TL;DR
Every token in a prompt competes for the model's attention. Filler words, polite preambles, repetition — they don't vanish, they dilute the signal. The result: the model spreads its attention across the noise and gives a fuzzy answer. SDE is a principle that says: cut the noise, keep the signal.
The specific pain: you ask for an explanation and get generalities. You ask for writing and get fluff. Not because the model is bad, but because half your prompt is phrases like "could you possibly," "tell me a little about," "if it's not too much trouble." They don't help — they crowd out the words that carry meaning.
The method takes one step and doesn't add a single extra token. You don't add, you subtract: strip the polite wrappers, swap abstract nouns for concrete instructions, cut repetition, and use active verbs instead of nominalizations.
Want this for your own case? Apply this study to your task: AI adapts its method to what you are working on and writes the prompt.
Method Blueprint
1 step (edit the prompt before sending):
BEFORE: [politeness] + [meta-commentary] + [vague request] + [repetition]
AFTER: [active verb] + [concrete object] + [output format] + [parameters]
All in one prompt, no iterations or separate requests.
Example
Task: Write an investor summary for a startup pitch — a farm-to-door grocery delivery service in Chicago
Prompt (diluted — the way people usually write):
Hi! I need some help with a text. I'm building a startup
that has to do with food. Could you maybe write something like
a short description for investors? I'd like it to be
interesting and convincing. Thanks in advance!
Prompt (SDE version):
Write an executive summary for an investor: farm delivery, Chicago,
B2C, average order $45, LTV 18 mo.
Format: problem (1 sentence), solution (1 sentence),
market (TAM in dollars), traction (metrics), ask (amount + use of funds).
Length: 120 words.
Result: The second version produces structured text that fits the requested format exactly — with concrete blocks (problem, solution, market, traction, ask) at the right length. The first version produces generic motivational copy — pretty, but with no pitch structure. The model simply doesn't know what you actually need.
Why It Works
LLM weakness: the model doesn't choose what to focus on — it weighs all the words at once. "Could you possibly" carries as much weight as "format" or "metrics." More junk words — less weight for the important ones.
LLM strength: when every word carries meaning, the model reproduces the requested structure precisely. Specific words — specific answers. This isn't a metaphor, it's literally transformer mechanics: attention is redistributed toward tokens with high information weight.
Control knobs: - Drop "explain X" → replace with "List 5 causes of X with dates" or "Compare X and Y on 3 parameters" - Drop "briefly" → replace with "in 80 words" or "in 3 bullet points" - Active verb instead of a noun: "calculate" > "perform a calculation"; "compare" > "provide a comparison" - Cut repeated context: once you've named the topic, don't repeat it in the next sentence - State the output format explicitly: table / numbered list / word count
Prompt Template
{Active verb}: {concrete object} — {key parameters, comma-separated}.
Format: {output structure}.
Length: {number of words / points / lines}.
Placeholders:
- {Active verb} → Write / Compare / Calculate / Extract / List / Analyze
- {concrete object} → not "a text about sales" but "a cold outreach email for B2B SaaS"
- {key parameters} → numbers, units, names, dates, constraints
- {output structure} → table / numbered list / paragraphs with headings
- {number of words / points} → 150 words / 5 points / 3 paragraphs
Before/after examples using SDE rules:
| ❌ Before | ✅ After |
|---|---|
| Tell me a little about marketing | List 5 B2C marketing channels for apps: CPL, typical CAC in dollars |
| Write something creative | Write a 200-word detective story: Boston 1998, a detective, missing money |
| Can you help with some code? | Python: function that sorts a dict by value, returns a list of tuples |
| Briefly explain blockchain | Explain blockchain: 3 paragraphs, ledger analogy, no technical jargon |
🚀 Quick start — paste into the chat:
Here is an SDE prompt template. Adapt it to my task: {your task}.
Ask me questions to fill in the fields.
[paste the template above]
The LLM will ask about the specific object of your request, the parameters you need, and the output format you want — because without those it can't build a dense prompt. It will take the pattern from the template and adapt it to your task.
Why It Works: The Mechanics
A transformer processes every token through the attention mechanism: each word "looks at" all the others and decides what matters. The weights are normalized through softmax — meaning they sum to 100%. The more empty words, the smaller the share left for the meaningful ones.
That explains why "Write a 200-word detective story: Chicago, 1929, Prohibition" gets a better result than "I would find it really interesting if you could perhaps write some sort of short story in the detective genre" — even though the second version is longer and seems "richer."
Three mechanical principles in action: 1. No noise — remove tokens that carry no information about the task 2. Specificity — numbers, units, and names "weigh" more than vague adjectives 3. No repetition — name the context once and you're done
Limitations
⚠️ Methodological concern: In the paper's appendix, the main results table contains placeholders
[run expt]— meaning the experiment is described but the data isn't filled in. The numbers from the abstract (+8.4%) appear in the text, but the results table shows a template stub. That calls the final verification of the specific numbers into question.
⚠️ The principle isn't new: The idea of "cut the fluff from your prompts" is well known to experienced LLM users. The paper's value is in formalization (a formula, density classes, concrete heuristics), not discovery.
⚠️ Reasoning mode: All tests were run with thinking/reasoning mode turned off. The effect on models with extended reasoning (Claude 3.7 thinking, o3) wasn't studied. The authors expect a neutral or slightly positive effect.
⚠️ Simple tasks: The gain is smallest on easy tasks with factual answers (+4.9% on arithmetic). A dense prompt helps complex, nested requests more.
How They Tested It
The team took five top models (Claude 3.7, GPT-4o, Gemini 2.0 Flash, GPT-4o-mini, DeepSeek V3) and, for each question from seven benchmarks, built three versions of the prompt: diluted (polite preambles, hedging words, and repeated context added — SDE < 0.35), standard (the original, unchanged), and ultra-dense (everything extra removed, specifics added — SDE > 0.80). Crucially, the correct answer was the same in all three cases — only the packaging changed.
An interesting design detail: two custom benchmarks — NameIndex and MiddleMatch — specifically tested tasks with long lists and finding items in the middle of the context. That's exactly where SDE delivered the biggest gains (+13.7% and +11.4%). Makes sense: the harder the task and the longer the context, the more each "extra" token in the prompt costs — it literally pushes the needed information out of the attention zone.
Another important result: ultra-dense prompts were on average 34% shorter — yet gave more accurate answers. That directly contradicts the intuition that "the more you explain, the better it understands."
Original from the Paper
Density classes table (original):
Diluted < 0.40 "Can you maybe help me understand what AI is?"
→ Vague, over-padded responses. Model latches onto filler words.
Standard 0.40–0.65 "Explain artificial intelligence briefly."
→ Adequate response. Moderate focus and specificity.
Dense 0.65–0.80 "How does backpropagation update weights step-by-step?"
→ Focused, structured response. Strong alignment to intent.
Ultra-Dense > 0.80 "Derive backpropagation gradient: dL/dW for cross-entropy loss."
→ Highest accuracy. Near-zero hallucination on factual queries.
Three versions of the same question (ARC benchmark, item arc_001):
[DILUTED, SDE=0.29, 102 words]
Hey, I was hoping you could help me out with a science question. I'm not sure if you'll
know this, but I want to understand something about mixtures. Could you maybe tell me
which of the following options is actually a mixture and not a compound? I'd really
appreciate it.
A. oxygen and nitrogen in air B. sodium and chlorine in salt
C. hydrogen and oxygen in water D. nitrogen and hydrogen in ammonia
Please just reply with the letter of the correct answer in this format: The answer is <LETTER>.
[STANDARD, SDE=0.58]
Which of the following is a mixture rather than a compound?
A. oxygen and nitrogen in air B. sodium and chlorine in salt
C. hydrogen and oxygen in water D. nitrogen and hydrogen in ammonia
Reply with one letter in the format: The answer is <LETTER>.
[ULTRA-DENSE, SDE=0.87, 24 words]
Identify the mixture (not compound):
A. O₂ + N₂ in air B. Na + Cl in salt
C. H₂ + O in water D. N₂ + H₂ in ammonia
Reply: The answer is <LETTER>.
Context: This is the same question in three different packages. The correct answer is identical. Only the density changes — and so does the result.
SDE heuristics (original from the paper):
4.1 Remove filler and hedging tokens
- Delete: "Can you please", "I was wondering if", "Is it possible to", "If you don't mind"
- Remove: "maybe", "kind of", "sort of", "a bit"
- Delete: "I want to know about", "Tell me something about", "I'm curious regarding"
4.2 Replace abstract nouns with concrete specifics
- "explain X" → "List 5 causes of X with dates" / "Derive X step-by-step"
- "briefly" → "in 80 words" / "in 3 bullet points"
- Add units, quantities, and named entities wherever applicable
4.3 Eliminate redundancy
- Never restate the context after introducing it.
- Remove: "As I mentioned", "As stated above"
4.4 Maximize concreteness
- Active verbs over nominalized forms: "derive" > "provide a derivation of"
- Specific over general: "React 18 concurrent rendering" > "modern JavaScript feature"
- Quantify: "< 100ms latency" > "fast response time"
Adaptations and Extrapolations
💡 SDE + IPE: a combo with zero extra tokens
The paper showed that SDE + IPE (instruction at the end of the prompt) gives +11.7pp versus +8.4% for SDE alone. It's easy — just put the task at the end, after the context:
❌ Usual order:
Write a pitch deck for an investor.
[context: startup, metrics, market]
✅ SDE + IPE:
[context: farm startup, Chicago, B2C, avg order $45, LTV 18 mo., CAC $15]
Write an executive summary: problem / solution / market / traction / ask. 120 words.
🔧 Diagnosing the "fluff" in your own prompts
Before rewriting, you can ask the model to rate the density of the prompt itself:
Rate my prompt using the SDE (semantic density) principle:
find all filler words, polite preambles, repetitions, and abstract nouns.
Suggest a dense version with no fluff.
My prompt: [paste prompt]
The model will find the weak spots and rewrite it. Works as a quick filter before sending a complex request.
💡 SDE for the system prompt
The principle works not only for one-off requests but also for system prompts (the role instructions at the start of a chat):
❌ Diluted system prompt:
You are an assistant who helps with marketing. Please
be helpful and answer professionally. Try to give
good advice and help the user with their tasks.
✅ Dense system prompt:
Role: B2B SaaS marketing strategist.
Answer structure: problem → solution → impact metric.
Format: bullet points, numbers where possible, no generalities.
Tone: direct, no preambles.
The system prompt sets the behavior pattern for the whole conversation. The denser it is, the more precisely the model holds the role.
Resources
Paper: Semantic Density Effect (SDE): Maximizing Information Per Token Improves LLM Accuracy
Author: Amr Kamel Khalil Ahmed, MD, MSc — Public Health Department, Riyadh First Health Cluster, Ministry of Health, Saudi Arabia
Related work cited in the paper: - Leviathan, Y., Kalman, M., Matias, Y. — Prompt Repetition Improves Non-Reasoning LLMs (arXiv:2512.14982, 2025) — source of IPE and Prompt Repetition - Wei et al. — Chain-of-thought prompting elicits reasoning in LLMs (NeurIPS 2023) - Liu et al. — Lost in the middle: How language models use long contexts (TACL 2024) - Xu et al. — Re-reading improves reasoning in LLMs (arXiv:2309.06275, 2024)