Skill 14: LLM Textbook + Practice Environments（LLM教科书 + 练习环境）

Source: https://x.com/karpathy/status/1885026028428681698 | https://x.com/karpathy/status/1960803117689397543 "Take LLMs to school" | "Environments for RL" posts

Core Principle

LLMs learn like students. Give them textbooks, worked problems, and practice gyms.

Karpathy's insight: the missing ingredient in LLM training isn't more parameters — it's practice environments where agents can try → fail → see feedback → try again. Like a student who reads theory but also needs problem sets.

Apply this to your agents: build environments where they can practice a skill with automatic scoring, not just generate output into the void.

The Three Training Data Types

Every good learning environment needs all three:

1. EXPOSITION (pretrain equivalent)
   → Background knowledge, concepts, context
   → The "textbook chapter" the agent reads before practicing
   
2. WORKED EXAMPLES (SFT equivalent)
   → Complete input-output pairs with reasoning shown
   → "Here's a solved problem — learn the pattern"
   
3. PRACTICE PROBLEMS with feedback (RL equivalent)
   → Problems with verifiable correct answers
   → Automatic scoring so agent knows how it did
   → Enough variety that memorization doesn't work

Building a Practice Gym (General Template)

For any skill you want an agent to get better at:

#!/usr/bin/env python3
"""
Practice Gym for: [SKILL_NAME]
Karpathy-style RL environment for agent skill development
"""

import json
import random
from typing import Callable

class PracticeGym:
    """
    A practice environment where an agent can repeatedly attempt
    a task and receive automatic feedback.
    """
    
    def __init__(self, task_generator: Callable, scorer: Callable):
        self.task_generator = task_generator  # generates new practice problems
        self.scorer = scorer                   # returns 0.0-1.0 score for an attempt
        self.history = []
    
    def sample_task(self):
        """Generate a new practice problem."""
        return self.task_generator()
    
    def evaluate(self, task, attempt):
        """Score an agent's attempt. Returns dict with score + feedback."""
        score = self.scorer(task, attempt)
        result = {
            "task": task,
            "attempt": attempt,
            "score": score,
            "passed": score >= 0.8,
        }
        self.history.append(result)
        return result
    
    def summary(self):
        """Summarize performance across all attempts."""
        if not self.history:
            return "No attempts yet."
        scores = [r["score"] for r in self.history]
        return {
            "total_attempts": len(scores),
            "avg_score": sum(scores) / len(scores),
            "pass_rate": sum(1 for s in scores if s >= 0.8) / len(scores),
            "recent_trend": "improving" if scores[-1] > scores[0] else "declining"
        }

Practice Environment Design Prompt

Build a practice gym for any skill:

Design a practice environment for training an LLM agent to [SKILL].

Skill description: [WHAT THE AGENT SHOULD GET BETTER AT]
Current performance: [HOW WELL IT DOES NOW]
Target performance: [WHAT GOOD LOOKS LIKE]

Design the gym with:

1. TASK GENERATOR
   - Input format: [what the task looks like]
   - Variation parameters: [what changes between tasks]
   - Difficulty levels: [easy / medium / hard criteria]
   - Example task: [concrete example]

2. SCORER  
   - What makes an attempt correct? (exact match / rubric / functional test)
   - Score breakdown: [what earns partial credit]
   - Automatic vs human evaluation: [which parts can be automated]
   - Example: good attempt vs bad attempt with scores

3. CURRICULUM
   - Start: [simplest tasks to build confidence]
   - Progress: [how to increase difficulty as performance improves]
   - Mastery criterion: [when is the skill "learned"?]

4. FEEDBACK FORMAT
   What should the agent receive after each attempt?
   - Score (0-1)
   - Specific error: [what went wrong]
   - Hint for next attempt: [one actionable tip]

Quick Eval Loop Prompt

For rapidly testing an agent on a set of practice problems:

Run an evaluation loop on this agent capability.

Agent task: [WHAT THE AGENT IS SUPPOSED TO DO]

Test cases:
1. Input: [test input 1]
   Expected output: [expected 1]
   
2. Input: [test input 2]
   Expected output: [expected 2]
   
3. Input: [test input 3]
   Expected output: [expected 3]

For each test case:
1. Attempt the task
2. Compare to expected output
3. Score: PASS / PARTIAL / FAIL
4. Explain the error (if any) in one sentence

Final report:
- Pass rate: N/3
- Most common failure mode: [pattern in errors]
- Suggested improvement: [one specific fix]

The Curriculum Design Template

Build a structured learning progression:

Design a learning curriculum for an agent to master [SKILL].

Like Karpathy's "take LLMs to school" approach — structure it as:

WEEK 1 — Foundations (exposition):
- Core concepts to internalize
- 3-5 worked examples with full reasoning traces
- Quiz: 5 basic problems with answers

WEEK 2 — Pattern Recognition (practice):
- 20 practice problems, graduated difficulty
- Automatic scoring criteria
- Common error analysis

WEEK 3 — Generalization (RL-style):
- Novel problems the agent hasn't seen
- Real-world variants
- Adversarial examples (edge cases designed to fail)

Mastery test: [describe the final eval that confirms the skill is learned]

Scoring Rubrics for Common Skills

Code Generation

Score 1.0: Correct output, handles edge cases, clean style
Score 0.8: Correct output, misses 1 edge case
Score 0.5: Core logic correct, fails on some inputs
Score 0.2: Wrong approach but partially useful
Score 0.0: Doesn't compile or clearly wrong

Reasoning/Analysis

Score 1.0: Correct conclusion + correct reasoning chain + appropriate confidence
Score 0.8: Correct conclusion, minor reasoning gap
Score 0.5: Correct conclusion, wrong reasoning
Score 0.2: Wrong conclusion but shows relevant knowledge
Score 0.0: Wrong conclusion, no relevant reasoning

Following Instructions

Score 1.0: All instructions followed, output matches spec exactly
Score 0.8: Minor deviation from spec, intent preserved
Score 0.5: Core task done, 1-2 instructions ignored
Score 0.2: Significant departure from instructions
Score 0.0: Instructions ignored entirely

Environment-in-a-Gist

Karpathy's pattern: publish the environment spec (not the implementation) so anyone can build their gym:

Write a Gist-style environment spec for [SKILL_GYM].

Format:
# [GYM_NAME] — Practice Environment Spec
## What this trains
## Task format
## Scoring criteria  
## Sample task + ideal response
## Curriculum (3 stages)
## How to evaluate mastery

This is a spec, not code. Anyone with an LLM should be able to implement it.

Workflow

属于工作流：月度体检（第3步）

完整链路：meta-reflection → understanding-first → practice-environments → education-first

Prompt Contract

Build a practice environment for <SKILL_OR_CAPABILITY>. Include: 1) Exposition — what this skill is and why it matters (3-5 sentences), 2) Worked examples — 2-3 complete input→output demonstrations, 3) Practice tasks — 5 exercises with increasing difficulty, 4) Automatic grading — for each task define pass/fail criteria that can be checked without human judgment, 5) Retry loop — if failed, what feedback to give and how to adjust difficulty.

Verification Checklist

• 练习环境有明确的技能定义（不是模糊的「变强」）
• Worked examples 覆盖了典型和边界情况
• 评分标准不需要人工判断（自动化）
• 失败时有具体反馈（不只是「错了」）
• 难度有递进（不是一步到位）
• Agent 可以自主重试直到通过