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Enable open-ended mathematical learning through co-evolutionary teacher-student self-play where a single model alternates roles to generate progressively harder problems and solve them, creating a virtuous cycle without external data.
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想先保存到本地？可下载 SkillsMP 当前能够提供的文件。
Convert arXiv papers into ready-to-use agent skills using category-aware extraction. First classifies the paper into one or more of 11 research categories, then applies a specialized extraction pipeline for each category — because different types of papers produce different types of usable knowledge. A single paper can yield multiple skills if it spans categories. Use this skill whenever the user wants to turn a paper into a skill, extract practical techniques from research, build a skill library from papers, convert arXiv papers into reusable agent instructions, or batch-process multiple papers into skills. Also trigger when someone asks about extracting actionable knowledge from papers, making research practical for LLM agents, or systematically converting academic contributions into structured agent capabilities.
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基于 SOC 职业分类
正在显示 SKILL.md
| name | opensir-self-play-reasoning |
| title | OpenSIR: Open-Ended Self-Improving Reasoner |
| version | 0.0.2 |
| engine | skillxiv-v0.0.2-claude-opus-4.6 |
| license | MIT |
| url | https://arxiv.org/abs/2511.00602 |
| keywords | ["Self-Play","Autonomous Learning","Mathematical Reasoning","Curriculum Learning","Problem Generation"] |
| description | Enable open-ended mathematical learning through co-evolutionary teacher-student self-play where a single model alternates roles to generate progressively harder problems and solve them, creating a virtuous cycle without external data. |
Traditional supervised learning requires massive annotated datasets. OpenSIR achieves autonomous improvement through co-evolutionary self-play: a single model acts as both problem-setter (teacher) and problem-solver (student), generating novel problems calibrated to current capability and solving them. The framework requires only a small seed of initial problems, then bootstraps to arbitrary complexity.
The key is maintaining optimal difficulty: problems easy enough to learn from but hard enough to improve capability.
Co-Evolutionary Teacher-Student Self-Play:
1. Implement Teacher (Problem Generation)
Design the teacher to generate diverse, well-formed mathematical problems.
class MathTeacher(nn.Module):
def __init__(self, model, difficulty_levels=[1, 2, 3, 4, 5]):
self.model = model
self.difficulty_levels = difficulty_levels
.concept_tracker = defaultdict()
():
difficulty :
difficulty = np.random.choice(.difficulty_levels)
prompt =
problem = .model.generate(prompt, max_tokens=)
concepts:
.concept_tracker[concepts] +=
problem, difficulty
():
problems = []
_ (num_problems):
difficulty = np.random.choice(.difficulty_levels)
problem, _ = .generate_problem(difficulty=difficulty)
problems.append(problem)
problems
2. Implement Student (Problem Solver)
Create the solver that learns from generated problems.
class MathStudent(nn.Module):
def __init__(self, model):
self.model = model
self.performance_tracker = defaultdict(lambda: {'solved': 0, 'attempts': 0})
def solve_problem(self, problem, return_confidence=False):
# Prompt model to solve problem with step-by-step reasoning
prompt = f"""Solve this problem step-by-step:
{problem}
Solution:"""
solution = self.model.generate(prompt, max_tokens=500)
# Extract final answer
answer = self.extract_answer(solution)
if return_confidence:
# Get confidence score from model
confidence_prompt = f"How confident are you in this answer (0-1)? {answer}"
confidence = float(self.model.generate(confidence_prompt, max_tokens=10))
return solution, answer, confidence
return solution, answer
def extract_answer(self, solution):
# Parse answer from solution text (problem-dependent)
# Try multiple extraction strategies
if 'answer is' in solution:
return solution.split('answer is')[-1].strip()
if '=' in solution:
return solution.split('=')[-1].strip()
return solution.split()[-1]
def verify_answer(self, problem, answer):
# Use ground truth verification or self-consistency
# For now, simplified
prompt = f"Is '{answer}' the correct answer to '{problem}'? Yes/No:"
response = self.model.generate(prompt, max_tokens=10)
return 'yes' in response.lower()
def track_performance(self, category, solved):
self.performance_tracker[category]['attempts'] += 1
if solved:
self.performance_tracker[category]['solved'] += 1
3. Implement Co-Evolution Training Loop
Train both teacher and student through self-play.
def co-evolutionary_training(model, initial_problems, num_iterations=100):
teacher = MathTeacher(model)
student = MathStudent(model)
# Initialize from seed problems
problem_pool = initial_problems.copy()
for iteration in range(num_iterations):
# Teacher phase: generate new problems
new_problems = teacher.sample_problems(num_problems=5)
problem_pool.extend(new_problems)
# Student phase: solve problems from pool
solve_correct = 0
solve_total = 0
for problem in problem_pool[-50:]: # Recent problems
solution, answer, confidence = student.solve_problem(
problem, return_confidence=True
)
verified = student.verify_answer(problem, answer)
solve_total += 1
if verified:
solve_correct += 1
# Track performance
category = extract_category(problem) # algebra, geometry, etc.
student.track_performance(category, verified)
# Compute solve rate
solve_rate = solve_correct / solve_total if solve_total > 0 else 0
# Curriculum adjustment
# If solve_rate > 0.7, increase difficulty
# If solve_rate < 0.5, decrease difficulty
if solve_rate > 0.7:
teacher.difficulty_levels = [d + 0.1 for d in teacher.difficulty_levels]
elif solve_rate < 0.5:
teacher.difficulty_levels = [max(1, d - 0.1) for d in teacher.difficulty_levels]
print(f"Iteration {iteration}: Solve Rate {solve_rate:.2%}, Pool Size {len(problem_pool)}")
# Periodic reinforcement signal
if iteration % 10 == 0:
# Train on successful problem-solution pairs
successful_pairs = [
(p, s) for p, s in problem_solution_pairs if verified[p]
]
# Fine-tune on successful patterns
update_model(model, successful_pairs)
4. Implement Diversity and Difficulty Rewards
Ensure teacher generates diverse problems while maintaining difficulty calibration.
def compute_teacher_reward(new_problem, problem_pool, solve_rate, category_coverage):
# Reward 1: Difficulty calibration
# Want solve rate around 70%
difficulty_reward = 1.0 - abs(solve_rate - 0.7)
# Reward 2: Diversity
# Penalize similar problems
similarity_to_existing = max(
cosine_similarity(embed(new_problem), embed(p)) for p in problem_pool[-20:]
)
diversity_reward = 1.0 - 0.5 * similarity_to_existing
# Reward 3: Coverage
# Encourage unexplored categories
new_category = extract_category(new_problem)
coverage_reward = 1.0 / (1.0 + category_coverage[new_category])
total_reward = 0.6 * difficulty_reward + 0.3 * diversity_reward + 0.1 * coverage_reward
return total_reward
When to Use:
Hyperparameters:
When NOT to Use:
Pitfalls:
Key Insight: Co-evolution only works if teacher and student improve together. If one diverges, the loop breaks. Monitor their relative performance.