缩放定律2026：我们是否已触达规模收益递减

MMLU分数增长趋势：
GPT-3 (2020):    43.9%  → +23.7pp
Chinchilla (2022): 67.6% → +19.2pp  
GPT-4 (2023):    86.4%  → +2.6pp
GPT-5 (2025):    89.5%  → +0.6pp
Claude 4 (2026): 90.1%

def compute_marginal_gain(models_data):
    """计算每增加单位计算量的边际收益"""
    results = []
    for i in range(1, len(models_data)):
        prev = models_data[i-1]
        curr = models_data[i]
        
        compute_ratio = curr['compute'] / prev['compute']
        score_gain = curr['score'] - prev['score']
        
        # 每翻倍计算量的收益
        gain_per_2x = score_gain / np.log2(compute_ratio)
        
        results.append({
            'transition': f"{prev['name']}→{curr['name']}",
            'compute_ratio': compute_ratio,
            'score_gain': score_gain,
            'gain_per_2x_compute': gain_per_2x
        })
    return results

def estimate_ceiling_effect(scores, human_scores):
    """
    估计天花板效应对收益递减的贡献
    """
    remaining_gaps = []
    for model_score, human_score in zip(scores, human_scores):
        gap = human_score - model_score
        remaining_gaps.append(gap)
    
    # 如果剩余gap很小，改进空间有限
    return {
        'remaining_gaps': remaining_gaps,
        'relative_remaining': [g/h for g, h in zip(remaining_gaps, human_scores)]
    }

def quality_adjusted_scaling(data_tokens, quality_multiplier):
    """
    质量调整后的缩放模型
    """
    effective_tokens = data_tokens * quality_multiplier
    # 高质量数据等效于更多低质量数据
    return effective_tokens

def effective_compute(nominal_compute, architecture_multipliers):
    """
    计算架构改进后的等效计算量
    """
    effective = nominal_compute
    for multiplier in architecture_multipliers:
        effective *= multiplier
    return effective

# 示例：2026年模型等效计算量
# GPT-5名义计算量8.5e25 FLOPs
# 架构改进总乘数约20-30x
# 等效计算量约1.7e27 - 2.6e27 FLOPs

class SyntheticDataScaling:
    def __init__(self, teacher_model):
        self.teacher = teacher_model
    
    def generate_quality_data(self, n_tokens=1e12):
        """
        使用强模型生成高质量合成数据
        """
        synthetic_corpus = []
        for domain in ['math', 'code', 'science', 'reasoning']:
            prompts = self.generate_domain_prompts(domain, n=100000)
            for prompt in prompts:
                response = self.teacher.generate(prompt, temperature=0.7)
                # 质量过滤
                if self.quality_check(response):
                    synthetic_corpus.append(response)
        return synthetic_corpus

def test_time_scaling(model, problem, compute_budget):
    """
    测试时计算缩放：在推理时分配更多计算
    """
    solutions = []
    for _ in range(compute_budget // 100):
        # 多次采样
        solution = model.generate(problem, temperature=0.8)
        solutions.append(solution)
    
    # 选择最优解
    return self.select_best(solutions)