are unknown, state your assumption and proceed, or ask up to three clarifying questions before completing the task.
163 words · scores 72/100 solid
A lengthy incident post-mortem 67
You are a concise technical writer tasked with compressing a lengthy incident post‑mortem into a highly information‑dense summary while preserving all critical details.

The summary must be crafted in three iterative passes:

1. Produce an initial sparse version that captures the core narrative and main findings in roughly the same length as the original.
2. Rewrite the version to increase information density, eliminating any redundancy and tightening language, while keeping the overall length unchanged.
3. Refine the text again to achieve maximum compactness, ensuring every sentence conveys essential insight and no important fact is omitted, still respecting the original length constraint.

The final output should be a single paragraph of approximately **[WORD COUNT]: specify the target word count for the compressed summary**.

Write in a clear, professional tone suitable for **[AUDIENCE]: e.g., engineering leadership, incident response team, or executive stakeholders**.

**Quality criteria:**
- All key incident details (timeline, root cause, impact, remediation steps, and lessons learned) are present.
- Language is precise, jargon‑appropriate for the audience, and free of unnecessary filler.
- The three‑pass process is evident in the progression of the text, showing increasing density without changing length.

**Boundary:** Do not include any speculative information beyond what is provided in the original post‑mortem. If any required detail is missing, state the assumption clearly before proceeding.
219 words · scores 67/100 workable
A long podcast episode 88
You are a concise content specialist tasked with creating a multi‑stage written summary of a long podcast episode.

The episode’s **topic** is: [TOPIC: brief description of the podcast subject].
Its **duration** is: [DURATION: total length in minutes].
The intended **reader** is: [AUDIENCE: who will read the summary, e.g., executives, students, general public].
The final summary should be **approximately**: [FINAL WORD COUNT: target length in words, e.g., 200].

**Task workflow**
1. Produce an initial sparse summary that captures the core narrative and main points, using roughly the same word count as the final target length.
2. Rewrite the summary, increasing information density while preserving the same word count, prioritizing the most critical details.
3. Perform a third rewrite that further compresses the content, again keeping the word count constant, to achieve maximal density without losing essential meaning.

**Output format**
- Three separate sections titled “Stage 1 – Sparse Summary,” “Stage 2 – Denser Summary,” and “Stage 3 – Maximal Density.”
- Each section must contain exactly the target word count (±5 words).
- Use clear, plain language; define any technical term on first use.

**Quality criteria**
- Accuracy: all key facts and arguments from the episode are correctly represented.
- Coherence: each version reads smoothly and logically despite compression.
- Brevity: no unnecessary filler or repetition.

If any of the placeholders above are unknown, state your assumptions explicitly and ask up to three clarifying questions before proceeding.
229 words · scores 88/100 strong
A policy document as a one-pager 77
You are a professional summarizer tasked with transforming a full policy document into a concise one‑page brief.

Your audience is [AUDIENCE: specify the primary readers, e.g., senior executives, compliance officers, staff]. The policy’s subject matter is [TOPIC: describe the main focus of the policy, e.g., data privacy, workplace safety]. The original document’s length is [ORIGINAL LENGTH: indicate approximate word or page count].

**Task**
1. Produce an initial sparse summary of the policy that captures all major sections and core points, limited to roughly 300–350 words (the length of one printed page).
2. Rewrite that summary to increase information density while keeping the same word count, ensuring that only the most critical details remain and any redundancies are removed.
3. Deliver the final dense one‑page version.

**Output format**
- Plain text, 300–350 words total.
- Begin with a brief heading that names the policy and its purpose.
- Follow with a concise paragraph for each major section (e.g., Scope, Responsibilities, Procedures, Enforcement).

**Quality criteria**
- Accuracy: all essential policy elements are retained.
- Clarity: language is clear and jargon‑free for the specified audience.
- Brevity: no unnecessary filler; each sentence adds substantive value.

**Boundary**
Do not include any examples, anecdotes, or background history that are not part of the core policy content.

If any of the placeholders above are unknown, state your assumption and proceed, or ask up to three clarifying questions before completing the summary.
238 words · scores 77/100 solid

Scores range from 67 to 95. They are shown as generated rather than cherry-picked — a library where every entry scores in the nineties tells you it was curated, not measured.

CoD vs the Alternatives

CoT Chain of Thought

The same iterative instinct pointed at reasoning rather than compression. CoT makes the steps of an argument explicit; CoD makes the passes of a summary explicit.

MECE Mutually Exclusive, Collectively Exhaustive

The structural approach to completeness. MECE asks whether your categories miss anything; CoD asks whether your summary does.

ICIO Instruction, Context, Input, Output

The production wrapper. In a pipeline, CoD is the Instruction and the document is the Input; ICIO handles the plumbing around it.

Zero-Shot No examples at all

The right first attempt. Try a properly specified plain summary before reaching for five rounds — most summarising does not need this.

SCQA Situation, Complication, Question, Answer

For when the summary needs to make an argument rather than convey a document. CoD is faithful; SCQA is persuasive.

Five Ways People Get CoD Wrong

1
Letting the length drift

The defining CoD failure, and it is silent. "Roughly the same length" gets you a summary that grows every round, which is expansion rather than densification. Give a number and a tolerance, then check the last round.

2
A first round that is already good

The sparse pass has to be genuinely sparse. If round one is dense, rounds two to five have nothing to add and you have paid five times for one summary.

3
Not saying what an entity is

Asked vaguely for "more detail", a model adds adjectives and clauses. Name the categories — people, dates, percentages, named segments — and you get detail rather than decoration.

4
Taking the last round automatically

The paper identifies a real informativeness-readability trade-off. The densest summary is often not the useful one; show every round and choose.

5
No prohibition on dropping

Without it, later rounds silently delete earlier entities to make room and the ladder stops accumulating. It looks like it worked.

6
Using it on a short source

Below a few thousand words there is nothing to compress, and the rounds become paraphrases of each other.

CoD Questions

What is chain of density prompting?

A summarisation technique: produce a deliberately sparse summary, then rewrite it several times, each pass adding missing entities while the word count stays fixed.

Where does it come from?

"From Sparse to Dense: GPT-4 Summarization with Chain of Density Prompting" (Adams, Fabbri, Ladhak, Lehman and Elhadad, 2023). The paper found CoD summaries more abstractive, with more fusion and less lead bias than summaries from a standard prompt.

Why does the length have to stay fixed?

Because that is the mechanism. If the summary may grow, new detail is simply appended. If it may not, the model has to compress and fuse what is already there to make room — which is what produces density rather than length.

How many rounds should I use?

Four or five is the usual working range. More matters less than seeing them all: show every round and pick the one that suits your reader, because the densest is often past the point of readability.

Is the last round always the best?

No, and the paper is explicit about the trade-off. Densification improves informativeness and costs readability. Read the final round aloud — if you stumble, use the one before it.

Can it be used on any document?

It needs enough source material to have entities worth surfacing. On short or already-terse input the rounds become paraphrases, and you would be better off with a well-specified plain summary.

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