Paper to Intuition

Transform dense academic papers into genuine understanding through layered explanation and visual intuition.

Process

Get the paper - Ask for the arXiv link, PDF, or paper title
Extract the core - Identify the single key insight (one sentence)
Build the ladder - Create explanations at 4 levels
Visualize intuition - Generate interactive diagrams
Stress test understanding - "What breaks if we remove X?"

The Explanation Ladder

Generate explanations at each level, with each building on the last:

Level 1: ELI5 (1 paragraph)

No jargon, no equations
Use familiar analogies from everyday life
A curious 10-year-old should roughly get it

Level 2: Undergraduate (2-3 paragraphs)

Assume calculus, basic linear algebra, intro ML
Introduce key terms with definitions
Connect to textbook concepts they'd know

Level 3: Graduate (3-4 paragraphs)

Assume ML fundamentals, optimization, probability
Discuss relationship to prior work
Explain why naive approaches don't work
Cover the key equations with plain-English annotations

Level 4: Researcher (2-3 paragraphs)

Assume field expertise
Subtle technical contributions
Limitations and open questions
How this changes what's possible

Key Equations Breakdown

For each important equation:

[Equation in LaTeX]

In words: [Plain English translation]

Each term:
- [symbol]: [what it represents] [why it's there]

Intuition: [Why this mathematical form? What would change if we used a different form?]

Visual Intuition Artifact

Generate a self-contained HTML file with:

Architecture diagram - Boxes and arrows showing information flow
Interactive sliders - Manipulate key parameters, see effects
Before/after comparisons - What the method improves over baselines
Failure case visualization - When and why it breaks down

Use SVG for diagrams, vanilla JavaScript for interactivity. Dark theme, clean typography.

<!DOCTYPE html>
<html>
<head>
  <title>[Paper Name] - Visual Intuition</title>
  <style>
    :root { --bg: #1a1a2e; --text: #eee; --accent: #4f8cff; }
    /* Clean, research-aesthetic styling */
  </style>
</head>
<body>
  <h1>[Paper Title]</h1>
  <p class="tldr">[One-sentence insight]</p>

  <section id="architecture">
    <svg><!-- Information flow diagram --></svg>
  </section>

  <section id="interactive">
    <!-- Parameter sliders with live updates -->
  </section>

  <section id="comparisons">
    <!-- Before/after, ablations -->
  </section>
</body>
</html>

The "What Breaks?" Analysis

For each major component, explain:

What it does - The role this component plays
What breaks without it - Concrete failure mode
Why this solution - Alternatives considered, why this won
The tradeoff - What we pay for this choice (compute, complexity, assumptions)

Output Structure

Deliver as a structured document:

# [Paper Title]

**TL;DR:** [One sentence]

**Why it matters:** [One paragraph on significance]

## The Explanation Ladder

### ELI5
[...]

### Undergraduate Level
[...]

### Graduate Level
[...]

### Researcher Level
[...]

## Key Equations

### Equation 1: [Name]
[Breakdown as specified above]

## What Breaks If We Remove...

### [Component 1]
[Analysis]

### [Component 2]
[Analysis]

## Visual Intuition

[Link to or embed HTML artifact]

## Further Reading

- [Prerequisite paper 1]
- [Follow-up work 1]

Quality Standards

Every analogy must be accurate, not just catchy
Equations must be explained, not just translated
Visuals must reveal structure, not just decorate
The researcher-level section should contain insight, not just summary
Admit when something is genuinely confusing or poorly explained in the original paper

paper-to-intuition

Installation

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SKILL.md